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.
The Robustness of Differentiable Causal Discovery in Misspecified Scenarios
School of Mathematics, Southeast University, Nanjing 210096, China（数学学院，东南大学，南京210096，中国）；School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China（网络科学与工程学院，东南大学，南京210096，中国）
Boosting Differentiable Causal Discovery via Adaptive Sample Reweighting
National University of Singapore（新加坡国立大学）；Tsinghua University（清华大学）；Renmin University of China（中国人民大学）；University of Science and Technology of China（中国科学技术大学）；Hefei Comprehensive National Science Center（合肥综合性国家科学中心）
Leveraging Differentiable PDE Solvers for Semi-Neural Spatial Reconstruction From Sparse Measurements
Department of Mathematics, Technion, Haifa, Israel（数学系，技术离子学院，海法，以色列）；Department of Civil and Environmental Engineering, Technion, Haifa, Israel（土木与环境工程系，技术离子学院，海法，以色列）
