MINDS Seminar Series | Kookjin Lee (Arizona state university) - Solving Parameterized PDEs with Low-rank Structured Physics-Informed Neural Networks

MINDS SEMINAR

period : 2024-07-08 ~ 2024-07-08

time : 14:00:00 ~ 15:30:00

개최 장소 : Math Bldg 402 & Online streaming (Zoom)

Topic : Solving Parameterized PDEs with Low-rank Structured Physics-Informed Neural Networks

개요

Date	2024-07-08 ~ 2024-07-08	Time	14:00:00 ~ 15:30:00
Speaker	Kookjin Lee	Affiliation	Arizona state university
Place	Math Bldg 402 & Online streaming (Zoom)	Streaming link	ID : 688 896 1076 / PW : 54321
Topic	Solving Parameterized PDEs with Low-rank Structured Physics-Informed Neural Networks
Contents	In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design parameters) and solvers are required to perform rapid execution. In this study, we suggest a path that potentially opens up a possibility for physics-informed neural networks (PINNs), emerging deep-learning-based solvers, to be considered as one such solver. Although PINNs have pioneered a proper integration of deep-learning and scientific computing, they require repetitive time-consuming training of neural networks, which is not suitable for many-query scenarios. To address this issue, we propose lightweight low-rank PINNs containing only hundreds of model parameters and an associated hypernetwork-based meta-learning algorithm, which allow efficient solution approximations for varying PDE input parameters. Moreover, we show that the proposed method is effective in overcoming a challenging issue, known as “failure modes” of PINNs.

MinDS · 2024-07-02 11:19 · Views 867

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