ICLR 2022 | GNN | MESSAGE PASSING NEURAL PDE SOLVERS 作者分享视频（带字幕）
https://www.youtube.com/watch?v=rmQ9TvI-gRk
ICLR2022文章《MESSAGE PASSING NEURAL PDE SOLVERS 》作者 Johannes Brandstetter, Daniel Worrall, Max Welling 的分享。本号PaperShare (微信公众号同名) 已取得LoGaG group的转载许可，从bilibili上的任何转载请与本人联系。
Abstract: The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, discretization, etc. in 1D and 2D. Our model outperforms state-of-the-art numerical solvers in the low resolution regime in terms of speed and accuracy.
- 字幕制作者（English(US)）：PaperShare
【B站AI论坛】欢迎写代码、做产品的AI开发者发帖加入
共建AI开发者交流地>>
顶部