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
on classical methods such as Jacobi, Gauss-Seidel, conjugate gradient, multigrid methods
and their more advanced variants, there is still a pressing need to develop faster, more
robust and reliable solvers. Based on recent advances in scientific deep learning for
operator regression, we propose HINTS, a hybrid, iterative, numerical, and transferable …

Neural networks suffer from spectral bias and have difficulty representing the high-frequency
components of a function, whereas relaxation methods can resolve high frequencies
efficiently but stall at moderate to low frequencies. We exploit the weaknesses of the two
approaches by combining them synergistically to develop a fast numerical solver of partial
differential equations (PDEs) at scale. Specifically, we propose HINTS, a hybrid, iterative,
numerical and transferable solver by integrating a Deep Operator Network (DeepONet) with …