Summary of Constrained or Unconstrained? Neural-network-based Equation Discovery From Data, by Grant Norman et al.
Constrained or Unconstrained? Neural-Network-Based Equation Discovery from Data
by Grant Norman, Jacqueline Wentz, Hemanth Kolla, Kurt Maute, Alireza Doostan
First submitted to arxiv on: 30 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 uses a constrained optimization strategy to discover ordinary and partial differential equations (PDEs) from noisy observations of state variables. This approach represents the PDE as a neural network and solves a constrained optimization problem that promotes matching the data while enforcing the PDE constraints at spatial collocation points. The authors compare two penalty methods, a widely used trust-region barrier method, and demonstrate that the latter outperforms the penalty method on numerical examples of Burgers’ and Korteweg-De Vreis equations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper uses a new way to find differential equations from noisy data. It’s like solving a puzzle! The method represents the equation as a special kind of neural network, then tries to find the right solution by making sure it matches the data and follows the rules of the equation. Two different ways of doing this are tested on some examples, and one way is better than the other. |
Keywords
» Artificial intelligence » Neural network » Optimization
