6 papers
Asymptotic Preservation and Uniform Accuracy of Diffusion and Flow-Matching Samplers
Shiheng Zhang
Diffusion and Gaussian-interpolant flow-matching samplers approach data through a terminal noise floor , a singular limit for manifold-supported or rank-deficient data…
Guidance Breaks the Fitted Operator: A Terminal-Fitted Repair for Classifier-Free Guidance
Shiheng Zhang
Classifier-free guidance (CFG) is the standard way to strengthen class-conditioning in diffusion and flow-matching samplers, yet at large guidance it oversaturates and destabilizes…
Planner-Admissible Graph-PDE Value Extensions for Sparse Goal-Conditioned Planning
Shiheng Zhang
Sparse goal-conditioned planning with few cost-to-go labels can be viewed as a graph-PDE Dirichlet extension problem: extend sparse labels on a goal-dependent boundary to unlabelle…
Low-Rank Evolutionary Deep Neural Networks via Adaptive Tangent-Space Reduction
Jiahao Zhang, Shiheng Zhang, Guang Lin
Evolutionary deep neural networks (EDNNs) solve time-dependent partial differential equations by evolving the neural-network parameters sequentially in time through a local least-s…
SAV-based entropy-dissipative schemes for a class of kinetic equations
Shiheng Zhang, Jie Shen, Jingwei Hu
We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first a…
Structure preserving schemes for a class of Wasserstein gradient flows
Shiheng Zhang, Jie Shen
We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass, positivity and to be uni…