6 citations · 6 across the 8 of their papers we have counts for
5 papers · 1 filter
From Basis to Basis: Gaussian Particle Representation for Interpretable PDE Operators
Zhihao Li, Yu Feng, Zhilu Lai +1
Learning PDE dynamics for fluids increasingly relies on neural operators and Transformer-based models, yet these approaches often lack interpretability and struggle with localized,…
Structure-Aware Epistemic Uncertainty Quantification for Neural Operator PDE Surrogates
Haoze Song, Zhihao Li, Mengyi Deng +4
Neural operators (NOs) provide fast, resolution-invariant surrogates for mapping input fields to PDE solution fields, but their predictions can exhibit significant epistemic uncert…
Reformulating Neural Operators in Dimensions for Embedding Evolution
Haoze Song, Zhihao Li, Xiaobo Zhang +3
Neural Operators (NOs) are powerful architectures for learning mappings between function spaces. While most advances focus on refining kernel parameterizations over the -dimensi…
Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries
Zhihao Li, Haoze Song, Di Xiao +2
Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geom…
M2NO: An Efficient Multi-Resolution Operator Framework for Dynamic Multi-Scale PDE Solvers
Zhihao Li, Zhilu Lai, Xiaobo Zhang +1
Solving high-dimensional partial differential equations (PDEs) efficiently requires handling multi-scale features across varying resolutions. To address this challenge, we present…