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UID:submissions.supercomputing.org_SC23_sess291_rpost200@linklings.com
SUMMARY:Neural Domain Decomposition for Variable Coefficient Poisson Solve
 rs
DESCRIPTION:Sebastian Barschkis and Zitong Li (University of California, I
 rvine); Hengjie Wang (Modular Inc); and Aparna Chandramowlishwaran (Univer
 sity of California, Irvine)\n\nThe computational bottleneck in many fluid 
 simulations arises from solving the variable coefficient Poisson equation.
  To tackle this challenge, we propose a novel neural domain decomposition 
 algorithm to accelerate its solution. Our approach hinges on two key ideas
 : first, using neural PDE solvers to approximate the solutions within subd
 omains, and second, ensuring continuity across subdomain boundaries by sol
 ving a Schur complement system derived from the cell-centered discretized 
 Poisson equation. A distinct advantage of our approach lies in generating 
 a large dataset consisting only of small-scale problems to train the subdo
 main solver. This trained model can subsequently be applied to problems wi
 th large and complex geometries. Moreover, by batching the independent sub
 domain solves, we achieve high GPU utilization with neural solvers compare
 d to state-of-the-art numerical methods. In contrast to neural domain deco
 mposition algorithms that rely on Schwarz overlapping methods, our optimiz
 ation-based approach, coupled with neural PDE solvers, improves accuracy a
 nd performance.\n\nTag: Artificial Intelligence/Machine Learning, Architec
 ture and Networks, Heterogeneous Computing, I/O and File Systems, Performa
 nce Measurement, Modeling, and Tools, Post-Moore Computing, Programming Fr
 ameworks and System Software, Quantum Computing\n\nRegistration Category: 
 Tech Program Reg Pass, Exhibits Reg Pass\n\n
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