Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications
This work addresses training efficiency for scientific machine learning applications, offering an incremental improvement through a novel preconditioner design.
The paper tackles the slow training of scientific machine learning models by introducing a two-level overlapping additive Schwarz preconditioner, which significantly speeds up convergence and yields more accurate models in experiments with physics-informed neural networks and operator learning.
We introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinear two-level overlapping additive Schwarz preconditioner. The neural network parameters are decomposed into groups (subdomains) with overlapping regions. In addition, the network's feed-forward structure is indirectly imposed through a novel subdomain-wise synchronization strategy and a coarse-level training step. Through a series of numerical experiments, which consider physics-informed neural networks and operator learning approaches, we demonstrate that the proposed two-level preconditioner significantly speeds up the convergence of the standard (LBFGS) optimizer while also yielding more accurate machine learning models. Moreover, the devised preconditioner is designed to take advantage of model-parallel computations, which can further reduce the training time.