Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations

Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization

The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

Solving differential equations in R using DifferentialEquations.jl and the SciML Scientific Machine Learning ecosystem

Neural Laplace: Differentiable Laplace Reconstructions for modelling any time observation with O(1) complexity.

Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differential-algebraic equations.

Thompson and Shampine's DDE_SOLVER, a Fortran library for delay differential equations.

Modelling of chatter vibration in thin-wall milling and its effect on surface roughness of job

Neural Laplace Control for Continuous-time Delayed Systems - an offline RL method combining Neural Laplace dynamics model and MPC planner to achieve near-expert policy performance in environments with irregular time intervals and an unknown constant delay.

Source code generator for differential equation solvers.

Some slides, code and videos about R, mostly for mathematical modellers

Julia package for solving Differential Equations with Discrete and Distributed delays

Matlab package for solving Differential Equations with Discrete and Distributed delays

Python package for solving Differential Equations with Discrete and Distributed delays

Mathematical research of stochastic processes with time delays

Differential equation models that incorporate waning immunity

COCO constructors for delay-differential-algebraic equations

Inoue, K. et al. Oscillation dynamics underlie functional switching of NF-κB for B-cell activation. npj Syst. Biol. Appl. 2, 16024 (2016).