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math.OC2025
A PDE Perspective on Generative Diffusion Models
Kang Liu, Enrique Zuazua
Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains. Despite their empirical success, their mat…
cs.LG2025
Deep Neural ODE Operator Networks for PDEs
Ziqian Li, Kang Liu, Yongcun Song +2
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often o…
math.NA2025
Moments, Time-Inversion and Source Identification for the Heat Equation
Kang Liu, Enrique Zuazua
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical T…