From 162a9013d696f0ef0317c198b523789c3babf402 Mon Sep 17 00:00:00 2001
From: Sachin Jalan <sachinjalan03@gmail.com>
Date: Fri, 11 Aug 2023 00:01:44 +0530
Subject: [PATCH 1/6] Inverse Solver example added

---
 inverse_solver.ipynb | 657 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 657 insertions(+)
 create mode 100644 inverse_solver.ipynb

diff --git a/inverse_solver.ipynb b/inverse_solver.ipynb
new file mode 100644
index 0000000..7fec2a3
--- /dev/null
+++ b/inverse_solver.ipynb
@@ -0,0 +1,657 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
+     ]
+    }
+   ],
+   "source": [
+    "import os, sys\n",
+    "\n",
+    "sys.path.append(os.getcwd())\n",
+    "from diffmpm.material import SimpleMaterial,LinearElastic\n",
+    "from diffmpm.particle import Particles\n",
+    "from diffmpm.element import Quadrilateral4Node\n",
+    "from diffmpm.constraint import Constraint\n",
+    "from diffmpm.mesh import Mesh2D\n",
+    "from diffmpm.solver import MPMExplicit\n",
+    "import jax.numpy as jnp\n",
+    "import numpy as np\n",
+    "\n",
+    "mesh_config = {}\n",
+    "density = 1\n",
+    "# poisson_ratio = 0\n",
+    "youngs_modulus = 1000\n",
+    "material = LinearElastic(\n",
+    "    {\n",
+    "        \"id\":0,\n",
+    "        \"youngs_modulus\": youngs_modulus,\n",
+    "        \"density\": density,\n",
+    "        \"poisson_ratio\": 0.0,\n",
+    "    }\n",
+    ")\n",
+    "particle_loc = jnp.array([[0.0, 0.0], [0.5, 0.0], [0.0, 0.5], [0.5, 0.5]]).reshape(\n",
+    "    4, 1, 2\n",
+    ")\n",
+    "particles = Particles(particle_loc, material, jnp.zeros(particle_loc.shape[0],dtype=jnp.int32))\n",
+    "particles.velocity=particles.velocity.at[:].set(0.0)\n",
+    "constraints = [(0, Constraint(1, 0.0))]\n",
+    "external_loading = jnp.array([0.0, -9.8]).reshape(1,2)\n",
+    "element = Quadrilateral4Node([1, 1], 1, [1,1], constraints)\n",
+    "mesh_config[\"particles\"] = [particles]\n",
+    "mesh_config[\"elements\"] = element\n",
+    "mesh_config[\"particle_surface_traction\"] = []\n",
+    "mesh = Mesh2D(mesh_config)\n",
+    "solver = MPMExplicit(mesh, 0.01,sim_steps=10)\n",
+    "\n",
+    "real_ans = solver.solve_jit(external_loading)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from jax import jit\n",
+    "@jit\n",
+    "def compute_loss(E,solver,target_stress):\n",
+    "    material_props=solver.mesh.particles[0].material.properties\n",
+    "    material_props[\"youngs_modulus\"]=E\n",
+    "    solver.mesh.particles[0].material=LinearElastic(material_props)\n",
+    "    external_loading_local=jnp.array([0.0, -9.8]).reshape(1,2)\n",
+    "    solver.mesh.particles[0].velocity = mesh.particles[0].velocity.at[:].set(0.0)\n",
+    "    result = solver.solve_jit(external_loading_local)\n",
+    "    stress = result[\"stress\"]\n",
+    "    loss = jnp.linalg.norm(stress - target_stress)\n",
+    "    return loss"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "E: 1000.3665161132812: 100%|██████████| 500/500 [00:11<00:00, 43.43it/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import optax\n",
+    "from tqdm import tqdm\n",
+    "from jax import jit, value_and_grad\n",
+    "\n",
+    "def optax_adam(params,niter,mpm,target_vel):\n",
+    "    start_alpha=0.1\n",
+    "    optimizer=optax.adam(start_alpha)\n",
+    "    opt_state=optimizer.init(params)\n",
+    "    param_list=[]\n",
+    "    loss_list=[]\n",
+    "    t=tqdm(range(niter),desc=f\"E: {params}\")\n",
+    "    for _ in t:\n",
+    "        lo,grads=value_and_grad(compute_loss)(params,mpm,target_vel)\n",
+    "        updates,opt_state=optimizer.update(grads,opt_state)\n",
+    "        params=optax.apply_updates(params,updates)\n",
+    "        t.set_description(f\"E: {params}\")\n",
+    "        param_list.append(params)\n",
+    "        loss_list.append(lo)\n",
+    "    return param_list,loss_list\n",
+    "params=1050.0\n",
+    "parameter_list,loss_list=optax_adam(params,500,solver,real_ans[\"stress\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
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+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "parameter_list"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "optaximpo",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.4"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

From 0a6e079c3ca215b3b04bbcf6f0890b7dafc13451 Mon Sep 17 00:00:00 2001
From: Sachin Jalan <sachinjalan03@gmail.com>
Date: Fri, 11 Aug 2023 01:05:58 +0530
Subject: [PATCH 2/6] bayesian added

---
 inverse_solver.ipynb | 588 ++++++-------------------------------------
 1 file changed, 76 insertions(+), 512 deletions(-)

