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UID:submissions.pasc-conference.org_PASC24_sess180_pap126@linklings.com
SUMMARY:PETScML: Second-Order Solvers for Training Regression Problems in 
 Scientific Machine Learning
DESCRIPTION:Paper\n\nStefano Zampini (King Abdullah University of Science 
 and Technology), Umberto Zerbinati (University of Oxford), and George Turk
 yyiah and David Keyes (King Abdullah University of Science and Technology)
 \n\nIn recent years, we have witnessed the emergence of scientific machine
  learning as a data-driven tool for the analysis, by means of deep-learnin
 g techniques, of data produced by computational science and engineering ap
 plications. <br /> At the core of these methods is the supervised training
  algorithm to learn the neural network realization, a highly non-convex op
 timization problem that is usually solved using stochastic gradient method
 s. However, distinct from deep-learning practice, scientific machine-learn
 ing training problems feature a much larger volume of smooth data and bett
 er characterizations of the empirical risk functions, which make them suit
 ed for conventional solvers for unconstrained optimization. <br /> We intr
 oduce a lightweight software framework built on top of the Portable and Ex
 tensible Toolkit for Scientific computation to bridge the gap between deep
 -learning software and conventional solvers for unconstrained minimization
 . <br /> We empirically demonstrate the superior efficacy of a trust regio
 n method based on the Gauss-Newton approximation of the Hessian in improvi
 ng the generalization errors arising from regression tasks when learning s
 urrogate models for a wide range of scientific machine-learning techniques
  and test cases. All the conventional second-order solvers tested, includi
 ng L-BFGS and inexact Newton with line-search, compare favorably, either i
 n terms of cost or accuracy, with the adaptive first-order methods used to
  validate the surrogate models.\n\nDomain: Computational Methods and Appli
 ed Mathematics\n\nSession Chair: Luca Muscarnera (Politecnico di Milano)
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