5 papers
Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications
Youngkyu Lee, Alena KopaniÄáková, George Em Karniadakis
We introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed pre…
Leveraging Operator Learning to Accelerate Convergence of the Preconditioned Conjugate Gradient Method
Alena KopaniÄáková, Youngkyu Lee, George Em Karniadakis
We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equation…
Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization
Serge Gratton, Alena KopaniÄáková, Philippe Toint
Two OFFO (Objective-Function Free Optimization) noise tolerant algorithms are presented that handle bound constraints, inexact gradients and use second-order information when avail…
Data-Parallel Neural Network Training via Nonlinearly Preconditioned Trust-Region Method
Samuel A. Cruz AlegrÃa, Ken Trotti, Alena KopaniÄáková +1
Parallel training methods are increasingly relevant in machine learning (ML) due to the continuing growth in model and dataset sizes. We propose a variant of the Additively Precond…
The limitations of a standard phase-field model in reproducing jointing in sedimentary rock layers
Edoardo Pezzulli, Patrick Zulian, Alena KopaniÄáková +2
Geological applications of phase-field methods for fracture are notably scarce. This work conducts a numerical examination of the applicability of standard phase-field models in re…