Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations · HackerPapers discussions

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations — mentioned by GistNoesis

Wed, 08 May 2024 17:51:40 GMT

The frontier in model space is kind of fluid. It's all about solving differential equations. In theoretical physics, you know the equations, you solve equations analytically, but you can only do that when the model is simple. In numerical physics, you know the equations, you discretize the problem on a grid, and you solve the constraint defined by the equations with various numerical integration schemes like RK4, but you can only do that when the model is small and you know the equations, and you find a single solution. Then you want the result faster, so you use mesh-free methods and…

Paper and discussion history. A mention is not an endorsement.

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations — mentioned by peter_d_sherman

Wed, 20 Dec 2023 05:05:06 GMT

Paper: "Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations" (by Maziar Raissi, Paris Perdikaris, and George Em Karniadakis) https://arxiv.org/abs/1711.10561 https://arxiv.org/pdf/1711.10561.pdf >"The resulting neural networks form a new class of data-efficient universal function approximators that naturally encode any underlying physical laws as prior information." Also: >"In this first part, we demonstrate how these networks can be used to infer solutions to partial differential equations" This is some seriously, seriously impressive…

Paper and discussion history. A mention is not an endorsement.

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations — mentioned by phonebucket

Tue, 24 Jan 2023 15:29:18 GMT

A lot depends on what you're interested in. Some papers that are runnable on a laptop CPU (so long as you stick to small image sizes/tasks): 1) Generative Adversarial Networks (https://arxiv.org/abs/1406.2661). Good practice to have a custom training loops, different optimisers and networks etc. 2) Neural Style Transfer (https://arxiv.org/abs/1508.06576). Nice to be able to manipulate pretrained networks and intercept intermediate layers. 3) Deep Image Prior (https://arxiv.org/abs/1711.10925). Nice low-data exercise in building out an autoencoder. 4) Physics Informed Neural Networks…

Paper and discussion history. A mention is not an endorsement.