PDENet-Gen

Published in IMT Atlantique, Brest, FR, 2020

Bridging physics and deep learning is a topical challenge. While deep learning frameworks open avenues in physical science, the design of physicallyconsistent deep neural network architectures is an open issue. In the spirit of physics-informed NNs, PDE-NetGen package provides new means to automatically translate physical equations, given as PDEs, into neural network architectures. PDE-NetGen combines symbolic calculus and a neural network generator. The later exploits NN-based implementations of PDE solvers using Keras. With some knowledge of a problem, PDE-NetGen is a plug-and-play tool to generate physics-informed NN architectures. They provide computationally-efficient yet compact representations to address a variety of issues, including among others adjoint derivation, model calibration, forecasting, data assimilation as well as uncertainty quantification. As an illustration, the workflow is first presented for the 2D diffusion equation, then applied to the data-driven and physics-informed identification of uncertainty dynamics for the Burgers equation. Related paper: Pannekoucke and Fablet. PDE-NetGen 1.0: from symbolic PDE representations of physical processes to trainable neural network representations. Arxiv, 2020 (link) Associated code: git