Robust Neural Network-Based Discovery of Dynamical Systems

Code

• github.com/santiago-a-serrano/robust_physics_constrained_nn
  jax★ 1

Abstract

Using neural networks to represent the dynamics of a system has multiple advantages over sparse regression techniques such as SINDy, as the applicability of the former is not constrained to systems with dynamics that can only be accurately expressed using analytical expressions. On top of that, progress has been made in the use of physics-informed architectures for neural networks, making them more precise when certain aspects of the laws governing the system are known. However, existing approaches of Physics Informed Neural Networks (PINNs) are not protected enough against noise in their training data, which makes them less reliable in real-life scenarios where information obtained from sensors or real observations is not noise-free. In this work, I propose two approaches for PINNs tailored to address Gaussian and adversarial noise, respectively, in the training data, by combining previous work on PINNs with existing techniques that aim to improve the generalization and robustness of models. These new approaches, named GPPhysMLP and GRPhysMLP respectively, demonstrate superior performance compared to counterparts that do not take noise into account significantly enough.

Reproductions