Parallel-in-Time Probabilistic Solutions for PDEs

Companion code for the paper "Parallel-in-Time Probabilistic Solutions for Time-Dependent Nonlinear Partial Differential Equations".

This code was written by Hany Abdulsamad, Sahel Iqbal and Tripp Cator

Installation

Create a conda environment

conda create -n NAME python=3.11

then install a GPU-supported version of JAX

pip install -U "jax[cuda12_pip]" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html

Finally, install parallel-in-time Kalman-smoothers toolbox

pip install git+https://github.com/hanyas/sqrt-parallel-smoothers

The Newton-smoother package is optional for second-order and regularized algorithms

pip install git+https://github.com/hanyas/second-order-smoothers

Install pytest for testing, matplotlib for plots, and py-pde for rereference solutions.

Examples

python examples/burgers_parallel.py

Cite

@inproceedings{iqbal2024parallel,
  title={Parallel-in-Time Probabilistic Solutions for Time-Dependent Nonlinear Partial Differential Equations}, 
  author={Iqbal, Sahel and Abdulsamad, Hany and Cator, Tripp and Braga-Neto, Ulisses and Särkkä, Simo},
  booktitle={2024 IEEE 34th International Workshop on Machine Learning for Signal Processing (MLSP)}, 
  year={2024},
}