5 papers · 1 filter
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…
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…
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…
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…