Author

Jian-Feng Liu

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#artificial intelligence Preprint Sep 2026

From Distributions to Stochastic Processes: Neural Approximation of Measure-Valued Maps

Learning mappings between probability distributions arises naturally when inputs and outputs are represented by populations of samples rather than individual observations. We develop an approximation-theoretic framework for distribution-to-distribution learning and extend it to mappings between stochastic processes. Fo...

Yi-Chen Wang, Zi-Yi Wang, Wen-Lian Lu et al. · 0 citations

Jul 2026

Freeze, Then Select: Structured Field Adapters and Stability-Validated Weak Selection for PDE Discovery from Sparse Observations

PDE discovery from sparse observations requires reconstructing a continuous field and selecting the correct differential terms. Our analysis of optimization paths in coupled neural PDE discovery reveals three behaviors: the exact support can persist to the end of training, appear only transiently, or fail to emerge. To...

Juncheng Zhong, Chen Shen, Jian-Feng Liu et al. · arXiv.org · 0 citations