Summary of Extremization to Fine Tune Physics Informed Neural Networks For Solving Boundary Value Problems, by Abhiram Anand Thiruthummal et al.
Extremization to Fine Tune Physics Informed Neural Networks for Solving Boundary Value Problems
by Abhiram Anand Thiruthummal, Sergiy Shelyag, Eun-jin Kim
First submitted to arxiv on: 7 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Engineering, Finance, and Science (cs.CE); 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 The proposed method trains physics-informed neural networks (PINNs) efficiently and accurately for solving boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining deep neural network (DNN) training with Extreme Learning Machines (ELMs), the model achieves DNN expressivity and ELM fine-tuning capabilities. The method is demonstrated by solving several BVPs and IBVPs, including linear and non-linear ordinary differential equations (ODEs), partial differential equations (PDEs), and coupled PDEs. Examples include a stiff coupled ODE system where traditional methods fail, 3+1D non-linear PDE, Kovasznay flow, Taylor-Green vortex solutions to incompressible Navier-Stokes equations, and pure advection solution of 1+1D compressible Euler equation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper develops a new way to train neural networks to solve math problems. It combines two existing techniques to create a model that’s good at both solving simple and complex problems. The method is tested on many different types of problems, including ones that traditional computers can’t solve easily. This could be useful for fields like physics, engineering, and science. |
Keywords
» Artificial intelligence » Fine tuning » Neural network