diff --git a/inverse_solver.ipynb b/inverse_solver.ipynb
index 7fec2a3..7c77961 100644
--- a/inverse_solver.ipynb
+++ b/inverse_solver.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [
     {
@@ -57,12 +57,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
     "from jax import jit\n",
-    "@jit\n",
+    "\n",
     "def compute_loss(E,solver,target_stress):\n",
     "    material_props=solver.mesh.particles[0].material.properties\n",
     "    material_props[\"youngs_modulus\"]=E\n",
@@ -114,522 +114,86 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Trying via Bayesian Optimization\n",
+    "target_stress=real_ans[\"stress\"]\n",
+    "def fun(E):\n",
+    "    material_props=solver.mesh.particles[0].material.properties\n",
+    "    material_props[\"youngs_modulus\"]=E\n",
+    "    solver.mesh.particles[0].material=LinearElastic(material_props)\n",
+    "    external_loading_local=jnp.array([0.0, -9.8]).reshape(1,2)\n",
+    "    solver.mesh.particles[0].velocity = mesh.particles[0].velocity.at[:].set(0.0)\n",
+    "    result = solver.solve_jit(external_loading_local)\n",
+    "    stress = result[\"stress\"]\n",
+    "    loss = jnp.linalg.norm(stress - target_stress)\n",
+    "    return -loss"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from bayes_opt import BayesianOptimization\n",
+    "\n",
+    "pbounds = {\"E\": (900, 1100)}\n",
+    "optimizer = BayesianOptimization(f=fun, pbounds=pbounds, random_state=1, verbose=2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
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-       " Array(1029.5519, dtype=float32),\n",
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-       " Array(1028.5579, dtype=float32),\n",
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-       " Array(1026.1731, dtype=float32),\n",
-       " Array(1026.0737, dtype=float32),\n",
-       " Array(1025.9744, dtype=float32),\n",
-       " Array(1025.875, dtype=float32),\n",
-       " Array(1025.7756, dtype=float32),\n",
-       " Array(1025.6763, dtype=float32),\n",
-       " Array(1025.5769, dtype=float32),\n",
-       " Array(1025.4777, dtype=float32),\n",
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-       " Array(1025.1799, dtype=float32),\n",
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-       " Array(1024.9814, dtype=float32),\n",
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-       " Array(1024.4852, dtype=float32),\n",
-       " Array(1024.386, dtype=float32),\n",
-       " Array(1024.2867, dtype=float32),\n",
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-       " Array(1020.71545, dtype=float32),\n",
-       " Array(1020.61633, dtype=float32),\n",
-       " Array(1020.5172, dtype=float32),\n",
-       " Array(1020.4181, dtype=float32),\n",
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-       " Array(1020.21985, dtype=float32),\n",
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-       " Array(1020.0216, dtype=float32),\n",
-       " Array(1019.9225, dtype=float32),\n",
-       " Array(1019.82336, dtype=float32),\n",
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-       " Array(1019.6251, dtype=float32),\n",
-       " Array(1019.526, dtype=float32),\n",
-       " Array(1019.4269, dtype=float32),\n",
-       " Array(1019.32776, dtype=float32),\n",
-       " Array(1019.22864, dtype=float32),\n",
-       " Array(1019.1296, dtype=float32),\n",
-       " Array(1019.0305, dtype=float32),\n",
-       " Array(1018.93146, dtype=float32),\n",
-       " Array(1018.8324, dtype=float32),\n",
-       " Array(1018.73334, dtype=float32),\n",
-       " Array(1018.6343, dtype=float32),\n",
-       " Array(1018.5352, dtype=float32),\n",
-       " Array(1018.43616, dtype=float32),\n",
-       " Array(1018.3371, dtype=float32),\n",
-       " Array(1018.23804, dtype=float32),\n",
-       " Array(1018.139, dtype=float32),\n",
-       " Array(1018.0399, dtype=float32),\n",
-       " Array(1017.94086, dtype=float32),\n",
-       " Array(1017.8418, dtype=float32),\n",
-       " Array(1017.74274, dtype=float32),\n",
-       " Array(1017.6437, dtype=float32),\n",
-       " Array(1017.5446, dtype=float32),\n",
-       " Array(1017.44556, dtype=float32),\n",
-       " Array(1017.34656, dtype=float32),\n",
-       " Array(1017.24756, dtype=float32),\n",
-       " Array(1017.14856, dtype=float32),\n",
-       " Array(1017.04956, dtype=float32),\n",
-       " Array(1016.95056, dtype=float32),\n",
-       " Array(1016.85156, dtype=float32),\n",
-       " Array(1016.75256, dtype=float32),\n",
-       " Array(1016.65356, dtype=float32),\n",
-       " Array(1016.55457, dtype=float32),\n",
-       " Array(1016.45557, dtype=float32),\n",
-       " Array(1016.35657, dtype=float32),\n",
-       " Array(1016.25757, dtype=float32),\n",
-       " Array(1016.15857, dtype=float32),\n",
-       " Array(1016.0596, dtype=float32),\n",
-       " Array(1015.9606, dtype=float32),\n",
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-       " Array(1015.56464, dtype=float32),\n",
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-       " Array(1015.36676, dtype=float32),\n",
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-       " Array(1015.06995, dtype=float32),\n",
-       " Array(1014.971, dtype=float32),\n",
-       " Array(1014.8721, dtype=float32),\n",
-       " Array(1014.77313, dtype=float32),\n",
-       " Array(1014.6742, dtype=float32),\n",
-       " Array(1014.57526, dtype=float32),\n",
-       " Array(1014.4763, dtype=float32),\n",
-       " Array(1014.3774, dtype=float32),\n",
-       " Array(1014.27844, dtype=float32),\n",
-       " Array(1014.1795, dtype=float32),\n",
-       " Array(1014.08057, dtype=float32),\n",
-       " Array(1013.9816, dtype=float32),\n",
-       " Array(1013.88275, dtype=float32),\n",
-       " Array(1013.7839, dtype=float32),\n",
-       " Array(1013.685, dtype=float32),\n",
-       " Array(1013.5861, dtype=float32),\n",
-       " Array(1013.48724, dtype=float32),\n",
-       " Array(1013.38837, dtype=float32),\n",
-       " Array(1013.2895, dtype=float32),\n",
-       " Array(1013.1906, dtype=float32),\n",
-       " Array(1013.09174, dtype=float32),\n",
-       " Array(1012.99286, dtype=float32),\n",
-       " Array(1012.894, dtype=float32),\n",
-       " Array(1012.7951, dtype=float32),\n",
-       " Array(1012.6962, dtype=float32),\n",
-       " Array(1012.59735, dtype=float32),\n",
-       " Array(1012.4985, dtype=float32),\n",
-       " Array(1012.3996, dtype=float32),\n",
-       " Array(1012.3007, dtype=float32),\n",
-       " Array(1012.20184, dtype=float32),\n",
-       " Array(1012.103, dtype=float32),\n",
-       " Array(1012.0042, dtype=float32),\n",
-       " Array(1011.9054, dtype=float32),\n",
-       " Array(1011.8066, dtype=float32),\n",
-       " Array(1011.70776, dtype=float32),\n",
-       " Array(1011.60895, dtype=float32),\n",
-       " Array(1011.51013, dtype=float32),\n",
-       " Array(1011.4113, dtype=float32),\n",
-       " Array(1011.3125, dtype=float32),\n",
-       " Array(1011.2137, dtype=float32),\n",
-       " Array(1011.11487, dtype=float32),\n",
-       " Array(1011.01605, dtype=float32),\n",
-       " Array(1010.91724, dtype=float32),\n",
-       " Array(1010.8184, dtype=float32),\n",
-       " Array(1010.7196, dtype=float32),\n",
-       " Array(1010.6208, dtype=float32),\n",
-       " Array(1010.522, dtype=float32),\n",
-       " Array(1010.4232, dtype=float32),\n",
-       " Array(1010.32446, dtype=float32),\n",
-       " Array(1010.2257, dtype=float32),\n",
-       " Array(1010.12695, dtype=float32),\n",
-       " Array(1010.0282, dtype=float32),\n",
-       " Array(1009.92944, dtype=float32),\n",
-       " Array(1009.8307, dtype=float32),\n",
-       " Array(1009.73193, dtype=float32),\n",
-       " Array(1009.6332, dtype=float32),\n",
-       " Array(1009.5344, dtype=float32),\n",
-       " Array(1009.43567, dtype=float32),\n",
-       " Array(1009.3369, dtype=float32),\n",
-       " Array(1009.23816, dtype=float32),\n",
-       " Array(1009.1394, dtype=float32),\n",
-       " Array(1009.04065, dtype=float32),\n",
-       " Array(1008.9419, dtype=float32),\n",
-       " Array(1008.84314, dtype=float32),\n",
-       " Array(1008.74445, dtype=float32),\n",
-       " Array(1008.64575, dtype=float32),\n",
-       " Array(1008.54706, dtype=float32),\n",
-       " Array(1008.44836, dtype=float32),\n",
-       " Array(1008.3497, dtype=float32),\n",
-       " Array(1008.251, dtype=float32),\n",
-       " Array(1008.1523, dtype=float32),\n",
-       " Array(1008.0536, dtype=float32),\n",
-       " Array(1007.9549, dtype=float32),\n",
-       " Array(1007.8562, dtype=float32),\n",
-       " Array(1007.7575, dtype=float32),\n",
-       " Array(1007.6588, dtype=float32),\n",
-       " Array(1007.5601, dtype=float32),\n",
-       " Array(1007.4614, dtype=float32),\n",
-       " Array(1007.36273, dtype=float32),\n",
-       " Array(1007.26404, dtype=float32),\n",
-       " Array(1007.16534, dtype=float32),\n",
-       " Array(1007.0667, dtype=float32),\n",
-       " Array(1006.9681, dtype=float32),\n",
-       " Array(1006.86945, dtype=float32),\n",
-       " Array(1006.7708, dtype=float32),\n",
-       " Array(1006.6722, dtype=float32),\n",
-       " Array(1006.57355, dtype=float32),\n",
-       " Array(1006.4749, dtype=float32),\n",
-       " Array(1006.3763, dtype=float32),\n",
-       " Array(1006.27765, dtype=float32),\n",
-       " Array(1006.179, dtype=float32),\n",
-       " Array(1006.0804, dtype=float32),\n",
-       " Array(1005.98175, dtype=float32),\n",
-       " Array(1005.8831, dtype=float32),\n",
-       " Array(1005.7845, dtype=float32),\n",
-       " Array(1005.68585, dtype=float32),\n",
-       " Array(1005.5872, dtype=float32),\n",
-       " Array(1005.48865, dtype=float32),\n",
-       " Array(1005.3901, dtype=float32),\n",
-       " Array(1005.2915, dtype=float32),\n",
-       " Array(1005.19293, dtype=float32),\n",
-       " Array(1005.09436, dtype=float32),\n",
-       " Array(1004.9958, dtype=float32),\n",
-       " Array(1004.8972, dtype=float32),\n",
-       " Array(1004.79865, dtype=float32),\n",
-       " Array(1004.7001, dtype=float32),\n",
-       " Array(1004.6015, dtype=float32),\n",
-       " Array(1004.5029, dtype=float32),\n",
-       " Array(1004.40436, dtype=float32),\n",
-       " Array(1004.3058, dtype=float32),\n",
-       " Array(1004.2072, dtype=float32),\n",
-       " Array(1004.10864, dtype=float32),\n",
-       " Array(1004.0101, dtype=float32),\n",
-       " Array(1003.9115, dtype=float32),\n",
-       " Array(1003.813, dtype=float32),\n",
-       " Array(1003.7145, dtype=float32),\n",
-       " Array(1003.61597, dtype=float32),\n",
-       " Array(1003.51746, dtype=float32),\n",
-       " Array(1003.41895, dtype=float32),\n",
-       " Array(1003.32043, dtype=float32),\n",
-       " Array(1003.2219, dtype=float32),\n",
-       " Array(1003.1234, dtype=float32),\n",
-       " Array(1003.0249, dtype=float32),\n",
-       " Array(1002.9264, dtype=float32),\n",
-       " Array(1002.8279, dtype=float32),\n",
-       " Array(1002.7294, dtype=float32),\n",
-       " Array(1002.63086, dtype=float32),\n",
-       " Array(1002.53235, dtype=float32),\n",
-       " Array(1002.43384, dtype=float32),\n",
-       " Array(1002.3353, dtype=float32),\n",
-       " Array(1002.2369, dtype=float32),\n",
-       " Array(1002.1384, dtype=float32),\n",
-       " Array(1002.04, dtype=float32),\n",
-       " Array(1001.9415, dtype=float32),\n",
-       " Array(1001.8431, dtype=float32),\n",
-       " Array(1001.7446, dtype=float32),\n",
-       " Array(1001.6462, dtype=float32),\n",
-       " Array(1001.5477, dtype=float32),\n",
-       " Array(1001.4493, dtype=float32),\n",
-       " Array(1001.3508, dtype=float32),\n",
-       " Array(1001.2524, dtype=float32),\n",
-       " Array(1001.15393, dtype=float32),\n",
-       " Array(1001.0555, dtype=float32),\n",
-       " Array(1000.95703, dtype=float32),\n",
-       " Array(1000.8586, dtype=float32),\n",
-       " Array(1000.76013, dtype=float32),\n",
-       " Array(1000.6617, dtype=float32),\n",
-       " Array(1000.5633, dtype=float32),\n",
-       " Array(1000.4649, dtype=float32),\n",
-       " Array(1000.3665, dtype=float32)]"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "|   iter    |  target   |     E     |\n",
+      "-------------------------------------\n",
+      "| \u001b[0m1        \u001b[0m | \u001b[0m-0.1767  \u001b[0m | \u001b[0m983.4    \u001b[0m |\n",
+      "| \u001b[0m2        \u001b[0m | \u001b[0m-0.4804  \u001b[0m | \u001b[0m1.044e+03\u001b[0m |\n",
+      "| \u001b[0m3        \u001b[0m | \u001b[0m-1.019   \u001b[0m | \u001b[0m900.0    \u001b[0m |\n",
+      "| \u001b[95m4        \u001b[0m | \u001b[95m-0.1635  \u001b[0m | \u001b[95m984.7    \u001b[0m |\n",
+      "| \u001b[0m5        \u001b[0m | \u001b[0m-1.108   \u001b[0m | \u001b[0m1.1e+03  \u001b[0m |\n",
+      "| \u001b[95m6        \u001b[0m | \u001b[95m-0.1306  \u001b[0m | \u001b[95m1.012e+03\u001b[0m |\n",
+      "| \u001b[95m7        \u001b[0m | \u001b[95m-0.002049\u001b[0m | \u001b[95m1e+03    \u001b[0m |\n",
+      "| \u001b[0m8        \u001b[0m | \u001b[0m-0.5549  \u001b[0m | \u001b[0m947.0    \u001b[0m |\n",
+      "=====================================\n"
+     ]
     }
    ],
    "source": [
-    "parameter_list"
+    "optimizer.maximize(init_points=3,n_iter=5)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{'target': -0.002048737835139036, 'params': {'E': 1000.1908124742653}}\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(optimizer.max)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {

From 77a4d7f58d28dc0acf813a0a32e372b776343fd1 Mon Sep 17 00:00:00 2001
From: Sachin Jalan <sachinjalan03@gmail.com>
Date: Fri, 11 Aug 2023 01:27:46 +0530
Subject: [PATCH 3/6] jitted the cost function

---
 inverse_solver.ipynb | 45 +++++++++++++++++++-------------------------
 1 file changed, 19 insertions(+), 26 deletions(-)

diff --git a/inverse_solver.ipynb b/inverse_solver.ipynb
index 7c77961..5af09a2 100644
--- a/inverse_solver.ipynb
+++ b/inverse_solver.ipynb
@@ -2,17 +2,9 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 45,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import os, sys\n",
     "\n",
@@ -114,18 +106,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 46,
    "metadata": {},
    "outputs": [],
    "source": [
     "#Trying via Bayesian Optimization\n",
     "target_stress=real_ans[\"stress\"]\n",
-    "def fun(E):\n",
+    "@jit\n",
+    "def fun(E,solver=solver,target_stress=target_stress):\n",
     "    material_props=solver.mesh.particles[0].material.properties\n",
     "    material_props[\"youngs_modulus\"]=E\n",
     "    solver.mesh.particles[0].material=LinearElastic(material_props)\n",
     "    external_loading_local=jnp.array([0.0, -9.8]).reshape(1,2)\n",
-    "    solver.mesh.particles[0].velocity = mesh.particles[0].velocity.at[:].set(0.0)\n",
+    "    # solver.mesh.particles[0].velocity = mesh.particles[0].velocity.at[:].set(0.0)\n",
     "    result = solver.solve_jit(external_loading_local)\n",
     "    stress = result[\"stress\"]\n",
     "    loss = jnp.linalg.norm(stress - target_stress)\n",
@@ -134,19 +127,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 63,
    "metadata": {},
    "outputs": [],
    "source": [
     "from bayes_opt import BayesianOptimization\n",
     "\n",
-    "pbounds = {\"E\": (900, 1100)}\n",
+    "pbounds = {\"E\": (800, 1500)}\n",
     "optimizer = BayesianOptimization(f=fun, pbounds=pbounds, random_state=1, verbose=2)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 64,
    "metadata": {},
    "outputs": [
     {
@@ -155,14 +148,14 @@
      "text": [
       "|   iter    |  target   |     E     |\n",
       "-------------------------------------\n",
-      "| \u001b[0m1        \u001b[0m | \u001b[0m-0.1767  \u001b[0m | \u001b[0m983.4    \u001b[0m |\n",
-      "| \u001b[0m2        \u001b[0m | \u001b[0m-0.4804  \u001b[0m | \u001b[0m1.044e+03\u001b[0m |\n",
-      "| \u001b[0m3        \u001b[0m | \u001b[0m-1.019   \u001b[0m | \u001b[0m900.0    \u001b[0m |\n",
-      "| \u001b[95m4        \u001b[0m | \u001b[95m-0.1635  \u001b[0m | \u001b[95m984.7    \u001b[0m |\n",
-      "| \u001b[0m5        \u001b[0m | \u001b[0m-1.108   \u001b[0m | \u001b[0m1.1e+03  \u001b[0m |\n",
-      "| \u001b[95m6        \u001b[0m | \u001b[95m-0.1306  \u001b[0m | \u001b[95m1.012e+03\u001b[0m |\n",
-      "| \u001b[95m7        \u001b[0m | \u001b[95m-0.002049\u001b[0m | \u001b[95m1e+03    \u001b[0m |\n",
-      "| \u001b[0m8        \u001b[0m | \u001b[0m-0.5549  \u001b[0m | \u001b[0m947.0    \u001b[0m |\n",
+      "| \u001b[0m1        \u001b[0m | \u001b[0m-1.017   \u001b[0m | \u001b[0m1.092e+03\u001b[0m |\n",
+      "| \u001b[0m2        \u001b[0m | \u001b[0m-3.452   \u001b[0m | \u001b[0m1.304e+03\u001b[0m |\n",
+      "| \u001b[0m3        \u001b[0m | \u001b[0m-1.895   \u001b[0m | \u001b[0m800.1    \u001b[0m |\n",
+      "| \u001b[0m4        \u001b[0m | \u001b[0m-1.031   \u001b[0m | \u001b[0m1.093e+03\u001b[0m |\n",
+      "| \u001b[95m5        \u001b[0m | \u001b[95m-0.4102  \u001b[0m | \u001b[95m961.1    \u001b[0m |\n",
+      "| \u001b[95m6        \u001b[0m | \u001b[95m-0.05521 \u001b[0m | \u001b[95m1.005e+03\u001b[0m |\n",
+      "| \u001b[0m7        \u001b[0m | \u001b[0m-5.561   \u001b[0m | \u001b[0m1.5e+03  \u001b[0m |\n",
+      "| \u001b[0m8        \u001b[0m | \u001b[0m-0.2243  \u001b[0m | \u001b[0m1.021e+03\u001b[0m |\n",
       "=====================================\n"
      ]
     }
@@ -173,14 +166,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 65,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "{'target': -0.002048737835139036, 'params': {'E': 1000.1908124742653}}\n"
+      "{'target': -0.0552130751311779, 'params': {'E': 1005.1373320945569}}\n"
      ]
     }
    ],

From 6f34507e0fe18f41f8014ea6388cdb29e8baca98 Mon Sep 17 00:00:00 2001
From: Sachin Jalan <sachinjalan03@gmail.com>
Date: Fri, 11 Aug 2023 03:53:41 +0530
Subject: [PATCH 4/6] Both python file and jupyter notebook added

---
 examples/inverse_solver_2d.ipynb | 191 +++++++++++++++++++++++++++
 examples/inverse_solver_2d.py    | 129 +++++++++++++++++++
 inverse_solver.ipynb             | 214 -------------------------------
 3 files changed, 320 insertions(+), 214 deletions(-)
 create mode 100644 examples/inverse_solver_2d.ipynb
 create mode 100644 examples/inverse_solver_2d.py
 delete mode 100644 inverse_solver.ipynb

