Physics-enhanced Neural Networks in the Small Data Regime

Abstract

Identifying the dynamics of physical systems requires a machine learning model that can assimilate observational data, but also incorporate the laws of physics. Neural Networks based on physical principles such as the Hamiltonian or Lagrangian NNs have recently shown promising results in generating extrapolative predictions and accurately representing the system's dynamics. We show that by additionally considering the actual energy level as a regularization term during training and thus using physical information as inductive bias, the results can be further improved. Especially in the case where only small amounts of data are available, these improvements can significantly enhance the predictive capability. We apply the proposed regularization term to a Hamiltonian Neural Network (HNN) and Constrained Hamiltonian Neural Network (CHHN) for a single and double pendulum, generate predictions under unseen initial conditions and report significant gains in predictive accuracy. * equal contribution Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021).

Deep learning in computational mechanics: a review

“…The two most prominent methodologies, i.e., modifying the cost function and enforcement by construction are similarly mentioned in [225], which correspondingly refers to them as physics-informed and physics-augmented. Further variations in terminology can be found in [182,226], who refer to physics-informed NNs for multiple solutions as physics-constrained deep learning, or [227] using the term physics-enhanced NNs for NNs enforcing the physics by construction. Due to the many names within the relatively new and interconnected field, we cover the variations under the overarching term of physics-informed learning.…”

Physics-informed Reinforcement Learning for Perception and Reasoning about Fluids

“…Con-versely, current proposals introduce physics-informed machine learning into the model's inference [38]. Among the plethora of existing approaches, knowledge distillation is mainly accomplished by learning PDEs' parameters [46] [4], the imposition of Hamiltonian or Lagrangian structures [9] [59] [14], or thermodynamics-informed simulators [39] [56] [58] [30].…”