Fully differentiable model discovery
This work addresses model discovery for researchers in scientific computing and machine learning by expanding Physics Informed Neural Networks to new architectures and connecting them to Bayesian inference, though it appears incremental as it builds on existing PINN and SBL methods.
The paper tackles the problem of autonomously discovering differential equations from data by proposing a fully-differentiable model that integrates neural network surrogates with Sparse Bayesian Learning, achieving robust performance across various datasets and extending to Physics Informed Normalizing Flows for density modeling from single particle data.
Model discovery aims at autonomously discovering differential equations underlying a dataset. Approaches based on Physics Informed Neural Networks (PINNs) have shown great promise, but a fully-differentiable model which explicitly learns the equation has remained elusive. In this paper we propose such an approach by integrating neural network-based surrogates with Sparse Bayesian Learning (SBL). This combination yields a robust model discovery algorithm, which we showcase on various datasets. We then identify a connection with multitask learning, and build on it to construct a Physics Informed Normalizing Flow (PINF). We present a proof-of-concept using a PINF to directly learn a density model from single particle data. Our work expands PINNs to various types of neural network architectures, and connects neural network-based surrogates to the rich field of Bayesian parameter inference.