Summary of Optimal Time Sampling in Physics-informed Neural Networks, by Gabriel Turinici
Optimal time sampling in physics-informed neural networks
by Gabriel Turinici
First submitted to arxiv on: 29 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
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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 A physics-informed neural network (PINN) approach is employed in scientific computing applications to solve equations efficiently. This paradigm involves minimizing an equation residual, which includes time-sampling when the equation is time-dependent. The literature suggests that non-uniform sampling should overweight initial time instants, but a rigorous explanation was lacking. This paper investigates prototypical examples under standard neural network convergence hypotheses and demonstrates that optimal time sampling follows a truncated exponential distribution. The findings are applied to linear equations, Burgers’ equation, and the Lorenz system. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Physics-informed neural networks (PINN) help solve complex scientific problems by minimizing errors in equations. One part of this process is choosing when to take “snapshots” of time-dependent events. Some experts think these snapshots should be more frequent at the beginning and less frequent later on, but they didn’t explain why. This study looks at simple examples under normal assumptions about how neural networks work and shows that the best way to take these snapshots follows an exponential curve. The results are shown with examples of solving linear equations, a traffic flow problem, and a weather forecasting model. |
Keywords
» Artificial intelligence » Neural network
