Author

Ze-Cheng Zhang

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Preprint Oct 2026

Numerical Neural Operator: Connection Between Numerical Analysis and the Operator Learning and Building Discretized Neural Operators from Finite Element Methods

Operator learning aims to learn mappings between function spaces and has been widely used for PDE-related problems. This raises two fundamental questions. First, is there a connection between standard numerical methods and neural operators, given that both are designed to approximate PDE solution operators? Second, whe...

Ze-Cheng Zhang · 0 citations

Controllable and Constrained Sampling in Diffusion Models via Initial Noise Perturbation

This work observes an interesting phenomenon: the relationship between the change of generation outputs and the scale of initial noise perturbation is highly linear through the diffusion ODE sampling, and proposes a novel C ontrollable and C onstrained S ampling ( CCS) method, along with a new controller algorithm for...

Bo-Wen Song, Ze-Cheng Zhang, Zhaoxu Luo et al. · 0 citations