diff --git a/examples/inverse_solver_2d.ipynb b/examples/inverse_solver_2d.ipynb
new file mode 100644
index 0000000..7b6bfee
--- /dev/null
+++ b/examples/inverse_solver_2d.ipynb
@@ -0,0 +1,191 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n",
+      "E: 1000.3665161132812: 100%|██████████| 500/500 [00:51<00:00,  9.74it/s]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time taken by adam: 51.358086347579956\n",
+      "parameter = 1000.3665161132812 and loss = 0.004986115265637636\n",
+      "|   iter    |  target   | youngs... |\n",
+      "-------------------------------------\n",
+      "| \u001b[0m1        \u001b[0m | \u001b[0m-0.1767  \u001b[0m | \u001b[0m983.4    \u001b[0m |\n",
+      "| \u001b[0m2        \u001b[0m | \u001b[0m-0.4804  \u001b[0m | \u001b[0m1.044e+03\u001b[0m |\n",
+      "| \u001b[0m3        \u001b[0m | \u001b[0m-1.019   \u001b[0m | \u001b[0m900.0    \u001b[0m |\n",
+      "| \u001b[95m4        \u001b[0m | \u001b[95m-0.1635  \u001b[0m | \u001b[95m984.7    \u001b[0m |\n",
+      "| \u001b[0m5        \u001b[0m | \u001b[0m-1.108   \u001b[0m | \u001b[0m1.1e+03  \u001b[0m |\n",
+      "| \u001b[95m6        \u001b[0m | \u001b[95m-0.1306  \u001b[0m | \u001b[95m1.012e+03\u001b[0m |\n",
+      "| \u001b[95m7        \u001b[0m | \u001b[95m-0.002043\u001b[0m | \u001b[95m1e+03    \u001b[0m |\n",
+      "| \u001b[0m8        \u001b[0m | \u001b[0m-0.5549  \u001b[0m | \u001b[0m947.0    \u001b[0m |\n",
+      "=====================================\n",
+      "Time taken by Bayesian Optimization: 3.525190830230713\n",
+      "{'target': -0.0020428309217095375, 'params': {'youngs_modulus': 1000.1903192810634}}\n"
+     ]
+    }
+   ],
+   "source": [
+    "import sys,os\n",
+    "sys.path.append(os.path.abspath('../'))\n",
+    "from diffmpm.material import SimpleMaterial, LinearElastic\n",
+    "from diffmpm.particle import Particles\n",
+    "from diffmpm.element import Quadrilateral4Node\n",
+    "from diffmpm.constraint import Constraint\n",
+    "from diffmpm.mesh import Mesh2D\n",
+    "from diffmpm.solver import MPMExplicit\n",
+    "import jax.numpy as jnp\n",
+    "import numpy as np\n",
+    "from jax import jit, value_and_grad\n",
+    "import optax\n",
+    "from tqdm import tqdm\n",
+    "import time\n",
+    "from bayes_opt import BayesianOptimization\n",
+    "\n",
+    "mesh_config = {}\n",
+    "density = 1\n",
+    "poisson_ratio = 0.0\n",
+    "youngs_modulus = 1000\n",
+    "# Linear Elastic Material with given parameters\n",
+    "material = LinearElastic(\n",
+    "    {\n",
+    "        \"id\": 0,\n",
+    "        \"youngs_modulus\": youngs_modulus,\n",
+    "        \"density\": density,\n",
+    "        \"poisson_ratio\": poisson_ratio,\n",
+    "    }\n",
+    ")\n",
+    "# location of the material points\n",
+    "particle_loc = jnp.array([[0.0, 0.0], [0.5, 0.0], [0.0, 0.5], [0.5, 0.5]]).reshape(\n",
+    "    4, 1, 2\n",
+    ")\n",
+    "# particle object for material points\n",
+    "particles = Particles(\n",
+    "    particle_loc, material, jnp.zeros(particle_loc.shape[0], dtype=jnp.int32)\n",
+    ")\n",
+    "particles.velocity = particles.velocity.at[:].set(0.0)\n",
+    "# velocity constraint for material point at (0,0)\n",
+    "constraints = [(0, Constraint(1, 0.0))]\n",
+    "# gravity loading\n",
+    "gravity_loading = jnp.array([0.0, -9.8]).reshape(1, 2)\n",
+    "element = Quadrilateral4Node([1, 1], 1, [1, 1], constraints)\n",
+    "mesh_config[\"particles\"] = [particles]\n",
+    "mesh_config[\"elements\"] = element\n",
+    "mesh_config[\"particle_surface_traction\"] = []\n",
+    "mesh = Mesh2D(mesh_config)\n",
+    "solver = MPMExplicit(mesh, 0.01, sim_steps=10)\n",
+    "# getting the target value for youngs modulus 1000\n",
+    "target_ans = solver.solve_jit(gravity_loading)\n",
+    "\n",
+    "\n",
+    "# using adam optimizer\n",
+    "@jit\n",
+    "def compute_loss(youngs_modulus, solver, target_stress):\n",
+    "    # creating a particle object with the given youngs modulus in the function\n",
+    "    material_props = solver.mesh.particles[0].material.properties\n",
+    "    material_props[\"youngs_modulus\"] = youngs_modulus\n",
+    "    #updating the mesh object\n",
+    "    solver.mesh.particles[0].material = LinearElastic(material_props)\n",
+    "    gravity_loading = jnp.array([0.0, -9.8]).reshape(1, 2)\n",
+    "    solver.mesh.particles[0].velocity = solver.mesh.particles[0].velocity.at[:].set(0.0)\n",
+    "    #solving for the given youngs_modulus and computing the loss with the expected stress\n",
+    "    result = solver.solve_jit(gravity_loading)\n",
+    "    #using stress to calculate loss\n",
+    "    loss = jnp.linalg.norm(result[\"stress\"] - target_stress)\n",
+    "    return loss\n",
+    "\n",
+    "#adam optimizer\n",
+    "def optax_adam(params, niter, mpm, target_stress):\n",
+    "    start_alpha = 0.1\n",
+    "    optimizer = optax.adam(start_alpha)\n",
+    "    opt_state = optimizer.init(params)\n",
+    "    param_list = []\n",
+    "    loss_list = []\n",
+    "    t = tqdm(range(niter), desc=f\"E: {params}\")\n",
+    "    for _ in t:\n",
+    "        lo, grads = value_and_grad(compute_loss)(params, mpm, target_stress)\n",
+    "        updates, opt_state = optimizer.update(grads, opt_state)\n",
+    "        params = optax.apply_updates(params, updates)\n",
+    "        t.set_description(f\"E: {params}\")\n",
+    "        param_list.append(params)\n",
+    "        loss_list.append(lo)\n",
+    "    return param_list, loss_list\n",
+    "\n",
+    "#initial guess for the youngs modulus\n",
+    "params = 1050.0\n",
+    "#measuring the time taken by the optimizer\n",
+    "start_t = time.time()\n",
+    "#calling the optimizer\n",
+    "parameter_list, loss_list = optax_adam(params, 500, solver, target_ans[\"stress\"])\n",
+    "end_time = time.time()\n",
+    "print(f\"Time taken by adam: {end_time-start_t}\")\n",
+    "print(f\"parameter = {parameter_list[-1]} and loss = {loss_list[-1]}\")\n",
+    "\n",
+    "# Using Bayesian Optimization model based on gaussian processes maximizes the\n",
+    "#given function using probability distributions\n",
+    "\n",
+    "#target stress for the given youngs modulus\n",
+    "target_stress = target_ans[\"stress\"]\n",
+    "\n",
+    "#loss function for bayesian optimization\n",
+    "@jit\n",
+    "def loss_func(youngs_modulus, solver=solver, target_stress=target_stress):\n",
+    "    material_props = solver.mesh.particles[0].material.properties\n",
+    "    material_props[\"youngs_modulus\"] = youngs_modulus\n",
+    "    solver.mesh.particles[0].material = LinearElastic(material_props)\n",
+    "    external_loading_local = jnp.array([0.0, -9.8]).reshape(1, 2)\n",
+    "    result = solver.solve_jit(external_loading_local)\n",
+    "    stress = result[\"stress\"]\n",
+    "    loss = jnp.linalg.norm(stress - target_stress)\n",
+    "    #returning negative of the loss as bayesian optimizer maximizes the function\n",
+    "    return -loss\n",
+    "\n",
+    "#giving bound to the value of the youngs_modulus for bayesian optimizer\n",
+    "pbounds = {\"youngs_modulus\": (900, 1100)}\n",
+    "optimizer = BayesianOptimization(\n",
+    "    f=loss_func, pbounds=pbounds, random_state=1, verbose=2\n",
+    ")\n",
+    "#measuring the time taken by the optimizer\n",
+    "start_t = time.time()\n",
+    "#calling the optimizer, init_points is the number of random points to be sampled\n",
+    "#n_iter is the number of iterations to be performed\n",
+    "optimizer.maximize(init_points=3, n_iter=5)\n",
+    "end_time = time.time()\n",
+    "print(f\"Time taken by Bayesian Optimization: {end_time-start_t}\")\n",
+    "print(optimizer.max)\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "optaximpo",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.4"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/examples/inverse_solver_2d.py b/examples/inverse_solver_2d.py
new file mode 100644
index 0000000..ab40d2b
--- /dev/null
+++ b/examples/inverse_solver_2d.py
@@ -0,0 +1,129 @@
+import sys
+import os
+
+sys.path.append(os.getcwd())
+from diffmpm.material import SimpleMaterial, LinearElastic
+from diffmpm.particle import Particles
+from diffmpm.element import Quadrilateral4Node
+from diffmpm.constraint import Constraint
+from diffmpm.mesh import Mesh2D
+from diffmpm.solver import MPMExplicit
+import jax.numpy as jnp
+import numpy as np
+from jax import jit, value_and_grad
+import optax
+from tqdm import tqdm
+import time
+from bayes_opt import BayesianOptimization
+
+mesh_config = {}
+density = 1
+poisson_ratio = 0.0
+youngs_modulus = 1000
+# Linear Elastic Material with given parameters
+material = LinearElastic(
+    {
+        "id": 0,
+        "youngs_modulus": youngs_modulus,
+        "density": density,
+        "poisson_ratio": poisson_ratio,
+    }
+)
+# location of the material points
+particle_loc = jnp.array([[0.0, 0.0], [0.5, 0.0], [0.0, 0.5], [0.5, 0.5]]).reshape(
+    4, 1, 2
+)
+# particle object for material points
+particles = Particles(
+    particle_loc, material, jnp.zeros(particle_loc.shape[0], dtype=jnp.int32)
+)
+particles.velocity = particles.velocity.at[:].set(0.0)
+# velocity constraint for material point at (0,0)
+constraints = [(0, Constraint(1, 0.0))]
+# gravity loading
+gravity_loading = jnp.array([0.0, -9.8]).reshape(1, 2)
+element = Quadrilateral4Node([1, 1], 1, [1, 1], constraints)
+mesh_config["particles"] = [particles]
+mesh_config["elements"] = element
