phiflow: A differentiable pde solving framework for deep learning via physical simulations
Holl, Philipp, Koltun, Vladlen, Um, Kiwon, and Thuerey, Nils

Publication: NeurIPS workshop

Abstract: In this context, we present phiflow (https://github.com/tum-pbs/PhiFlow), a fully differentiable Eulerian PDE framework that provides operators and solvers for a large class of PDEs with analytic gradients. By fully integrating the numerical solver into the training process, neural networks (NNs) can, e.g., learn to reduce numerical errors of PDE solvers, and to optimally control a physical system given an initial state and a target state. We show the capabilities of phiflow with a wide range of correction and control tasks for various advection-diffusion type PDEs, and demonstrate that long time frames can be handled via a specialized architecture and evaluation scheme that separates the learning of physical behavior for different time scales.

Bibtex: 

@inproceedings{holl-2020-phiflow-simulations,
  title = {phiflow: A differentiable pde solving framework for deep learning via physical simulations},
  author = {Holl, Philipp and Koltun, Vladlen and Um, Kiwon and Thuerey, Nils},
  year = {2020},
  booktitle = {NeurIPS workshop},
  volume = {2}
}