GradINN: Gradient Informed Neural Network
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912013521780736 |
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| author | Aglietti, Filippo Della Santa, Francesco Piano, Andrea Aglietti, Virginia |
| author_facet | Aglietti, Filippo Della Santa, Francesco Piano, Andrea Aglietti, Virginia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01914 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | GradINN: Gradient Informed Neural Network Aglietti, Filippo Della Santa, Francesco Piano, Andrea Aglietti, Virginia Machine Learning Artificial Intelligence 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. |
| title | GradINN: Gradient Informed Neural Network |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2409.01914 |