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UID:submissions.pasc-conference.org_PASC24_sess153_msa106@linklings.com
SUMMARY:Low-Rank PINNs for Model Reduction of Nonlinear Hyperbolic Conserv
 ation Laws
DESCRIPTION:Minisymposium\n\nRandall LeVeque (University of Washington), D
 onsub Rim (Washington University in St. Louis), and Gerrit Welper (Univers
 ity of Central Florida)\n\nModel reduction for hyperbolic PDEs using class
 ical techniques is difficult due to the slow decay in the Kolmogorov n-wid
 th, making it necessary to explore new forms of approximation. We will dis
 cuss a new approach using deep neural networks endowed with a particular l
 ow-rank structure, which we call low-rank Physics-Informed Neural Networks
  (LR-PINNs). LR-PINNs are a form of implicit neural representation in whic
 h the weights and biases belong to linear spaces of small dimensions.  We 
 will show that entropy solutions to scalar conservation laws can be repres
 ented efficiently by such a representation.  Numerical examples illustrati
 ng the efficacy of the neural network will be shown, and we will also disc
 uss applications of LR-PINNs regarding the so-called failure modes of PINN
 s.\n\nDomain: Climate, Weather, and Earth Sciences, Engineering, Life Scie
 nces, Computational Methods and Applied Mathematics\n\nSession Chair: Robe
 rt Baraldi (Sandia National Laboratories)
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