GradINN: Gradient Informed Neural Network

• URL: http://arxiv.org/abs/2409.01914v1
• Date: Tue, 3 Sep 2024 14:03:29 GMT
• Title: GradINN: Gradient Informed Neural Network
• Authors: Filippo Aglietti, Francesco Della Santa, Andrea Piano, Virginia Aglietti,
• Abstract summary: We propose a methodology inspired by Physics Informed Neural Networks (PINNs) GradINNs leverage prior beliefs about a system's gradient to constrain the predicted function's gradient across all input dimensions. We demonstrate the advantages of GradINNs, particularly in low-data regimes, on diverse problems spanning non time-dependent systems.
• Score: 2.287415292857564
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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