+mesh_config["particle_surface_traction"] = []
+mesh = Mesh2D(mesh_config)
+solver = MPMExplicit(mesh, 0.01, sim_steps=10)
+# getting the target value for youngs modulus 1000
+target_ans = solver.solve_jit(gravity_loading)
+
+
+# using adam optimizer
+@jit
+def compute_loss(youngs_modulus, solver, target_stress):
+    # creating a particle object with the given youngs modulus in the function
+    material_props = solver.mesh.particles[0].material.properties
+    material_props["youngs_modulus"] = youngs_modulus
+    #updating the mesh object
+    solver.mesh.particles[0].material = LinearElastic(material_props)
+    gravity_loading = jnp.array([0.0, -9.8]).reshape(1, 2)
+    solver.mesh.particles[0].velocity = solver.mesh.particles[0].velocity.at[:].set(0.0)
+    #solving for the given youngs_modulus and computing the loss with the expected stress
+    result = solver.solve_jit(gravity_loading)
+    #using stress to calculate loss
+    loss = jnp.linalg.norm(result["stress"] - target_stress)
+    return loss
+
+#adam optimizer
+def optax_adam(params, niter, mpm, target_stress):
+    start_alpha = 0.1
+    optimizer = optax.adam(start_alpha)
+    opt_state = optimizer.init(params)
+    param_list = []
+    loss_list = []
+    t = tqdm(range(niter), desc=f"E: {params}")
+    for _ in t:
+        lo, grads = value_and_grad(compute_loss)(params, mpm, target_stress)
+        updates, opt_state = optimizer.update(grads, opt_state)
+        params = optax.apply_updates(params, updates)
+        t.set_description(f"E: {params}")
+        param_list.append(params)
+        loss_list.append(lo)
+    return param_list, loss_list
+
+#initial guess for the youngs modulus
+params = 1050.0
+#measuring the time taken by the optimizer
+start_t = time.time()
+#calling the optimizer
+parameter_list, loss_list = optax_adam(params, 500, solver, target_ans["stress"])
+end_time = time.time()
+print(f"Time taken by adam: {end_time-start_t}")
+print(f"parameter = {parameter_list[-1]} and loss = {loss_list[-1]}")
+
+# Using Bayesian Optimization model based on gaussian processes maximizes the
+#given function using probability distributions
+
+#target stress for the given youngs modulus
+target_stress = target_ans["stress"]
+
+#loss function for bayesian optimization
+@jit
+def loss_func(youngs_modulus, solver=solver, target_stress=target_stress):
+    material_props = solver.mesh.particles[0].material.properties
+    material_props["youngs_modulus"] = youngs_modulus
+    solver.mesh.particles[0].material = LinearElastic(material_props)
+    external_loading_local = jnp.array([0.0, -9.8]).reshape(1, 2)
+    result = solver.solve_jit(external_loading_local)
+    stress = result["stress"]
+    loss = jnp.linalg.norm(stress - target_stress)
+    #returning negative of the loss as bayesian optimizer maximizes the function
+    return -loss
+
+#giving bound to the value of the youngs_modulus for bayesian optimizer
+pbounds = {"youngs_modulus": (900, 1100)}
+optimizer = BayesianOptimization(
+    f=loss_func, pbounds=pbounds, random_state=1, verbose=2
+)
+#measuring the time taken by the optimizer
+start_t = time.time()
+#calling the optimizer, init_points is the number of random points to be sampled
+#n_iter is the number of iterations to be performed
+optimizer.maximize(init_points=3, n_iter=5)
+end_time = time.time()
+print(f"Time taken by Bayesian Optimization: {end_time-start_t}")
+print(optimizer.max)
diff --git a/inverse_solver.ipynb b/inverse_solver.ipynb
deleted file mode 100644
index 5af09a2..0000000
--- a/inverse_solver.ipynb
+++ /dev/null
@@ -1,214 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import os, sys\n",
-    "\n",
-    "sys.path.append(os.getcwd())\n",
-    "from diffmpm.material import SimpleMaterial,LinearElastic\n",
-    "from diffmpm.particle import Particles\n",
-    "from diffmpm.element import Quadrilateral4Node\n",
-    "from diffmpm.constraint import Constraint\n",
-    "from diffmpm.mesh import Mesh2D\n",
-    "from diffmpm.solver import MPMExplicit\n",
-    "import jax.numpy as jnp\n",
-    "import numpy as np\n",
-    "\n",
-    "mesh_config = {}\n",
-    "density = 1\n",
-    "# poisson_ratio = 0\n",
-    "youngs_modulus = 1000\n",
-    "material = LinearElastic(\n",
-    "    {\n",
-    "        \"id\":0,\n",
-    "        \"youngs_modulus\": youngs_modulus,\n",
-    "        \"density\": density,\n",
-    "        \"poisson_ratio\": 0.0,\n",
-    "    }\n",
-    ")\n",
-    "particle_loc = jnp.array([[0.0, 0.0], [0.5, 0.0], [0.0, 0.5], [0.5, 0.5]]).reshape(\n",
-    "    4, 1, 2\n",
-    ")\n",
-    "particles = Particles(particle_loc, material, jnp.zeros(particle_loc.shape[0],dtype=jnp.int32))\n",
-    "particles.velocity=particles.velocity.at[:].set(0.0)\n",
-    "constraints = [(0, Constraint(1, 0.0))]\n",
-    "external_loading = jnp.array([0.0, -9.8]).reshape(1,2)\n",
-    "element = Quadrilateral4Node([1, 1], 1, [1,1], constraints)\n",
-    "mesh_config[\"particles\"] = [particles]\n",
-    "mesh_config[\"elements\"] = element\n",
-    "mesh_config[\"particle_surface_traction\"] = []\n",
-    "mesh = Mesh2D(mesh_config)\n",
-    "solver = MPMExplicit(mesh, 0.01,sim_steps=10)\n",
-    "\n",
-    "real_ans = solver.solve_jit(external_loading)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from jax import jit\n",
-    "\n",
-    "def compute_loss(E,solver,target_stress):\n",
-    "    material_props=solver.mesh.particles[0].material.properties\n",
-    "    material_props[\"youngs_modulus\"]=E\n",
-    "    solver.mesh.particles[0].material=LinearElastic(material_props)\n",
-    "    external_loading_local=jnp.array([0.0, -9.8]).reshape(1,2)\n",
-    "    solver.mesh.particles[0].velocity = mesh.particles[0].velocity.at[:].set(0.0)\n",
-    "    result = solver.solve_jit(external_loading_local)\n",
-    "    stress = result[\"stress\"]\n",
-    "    loss = jnp.linalg.norm(stress - target_stress)\n",
-    "    return loss"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "E: 1000.3665161132812: 100%|██████████| 500/500 [00:11<00:00, 43.43it/s]\n"
-     ]
-    }
-   ],
-   "source": [
-    "import optax\n",
-    "from tqdm import tqdm\n",
-    "from jax import jit, value_and_grad\n",
-    "\n",
-    "def optax_adam(params,niter,mpm,target_vel):\n",
-    "    start_alpha=0.1\n",
-    "    optimizer=optax.adam(start_alpha)\n",
-    "    opt_state=optimizer.init(params)\n",
-    "    param_list=[]\n",
-    "    loss_list=[]\n",
-    "    t=tqdm(range(niter),desc=f\"E: {params}\")\n",
-    "    for _ in t:\n",
-    "        lo,grads=value_and_grad(compute_loss)(params,mpm,target_vel)\n",
-    "        updates,opt_state=optimizer.update(grads,opt_state)\n",
-    "        params=optax.apply_updates(params,updates)\n",
-    "        t.set_description(f\"E: {params}\")\n",
-    "        param_list.append(params)\n",
-    "        loss_list.append(lo)\n",
-    "    return param_list,loss_list\n",
-    "params=1050.0\n",
-    "parameter_list,loss_list=optax_adam(params,500,solver,real_ans[\"stress\"])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "#Trying via Bayesian Optimization\n",
-    "target_stress=real_ans[\"stress\"]\n",
-    "@jit\n",
-    "def fun(E,solver=solver,target_stress=target_stress):\n",
-    "    material_props=solver.mesh.particles[0].material.properties\n",
-    "    material_props[\"youngs_modulus\"]=E\n",
-    "    solver.mesh.particles[0].material=LinearElastic(material_props)\n",
-    "    external_loading_local=jnp.array([0.0, -9.8]).reshape(1,2)\n",
-    "    # solver.mesh.particles[0].velocity = mesh.particles[0].velocity.at[:].set(0.0)\n",
-    "    result = solver.solve_jit(external_loading_local)\n",
-    "    stress = result[\"stress\"]\n",
-    "    loss = jnp.linalg.norm(stress - target_stress)\n",
-    "    return -loss"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from bayes_opt import BayesianOptimization\n",
-    "\n",
-    "pbounds = {\"E\": (800, 1500)}\n",
-    "optimizer = BayesianOptimization(f=fun, pbounds=pbounds, random_state=1, verbose=2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "|   iter    |  target   |     E     |\n",
-      "-------------------------------------\n",
-      "| \u001b[0m1        \u001b[0m | \u001b[0m-1.017   \u001b[0m | \u001b[0m1.092e+03\u001b[0m |\n",
-      "| \u001b[0m2        \u001b[0m | \u001b[0m-3.452   \u001b[0m | \u001b[0m1.304e+03\u001b[0m |\n",
-      "| \u001b[0m3        \u001b[0m | \u001b[0m-1.895   \u001b[0m | \u001b[0m800.1    \u001b[0m |\n",
-      "| \u001b[0m4        \u001b[0m | \u001b[0m-1.031   \u001b[0m | \u001b[0m1.093e+03\u001b[0m |\n",
-      "| \u001b[95m5        \u001b[0m | \u001b[95m-0.4102  \u001b[0m | \u001b[95m961.1    \u001b[0m |\n",
-      "| \u001b[95m6        \u001b[0m | \u001b[95m-0.05521 \u001b[0m | \u001b[95m1.005e+03\u001b[0m |\n",
-      "| \u001b[0m7        \u001b[0m | \u001b[0m-5.561   \u001b[0m | \u001b[0m1.5e+03  \u001b[0m |\n",
-      "| \u001b[0m8        \u001b[0m | \u001b[0m-0.2243  \u001b[0m | \u001b[0m1.021e+03\u001b[0m |\n",
-      "=====================================\n"
-     ]
-    }
-   ],
-   "source": [
-    "optimizer.maximize(init_points=3,n_iter=5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "{'target': -0.0552130751311779, 'params': {'E': 1005.1373320945569}}\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(optimizer.max)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "optaximpo",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.11.4"
-  },
-  "orig_nbformat": 4
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}

