**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Wednesday, October 5, 2022 — 10:00 AM EDT

MC 6460

Phuong Dong Le | Applied Mathematics, University of Waterloo

Neural Network Architecture to Solve the Partial Differential Equations

Neural network models have shown a great potential in solving partial differential equations (PDE). Once trained with numerical simulation data, these models can provide faster alternative to traditional simulators and be efficient. However, they suffer from the generalization problem. There have been previous works that address the issue by applying universal approximation theorem for operator (DeepONet) using two sub-neural-networks. This approach has been generalized to neural network models that can learn mappings between function spaces. A recent work of neural operator (FNO) has been formulated as a new method by parameterizing the integral kernel into a Fourier space. We perform experiments on inviscid Burgers' equation and Darcy flow on proposed neural network operator architectures. Our preliminary results showed that they can achieve an error rate up to 0.0024 on Darcy's flow.

Event tags

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.