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X-WR-CALNAME:Biomedical Mathematics Group
X-ORIGINAL-URL:https://www.ibs.re.kr/bimag
X-WR-CALDESC:Events for Biomedical Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20221111T150000
DTEND;TZID=Asia/Seoul:20221111T170000
DTSTAMP:20260425T094952
CREATED:20221028T015855Z
LAST-MODIFIED:20221107T064232Z
UID:6740-1668178800-1668186000@www.ibs.re.kr
SUMMARY:PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations
DESCRIPTION:We will discuss about “PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations”\,\nZhong\, Weiheng\, and Hadi Meidani\, Computer Methods in Applied Mechanics and Engineering 403 (2023): 115664. \nAbstract\nWe propose a new class of physics-informed neural networks\, called the Physics-Informed Variational Auto-Encoder (PI-VAE)\, to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing equations are known but only a limited number of measurements of system parameters are available. PI-VAE consists of a variational autoencoder (VAE)\, which generates samples of system variables and parameters. This generative model is integrated with the governing equations. In this integration\, the derivatives of VAE outputs are readily calculated using automatic differentiation\, and used in the physics-based loss term. In this work\, the loss function is chosen to be the Maximum Mean Discrepancy (MMD) for improved performance\, and neural network parameters are updated iteratively using the stochastic gradient descent algorithm. We first test the proposed method on approximating stochastic processes. Then we study three types of problems related to SDEs: forward and inverse problems together with mixed problems where system parameters and solutions are simultaneously calculated. The satisfactory accuracy and efficiency of the proposed method are numerically demonstrated in comparison with physics-informed Wasserstein generative adversarial network (PI-WGAN).
URL:https://www.ibs.re.kr/bimag/event/2022-11-11-jc/
LOCATION:B378 Seminar room\, IBS\, 55 Expo-ro Yuseong-gu\, Daejeon\, 34126\, Korea\, Republic of
CATEGORIES:Journal Club
ORGANIZER;CN="Jae Kyoung Kim":MAILTO:jaekkim@kaist.ac.kr
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