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Tea time:15:30, Room 707
Abstract:
Neural networks have emerged as powerful tools for solving partial differential equations (PDEs) numerically. Traditional numerical methods for solving PDEs, such as finite difference, finite element, or spectral methods, can be computationally expensive and may require considerable expertise to implement. In contrast, neural networks can be trained to approximate the solution to a PDE directly from input data, making them potentially faster and more accessible.
In this talk, we will introduce a machine learning methodology based on neural networks to solve PDEs. We will discuss our recent work on solving elliptic interface problems using neural network methods. Specifically, we will introduce a topology enforcement layer in the network to enforce the underlying topology of the problem. This makes it possible to represent discontinuous functions and solve problems on periodic domains more efficiently by including appropriate units in the layer. The topology enforcement layer provides a new approach to solving such problems compared to traditional neural networks, which may struggle to represent discontinuous functions and may not have built-in periodicity.
2023-03-20 15:00 ~ 2023-03-20 16:00
林得勝 教授 (陽交大應數系)
第三綜合大樓2F 201