Neural Preconditioners

Neural preconditioners leverage machine learning, particularly graph neural networks (GNNs) and convolutional neural networks (CNNs), to accelerate the solution of large, sparse linear systems—a ubiquitous computational bottleneck in scientific computing. Research focuses on designing efficient neural network architectures, often integrated with established methods like multigrid, to create preconditioners that are both fast and generalize well across diverse problem instances and scales. These advancements promise significant improvements in the efficiency of solving large-scale problems arising in fields such as physics simulations, seismic imaging, and quantum field theory, ultimately enabling more complex and computationally intensive scientific investigations.