Convolutional Neural Networks (CNNs) for Physics Constrained PDEs

Relevant Research:

Chiyu "Max" Jiang, Karthik Kashinath, Prabhat, Philip S. Marcus (2020) Enforcing Physical Constraints in CNNs through Differentiable PDE Layer, ICLR 2020 Workshop on Integration of Deep Neural Models and Differential Equations, pdf

Chiyu "Max" Jiang, Dequan Wang, Jingwei Huang, Philip S. Marcus, Matthias Nießner (2018) Convolutional Neural Networks on Non-uniform Geometrical Signals Using Euclidean Spectral Transformation, International Conference on Learning Representations, pdf

Sahuck Oh, Chung-Hsiang Jiang, Chiyu "Max" Jiang, Philip S. Marcus (2018) Finding the optimal shape of the leading-and-trailing car of a high-speed train using design-by-morphing, Computational Mechanics 62(1), p. 23-45, pdf, doi:10.1007/s00466-017-1482-4

Abstracts

Karthik Kashinath, Chiyu "Max" Jiang, Gavin E. Jergensen, Prabhat, Philip S. Marcus (2019) Neural Network Optimization Under Partial Differential Equation Constraints, APS Division of Fluid Dynamics Meeting Abstracts, p. C17–008, url

Dana Lansigan, Chiyu "Max" Jiang, Philip S. Marcus (2018) Neural Network Powered Adjoint Methods-Gradient Based Shape Optimization with Deep Learning, APS Division of Fluid Dynamics Meeting Abstracts 63, p. F32-002, url

Chiyu "Max" Jiang, Karthik Kashinath, Philip S. Marcus, Prabhat (2018) Bridging simulation and deep learning-convolutional neural networks on unstructured grids, APS Division of Fluid Dynamics Meeting Abstracts 63, p. F32-005, url

Chiyu "Max" Jiang, Karthik Kashinath, Mayur Mudigonda, Ankur Mahesh, Travis Allen O'Brien, Philip S. Marcus, Prabhat (2018) Deep learning on the Sphere: Convolutional Neural Network on Unstructured Mesh, AGU Fall Meeting Abstracts 2018, p. IN33A–01, url