Operator learning trains a neural network to map functions to functions. An ideal operator
learning framework should be mesh-free in the sense that the training does not require a …

For the nonlinear Richards equation as an unsaturated flow through heterogeneous media,
we build a new coarse-scale approximation algorithm utilizing numerical homogenization …

The limitations of prohibitive computation and Frequency Principle remain difficult for deep
learning methods to effectively resolve multi-scale problems. In this work, a novel higher …

We present a new framework for computing fine-scale solutions of multiscale partial
differential equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of …

Operator learning trains a neural network to map functions to functions. An ideal operator
learning framework should be mesh-free in the sense that the training does not require a …

In this paper, we propose a new mathematical model of language interactions considering
bilingualism. We assume diffusive and convective language spreads with language …

We develop a new coarse-scale approximation strategy for the nonlinear single-continuum
Richards equation as an unsaturated flow over heterogeneous non-periodic media, using …

In this work, we propose a partial learning approach using partially explicit discretization for
solving the wave equations. The considered mathematical model involves a dual-continuum …

Multi-physics are widely studied and used in numerical analysis and simulation. Physics-
based splitting methods are introduced, in which different methods are applied to solve each …

In this paper, we propose Meshfree Generalized Multiscale Finite Element Method with a
partially explicit time scheme for solving the nonlinear Stefan problem with high-contrast …