PDE with a spatially correlated stochastic term

[JonasVeenstra]

Hi Dr. Zwicker,

Thanks for developing a great and userfriendly package!

I understand the package supports PDE's with additive noise but so far I've only been able to generate a Gaussian noise term that depends both on time and space, as in the following PDE:

However, I would like the noise to be white only in time and harmonic in space, similar to the classmethod random_harmonic:

with a the amplitude, L the box size and j the mode number.

That mentioned classmethod seems intended to be used for generating a field as an initial condition, but I would like it to function as the noise term. Is there a way to do this? If so, could you point me in the right direction?

Many thanks in advance!

[david-zwicker]

You can define your own noise term by subclassing PDEBase; see documentation. Essentially, you need to overwrite the methods noise_realization (for the numpy backend) and/or _make_noise_realization_numba (for the numba backend).

[JonasVeenstra]

Many thanks, I got it to work! (I overlooked this example which helped a lot.)

[david-zwicker]

It's not surprising that you didn't see the example, since I just added it inspired by your question :)