Shape-Morphing Solutions for PDEs with Conserved Quantities|Mohammad Farazmand (NC State)|2025 CSRC
Автор: SDSU Computational Science Research Center
Загружено: 2025-11-14
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Computational Science Research Center - Fall 2025 Colloquium
Date of Talk - November 7, 2025
Speaker - Mohammad Farazmand, North Carolina State University
Title - Shape-Morphing Solutions for PDEs with Conserved Quantities
In this colloquium, Dr. Mohammad Farazmand discusses classical spectral methods for numerically solving PDEs assume the solution as the linear combination of prescribed basis functions (or modes). This assumption limits their efficacy for time-dependent multi-scale problems with localized time-varying features. I will first introduce the notion of Shape-Morphing Solutions (SMS), which allow the modes to change shape over time, in a predictable fashion, in order to automatically adapt to the true solution of the PDE. This allows the SMS to approximate the PDE's solution more economically. I will also discuss several attractive features of SMS: (i) It is also easy to enforce known conserved quantities of the PDE in the numerical solution. (ii) Classical Galerkin methods turn out to be a special case of SMS. (iii) Interpretation of SMS as a neural network with time-dependent weights and biases. (iv) Efficient reduced-order modeling with SMS. Finally, I demonstrate the application of SMS to several problems including rogue waves, vortex dynamics, and heat transfer.
Hosted by: Computational Science Research Center (CSRC), San Diego State University
Series: Fall 2025 Colloquium Talks
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