GradINN: Gradient Informed Neural Network
This addresses complex engineering problems where equations are unknown, offering an incremental improvement over Physics Informed Neural Networks.
The authors tackled the problem of approximating physical systems with unknown governing equations by proposing Gradient Informed Neural Networks (GradINNs), which use gradient constraints from an auxiliary network to improve predictions, achieving strong performance in low-data regimes across various systems like Stokes Flow and Burger's equation.
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.