51 citations · 99 across the 23 of their papers we have counts for
8 papers · 1 filter
PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations
Zhanhong Ye, Zining Liu, Bingyang Wu +7
Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiab…
MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation
Qi Wang, Yuan Mi, Haoyun Wang +5
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are req…
PCNet: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics
Qi Wang, Pu Ren, Hao Zhou +10
When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergenc…
PDEformer-1: A Foundation Model for One-Dimensional Partial Differential Equations
Zhanhong Ye, Xiang Huang, Leheng Chen +5
This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a compu…
PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations
Zhanhong Ye, Xiang Huang, Leheng Chen +3
This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the P…
Analysis of the Decoder Width for Parametric Partial Differential Equations
Zhanhong Ye, Hongsheng Liu, Zidong Wang +1
Recently, Meta-Auto-Decoder (MAD) was proposed as a novel reduced order model (ROM) for solving parametric partial differential equations (PDEs), and the best possible performance…
Solving Boltzmann equation with neural sparse representation
Zhengyi Li, Yanli Wang, Hongsheng Liu +2
We consider the neural sparse representation to solve Boltzmann equation with BGK and quadratic collision model, where a network-based ansatz that can approximate the distribution…
Meta-Auto-Decoder: A Meta-Learning Based Reduced Order Model for Solving Parametric Partial Differential Equations
Zhanhong Ye, Xiang Huang, Hongsheng Liu +1
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, bo…