DGM: A deep learning algorithm for solving partial differential equations — mentioned by activatedgeek

Sun, 28 Mar 2021 02:50:13 GMT

And, guess what? Since, the Galerkin approximation requires one to choose a basis that is appropriate to the problem at hand, we now have a deep learning solution too (since neural network learning is essentially equivalent to learning an adaptive basis). It is called the Deep Galerkin Method [1]. In a nutshell, the method directly minimizes the L2 error over the PDE, boundary conditions and initial conditions. The integral is tricky though, and computed via a Monte Carlo approximation. [1]: https://arxiv.org/abs/1708.07469

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

DGM: A deep learning algorithm for solving partial differential equations — mentioned by syntaxing

Wed, 21 Oct 2020 19:15:58 GMT

Fun article to read but using incompressible flow as an assumption is extremely dangerous. The main effect of the assumption is that density does not change which is not the case for airfoils, particularly near the wake which usually ends up as P_0 (ambient pressure). It would be even more awesome if the author left NS in it's standard form and add the new deep learning PDE solvers [1]. [1]https://arxiv.org/abs/1708.07469

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

DGM: A deep learning algorithm for solving partial differential equations · HackerPapers discussions

DGM: A deep learning algorithm for solving partial differential equations — mentioned by activatedgeek

DGM: A deep learning algorithm for solving partial differential equations — mentioned by syntaxing