From e31d8db519650b20387005f5cbfdf8bc53c2fd5e Mon Sep 17 00:00:00 2001
From: Sachin Jalan <sachinjalan03@gmail.com>
Date: Fri, 11 Aug 2023 04:10:06 +0530
Subject: [PATCH 5/6] plot added

---
 examples/inverse_solver_2d.ipynb | 46 +++++++++++++++++++++++++-------
 1 file changed, 36 insertions(+), 10 deletions(-)

diff --git a/examples/inverse_solver_2d.ipynb b/examples/inverse_solver_2d.ipynb
index 7b6bfee..33ca064 100644
--- a/examples/inverse_solver_2d.ipynb
+++ b/examples/inverse_solver_2d.ipynb
@@ -2,23 +2,38 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n",
-      "E: 1000.3665161132812: 100%|██████████| 500/500 [00:51<00:00,  9.74it/s]\n"
+      "Youngs_modulus: 1000.3665161132812: 100%|██████████| 500/500 [00:53<00:00,  9.33it/s]\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Time taken by adam: 51.358086347579956\n",
-      "parameter = 1000.3665161132812 and loss = 0.004986115265637636\n",
+      "Time taken by adam: 53.58390808105469\n",
+      "parameter = 1000.3665161132812 and loss = 0.004986115265637636\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "|   iter    |  target   | youngs... |\n",
       "-------------------------------------\n",
       "| \u001b[0m1        \u001b[0m | \u001b[0m-0.1767  \u001b[0m | \u001b[0m983.4    \u001b[0m |\n",
@@ -30,7 +45,7 @@
       "| \u001b[95m7        \u001b[0m | \u001b[95m-0.002043\u001b[0m | \u001b[95m1e+03    \u001b[0m |\n",
       "| \u001b[0m8        \u001b[0m | \u001b[0m-0.5549  \u001b[0m | \u001b[0m947.0    \u001b[0m |\n",
       "=====================================\n",
-      "Time taken by Bayesian Optimization: 3.525190830230713\n",
+      "Time taken by Bayesian Optimization: 3.81498646736145\n",
       "{'target': -0.0020428309217095375, 'params': {'youngs_modulus': 1000.1903192810634}}\n"
      ]
     }
@@ -51,7 +66,7 @@
     "from tqdm import tqdm\n",
     "import time\n",
     "from bayes_opt import BayesianOptimization\n",
-    "\n",
+    "import matplotlib.pyplot as plt\n",
     "mesh_config = {}\n",
     "density = 1\n",
     "poisson_ratio = 0.0\n",
@@ -111,12 +126,12 @@
     "    opt_state = optimizer.init(params)\n",
     "    param_list = []\n",
     "    loss_list = []\n",
-    "    t = tqdm(range(niter), desc=f\"E: {params}\")\n",
+    "    t = tqdm(range(niter), desc=f\"Youngs_modulus: {params}\")\n",
     "    for _ in t:\n",
     "        lo, grads = value_and_grad(compute_loss)(params, mpm, target_stress)\n",
     "        updates, opt_state = optimizer.update(grads, opt_state)\n",
     "        params = optax.apply_updates(params, updates)\n",
-    "        t.set_description(f\"E: {params}\")\n",
+    "        t.set_description(f\"Youngs_modulus: {params}\")\n",
     "        param_list.append(params)\n",
     "        loss_list.append(lo)\n",
     "    return param_list, loss_list\n",
@@ -130,7 +145,11 @@
     "end_time = time.time()\n",
     "print(f\"Time taken by adam: {end_time-start_t}\")\n",
     "print(f\"parameter = {parameter_list[-1]} and loss = {loss_list[-1]}\")\n",
-    "\n",
+    "plt.plot(parameter_list,loss_list)\n",
+    "plt.xlabel(\"Youngs_modulus\")\n",
+    "plt.ylabel(\"Loss calculated in stress\")\n",
+    "plt.title(\"Adam optimizer\")\n",
+    "plt.show()\n",
     "# Using Bayesian Optimization model based on gaussian processes maximizes the\n",
     "#given function using probability distributions\n",
     "\n",
@@ -164,6 +183,13 @@
     "print(f\"Time taken by Bayesian Optimization: {end_time-start_t}\")\n",
     "print(optimizer.max)\n"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {

From 4916f731bb9e824f5a841eb4da8302b178908f38 Mon Sep 17 00:00:00 2001
From: Sachin Jalan <sachinjalan03@gmail.com>
Date: Thu, 17 Aug 2023 01:34:39 +0530
Subject: [PATCH 6/6] Explaination added

