GradINN: Gradient Informed Neural Network

TL;DR

GradINNs introduce a neural network approach that incorporates prior gradient beliefs to efficiently model complex physical systems with unknown governing equations, especially effective in low-data scenarios.

Contribution

This paper presents GradINNs, a novel neural network framework that uses gradient priors to approximate physical systems without known equations, outperforming existing methods.

Findings

Effective in low-data regimes

Outperforms standard neural networks and PINNs

Applicable to diverse physical systems

Abstract

We propose Gradient Informed Neural Networks (GradINNs), a methodology inspired by Physics Informed Neural Networks (PINNs) that can be used to efficiently approximate a wide range of physical systems for which the underlying governing equations are completely unknown or cannot be defined, a condition that is often met in complex engineering problems. GradINNs leverage prior beliefs about a system's gradient to constrain the predicted function's gradient across all input dimensions. This is achieved using two neural networks: one modeling the target function and an auxiliary network expressing prior beliefs, e.g., smoothness. A customized loss function enables training the first network while enforcing gradient constraints derived from the auxiliary network. We demonstrate the advantages of GradINNs, particularly in low-data regimes, on diverse problems spanning non time-dependent systems (Friedman function, Stokes Flow) and time-dependent systems (Lotka-Volterra, Burger's equation). Experimental results showcase strong performance compared to standard neural networks and PINN-like approaches across all tested scenarios.