# GradINN: Gradient Informed Neural Network

arXiv: https://arxiv.org/abs/2409.01914 · HTML: https://mlsanity.com/paper/2409.01914/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 8 of 8)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Hamiltonian neural networks for solving equations of motion](https://mlsanity.com/paper/2001.11107/) (2020)
- [Universal approximation property of invertible neural networks](https://mlsanity.com/paper/2204.07415/) (2022)

## Abstract (arXiv)

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.