GradINN: Gradient Informed Neural Network
<|reference_start|>GradINN: Gradient Informed Neural Network: 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.<|reference_end|>
@article{aglietti2024gradinn:,
    title={GradINN: Gradient Informed Neural Network},
    author={Filippo Aglietti, Francesco Della Santa, Andrea Piano, Virginia
  Aglietti},
    journal={arXiv preprint arXiv:2409.01914},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01914},
    primaryClass={cs.LG cs.AI}
}