Summary of Score-based Physics-informed Neural Networks For High-dimensional Fokker-planck Equations, by Zheyuan Hu et al.
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
by Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi
First submitted to arxiv on: 12 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Dynamical Systems (math.DS); Numerical Analysis (math.NA); Machine Learning (stat.ML)
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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 tackles the curse of dimensionality in Fokker-Planck equations by utilizing a novel score-based solver. This approach models the logarithm likelihood via Physics-Informed Neural Networks (PINNs), transforming the equation into a challenging HJB problem. The solution is achieved through three fitting methods: Score Matching, Sliced SM, and Score-PINN. Comparative evaluations highlight varying trade-offs among these methods. The proposed method demonstrates stability, speed, and performance across different scenarios, showcasing its potential as a solution to CoD for high-dimensional FP equations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A team of researchers has developed a new way to solve complex math problems related to Brownian motion. They used artificial intelligence (AI) techniques to create a model that can handle very high dimensions, which is important because many real-world phenomena involve many variables. The traditional methods for solving these types of problems are not accurate enough, so the team created three different approaches to improve accuracy. Their method uses something called a “score function” to solve the problem, and it’s much faster than previous methods. |
Keywords
* Artificial intelligence * Likelihood
