arXiv Machine Learning

Modeling Stochastic Conditional Dynamics from Sparse Observations via Kernel-Stabilized Flow Matching

arXiv:2411. 08314v5 Announce Type: replace Abstract: Learning to transform conditional probability densities over time is a fundamental challenge spanning probabilistic modeling and the natural sciences.

arXiv Machine Learning
Jun 16

Graphical conditional generative modeling for digital twin modeling

arXiv:2606. 16219v1 Announce Type: cross Abstract: Digital twin modeling, including control and data assimilation under model uncertainty, often faces an open-ended fidelity problem: adding variables, data streams, and time scales can indefinitely increase model complexity, ultimately producing systems that are difficult to maintain, validate, interpret, and use for stress or safety testing.

By Zongren Zou, Th\'eo Bourdais, Ricardo Baptista, Houman Owhadi
arXiv Machine Learning
Jun 18

Generative models for decision-making under distributional shift

arXiv:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.

By Xiuyuan Cheng, Yunqin Zhu, Yao Xie
arXiv Machine Learning
Jun 30

Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences

arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.

By Ziyu Chen, Markos A. Katsoulakis, Benjamin J. Zhang