4 citations · 4 across the 5 of their papers we have counts for
6 papers
Cluster Attention Neural Operators for Solving Parametric Partial Differential Equations
Ming Zhong, Antonio Colanera, Gianluigi Rozza +1
Traditional simulations of parametric partial differential equations (PDEs) rely on repetitive computations for each parameter, which makes high-fidelity design impractical. Neural…
Efficient High-Accuracy PDEs Solver with the Linear Attention Neural Operator
Ming Zhong, Zhenya Yan
Neural operators offer a powerful data-driven framework for learning mappings between function spaces, in which the transformer-based neural operator architecture faces a fundament…
PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations
Jin Song, Kenji Kawaguchi, Zhenya Yan
Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. How…
Two-dimensional fractional discrete NLS equations: dispersion relations, rogue waves, fundamental and vortex solitons
Ming Zhong, Boris A. Malomed, Jin Song +1
We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing.…
Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning
Jin Song, Zhenya Yan
In this paper, we develop a systematic deep learning approach to solve two-dimensional (2D) stationary quantum droplets (QDs) and investigate their wave propagation in the 2D amend…
Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations
Jin Song, Ming Zhong, George Em Karniadakis +1
We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterati…