Neural networks suffer from spectral bias and have difficulty representing the high-frequency
components of a function, whereas relaxation methods can resolve high frequencies …

Accurate hydrological understanding and water cycle prediction are crucial for addressing
scientific and societal challenges associated with the management of water resources …

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful
information from multiple tasks to improve generalization performance compared to single …

Iterative solvers of linear systems are a key component for the numerical solutions of partial
differential equations (PDEs). While there have been intensive studies through past decades …

Abstract We present Basis-to-Basis (B2B) operator learning, a novel approach for learning
operators on Hilbert spaces of functions based on the foundational ideas of function …

Current groundwater models face significant challenges in their implementation due to
heavy computational burdens. To overcome this, our work proposes a cost-effective …

We extend a recently proposed machine-learning-based iterative solver, ie the hybrid
iterative transferable solver (HINTS), to solve the scattering problem described by the …

We propose machine learning (ML) based smart interpolation functions to enhance the finite
element computation (named as smart-I finite element) for the heterogeneous structures (eg …

Big data is transforming scientific progress by enabling the discovery of novel models,
enhancing existing frameworks, and facilitating precise uncertainty quantification, while …

We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing
PDEs by combining neural operators with either simple iterative solvers, eg, Jacobi and …