---
 examples/inverse_solver_2d.ipynb | 149 +++++++++++++++++++++----------
 1 file changed, 103 insertions(+), 46 deletions(-)

diff --git a/examples/inverse_solver_2d.ipynb b/examples/inverse_solver_2d.ipynb
index 33ca064..589c078 100644
--- a/examples/inverse_solver_2d.ipynb
+++ b/examples/inverse_solver_2d.ipynb
@@ -1,52 +1,27 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Inverse solver example for body under uniform gravity loading\n",
+    "This notebook demonstrates an example for inverse solver for a body under uniform gravity loading and tries to estimate the youngs modulus of the body needed to get the observed stress.  \n",
+    "\n",
+    "First we solved the problem of calculating the stress on the body under the given conditions and given youngs modulus of 1000.  \n",
+    "\n",
+    "The following code runs the MPM solver for a body represented by 4 material points and a unit cell mesh. The body is modelled as linear elastic material with density=1, youngs modulus=1000. The particles are located at [(0,0),(0.5,0),(0,0.5),(0.5,0.5)].\n"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "Youngs_modulus: 1000.3665161132812: 100%|██████████| 500/500 [00:53<00:00,  9.33it/s]\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Time taken by adam: 53.58390808105469\n",
-      "parameter = 1000.3665161132812 and loss = 0.004986115265637636\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "|   iter    |  target   | youngs... |\n",
-      "-------------------------------------\n",
-      "| \u001b[0m1        \u001b[0m | \u001b[0m-0.1767  \u001b[0m | \u001b[0m983.4    \u001b[0m |\n",
-      "| \u001b[0m2        \u001b[0m | \u001b[0m-0.4804  \u001b[0m | \u001b[0m1.044e+03\u001b[0m |\n",
-      "| \u001b[0m3        \u001b[0m | \u001b[0m-1.019   \u001b[0m | \u001b[0m900.0    \u001b[0m |\n",
-      "| \u001b[95m4        \u001b[0m | \u001b[95m-0.1635  \u001b[0m | \u001b[95m984.7    \u001b[0m |\n",
-      "| \u001b[0m5        \u001b[0m | \u001b[0m-1.108   \u001b[0m | \u001b[0m1.1e+03  \u001b[0m |\n",
-      "| \u001b[95m6        \u001b[0m | \u001b[95m-0.1306  \u001b[0m | \u001b[95m1.012e+03\u001b[0m |\n",
-      "| \u001b[95m7        \u001b[0m | \u001b[95m-0.002043\u001b[0m | \u001b[95m1e+03    \u001b[0m |\n",
-      "| \u001b[0m8        \u001b[0m | \u001b[0m-0.5549  \u001b[0m | \u001b[0m947.0    \u001b[0m |\n",
-      "=====================================\n",
-      "Time taken by Bayesian Optimization: 3.81498646736145\n",
-      "{'target': -0.0020428309217095375, 'params': {'youngs_modulus': 1000.1903192810634}}\n"
+      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
      ]
     }
    ],
@@ -100,9 +75,52 @@
     "mesh = Mesh2D(mesh_config)\n",
     "solver = MPMExplicit(mesh, 0.01, sim_steps=10)\n",
     "# getting the target value for youngs modulus 1000\n",
-    "target_ans = solver.solve_jit(gravity_loading)\n",
+    "target_ans = solver.solve_jit(gravity_loading)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "After getting the target stress. The following code tries to estimate the youngs_modulus for the body. The following code uses Adam optimizer for estimating the youngs modulus of the body by calculating error between target stress and estimated stress. The estimated stress is calculated by running the MPM solver for the estimated youngs modulus.  \n",
     "\n",
+    "The compute loss function generates a material object at each iteration for the youngs modulus at the given iteration and solves the generated configuration.  \n",
     "\n",
+    "The optax_adam function calculates gradient of the stress with respect to the youngs_modulus and updates the parameter. The inital guess for the youngs modulus is 1050"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Youngs_modulus: 1000.3665161132812: 100%|██████████| 500/500 [00:51<00:00,  9.65it/s]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time taken by adam: 51.79610347747803\n",
+      "parameter = 1000.3665161132812 and loss = 0.004986115265637636\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
     "# using adam optimizer\n",
     "@jit\n",
     "def compute_loss(youngs_modulus, solver, target_stress):\n",
@@ -149,7 +167,44 @@
     "plt.xlabel(\"Youngs_modulus\")\n",
     "plt.ylabel(\"Loss calculated in stress\")\n",
     "plt.title(\"Adam optimizer\")\n",
-    "plt.show()\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The ADAM optimizer based method is takes a lot of time in estimating the youngs modulus which is not ideal for large simulations. Hence a much better method of Bayesian Optimization can be used which is very fast compared to ADAM optimizer, and generates a much better estimate of youngs modulus. In Bayesian Optimization method we need to provide a prior, a range where our youngs modulus would be estimated to lie, in most practical applications this information would be known. We also need to provide the number if random points Bayesian Optimization can explore and the number of iterations for which our it should run.  \n",
+    "\n",
+    "In the following code block we will be using Bayesian Optimization to estimate the youngs modulus of the material. The number if iterations for which our solver is run is 8 while in ADAM optimizer it was 500, as the solver function is very costly hence minimizing the number if iterations would speed up the simulation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "|   iter    |  target   | youngs... |\n",
+      "-------------------------------------\n",
+      "| \u001b[0m1        \u001b[0m | \u001b[0m-0.1767  \u001b[0m | \u001b[0m983.4    \u001b[0m |\n",
+      "| \u001b[0m2        \u001b[0m | \u001b[0m-0.4804  \u001b[0m | \u001b[0m1.044e+03\u001b[0m |\n",
+      "| \u001b[0m3        \u001b[0m | \u001b[0m-1.019   \u001b[0m | \u001b[0m900.0    \u001b[0m |\n",
+      "| \u001b[95m4        \u001b[0m | \u001b[95m-0.1635  \u001b[0m | \u001b[95m984.7    \u001b[0m |\n",
+      "| \u001b[0m5        \u001b[0m | \u001b[0m-1.108   \u001b[0m | \u001b[0m1.1e+03  \u001b[0m |\n",
+      "| \u001b[95m6        \u001b[0m | \u001b[95m-0.1306  \u001b[0m | \u001b[95m1.012e+03\u001b[0m |\n",
+      "| \u001b[95m7        \u001b[0m | \u001b[95m-0.002043\u001b[0m | \u001b[95m1e+03    \u001b[0m |\n",
+      "| \u001b[0m8        \u001b[0m | \u001b[0m-0.5549  \u001b[0m | \u001b[0m947.0    \u001b[0m |\n",
+      "=====================================\n",
+      "Time taken by Bayesian Optimization: 3.57847261428833\n",
+      "{'target': -0.0020428309217095375, 'params': {'youngs_modulus': 1000.1903192810634}}\n"
+     ]
+    }
+   ],
+   "source": [
     "# Using Bayesian Optimization model based on gaussian processes maximizes the\n",
     "#given function using probability distributions\n",
     "\n",
@@ -181,15 +236,17 @@
     "optimizer.maximize(init_points=3, n_iter=5)\n",
     "end_time = time.time()\n",
     "print(f\"Time taken by Bayesian Optimization: {end_time-start_t}\")\n",
-    "print(optimizer.max)\n"
+    "print(optimizer.max)"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "source": [
+    "After analysing the result of both the estimations we observe that both methods correctly estimates the youngs modulus to be 1000 as stated in the original MPM solver. We can also notice that the ADAM solver took almost 50 seconds for the simulation while the bayesian optimization took only 3 seconds, this shows the significant benefit of using probability based methods over Linear Regression based methods.  \n",
+    "\n",
+    "The Inverse Solver has many practical applications, it can be used to estimate the necessary properties that a material should possess to have a certain behaviour under different loading conditions."
+   ]
   }
  ],
  "metadata": {