Summary of Improvement Of Bayesian Pinn Training Convergence in Solving Multi-scale Pdes with Noise, by Yilong Hou et al.
Improvement of Bayesian PINN Training Convergence in Solving Multi-scale PDEs with Noise
by Yilong Hou, Xi’an Li, Jinran Wu
First submitted to arxiv on: 18 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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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 Bayesian Physics Informed Neural Networks (BPINN) method is improved by integrating multi-scale deep neural networks (MscaleDNN) and Bayesian inference. The new approach, called MBPINN, reframes Hamiltonian Monte Carlo (HMC) with Stochastic Gradient Descent (SGD) to provide the most “likely” estimation while reducing computational cost. The MBPINN method is more robust than HMC and can handle complex partial differential equations (PDE). It outperforms traditional methods in solving general Poisson and multi-scale elliptic problems in one- to three-dimensional spaces. The results show that MBPINN can avoid HMC failures and produce valid results, making it a promising approach for physics-informed machine learning. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new method called MBPINN combines ideas from Bayesian Physics Informed Neural Networks (BPINN) and multi-scale deep neural networks (MscaleDNN). This helps solve complex problems more accurately. The old way of doing things, called HMC, was slow and didn’t work well. The new way uses something called Stochastic Gradient Descent (SGD) to make it faster and better. MBPINN can solve different types of problems in 1D, 2D, or 3D spaces. It works really well and is a great step forward for using computers to help us understand the world. |
Keywords
» Artificial intelligence » Bayesian inference » Machine learning » Stochastic gradient descent
