**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

Monday, February 6, 2023 10:00 AM EST

DC 2314

Phuong Dong Le | Applied Mathematics, University of Waterloo

Machine Learning Methods for Solving Partial Differential Equations

One of the fundamental problems in fields of science, physical phenomena and engineering is partial differential equations (PDE). Those are used to formulate problems of propagation of sound or heat, electrostatics, fluid flow and elasticity. 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. In the proposal, we review a recent literature in the field of deep learning methods to approximate solution for partial differential equations. We consider the proposed neural architecture in solving examples of elliptic and hyperbolic partial differential equations.an more responsibly administer antibiotics.

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**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 co-ordinated within the Office of Indigenous Relations.