Summary of Gradinn: Gradient Informed Neural Network, by Filippo Aglietti et al.
GradINN: Gradient Informed Neural Network
by Filippo Aglietti, Francesco Della Santa, Andrea Piano, Virginia Aglietti
First submitted to arxiv on: 3 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed Gradient Informed Neural Networks (GradINNs) is a methodology inspired by Physics Informed Neural Networks (PINNs), which can efficiently approximate physical systems without knowing the underlying governing equations. GradINNs leverage prior beliefs about a system’s gradient to constrain the predicted function’s gradient across all input dimensions, using two neural networks: one modeling the target function and an auxiliary network expressing prior beliefs, such as smoothness. A customized loss function enables training the first network while enforcing gradient constraints derived from the auxiliary network. This approach demonstrates strong performance compared to standard neural networks and PINN-like approaches in low-data regimes on diverse problems, including non time-dependent systems (Friedman function, Stokes Flow) and time-dependent systems (Lotka-Volterra, Burger’s equation). |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper proposes a new way to use artificial intelligence to solve complex engineering problems. They developed a type of neural network called Gradient Informed Neural Networks (GradINNs). This helps predict the behavior of physical systems even when we don’t know the rules that govern them. The approach uses two types of networks: one that tries to guess the system’s behavior and another that gives us hints about what the answer should look like. By combining these, GradINNs can make more accurate predictions than other methods, especially with limited data. |
Keywords
» Artificial intelligence » Loss function » Neural network
