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UID:submissions.supercomputing.org_SC25_sess620_post142@linklings.com
SUMMARY:Fast Linear Solvers via AI-Tuned Markov Chain Monte Carlo-Based Ma
 trix Inversion
DESCRIPTION:Anton Lebedev and Won Kyung Lee (STFC Hartree Centre); Soumyad
 ip Ghosh (IBM Thomas J. Watson Research Center); Olha I. Yaman (STFC Hartr
 ee Centre); Vassilis Kalantzis, Yingdong Lu, Tomasz Nowicki, Shashanka Uba
 ru, and Lior Horesh (IBM Thomas J. Watson Research Center); and Vassil Ale
 xandrov (STFC Hartree Centre)\n\nLarge, sparse linear systems are pervasiv
 e in modern science and engineering, and Krylov subspace solvers are an es
 tablished means of solving them. Yet convergence can be slow for ill-condi
 tioned matrices, so practical deployments usually require preconditioners.
  Markov chain Monte Carlo (MCMC)-based inversion can generate such precond
 itioners and accelerate Krylov iterations, but its effectiveness depends o
 n parameters whose optima vary across matrices; manual or grid search is c
 ostly. We present an AI-driven framework recommending MCMC parameters for 
 a given linear system. A graph neural surrogate predicts preconditioning s
 peed from A and MCMC parameters. A Bayesian acquisition function then choo
 ses the parameter sets most likely to minimize iterations. On a previously
  unseen ill-conditioned system, the framework achieves better precondition
 ing with 50% of the search budget of conventional methods, yielding about 
 a 10% reduction in iterations to convergence. These results suggest a rout
 e for incorporating MCMC-based preconditioners into large-scale systems.\n
 \nTag: Research & ACM SRC Posters\n\nRegistration Category: Technical Prog
 ram Reg Pass\n\nSession Chairs: Kento Sato (RIKEN Center for Computational
  Science (R-CCS)); Anja Gerbes (Georg-August-Universität Göttingen); and C
 hris Schlipalius (Pawsey Supercomputing Research Centre; Commonwealth Scie
 ntific and Industrial Research Organisation (CSIRO), Australia)\n\n
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