Summary of Separable Deeponet: Breaking the Curse Of Dimensionality in Physics-informed Machine Learning, by Luis Mandl et al.
Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning
by Luis Mandl, Somdatta Goswami, Lena Lambers, Tim Ricken
First submitted to arxiv on: 21 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 deep operator network (DeepONet) is a neural architecture that shows promise in solving partial differential equations (PDEs). Without labeled datasets, it uses the PDE residual loss to learn physical systems. However, this approach faces computational challenges due to the curse of dimensionality. To address these issues, we introduce the Separable DeepONet framework, which factorizes sub-networks for individual one-dimensional coordinates. This reduces forward passes and Jacobian matrix size, optimizing computational cost with forward-mode automatic differentiation. The separable architecture achieves linear scaling with discretization density, making it suitable for high-dimensional PDEs. We validate this framework through three benchmark PDE models: viscous Burgers equation, Biot’s consolidation theory, and a parametrized heat equation. Separable DeepONet achieves comparable or improved accuracy while reducing computational time compared to conventional DeepONet. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The deep operator network (DeepONet) is a way that computers can solve complex math problems called partial differential equations (PDEs). Usually, these computers need labeled data, but sometimes they don’t. To help them learn anyway, scientists use the leftover math problems to figure out how things work. However, this approach gets really slow and hard when dealing with lots of numbers. To fix this problem, researchers came up with a new way to break down the math problems into smaller pieces that computers can handle more easily. This makes it possible for computers to solve these complex math problems quickly and accurately. |
