Special Session 130: Data driven approaches for complex physical systems

Proximal Optimal Transport Divergences and Stable Gradient Flows

Markos Katsoulakis UMass Amherst USA Co-Author(s):

Abstract: We introduce proximal optimal transport divergences that provide a unifying variational framework interpolating between classical f-divergences and Wasserstein metrics. From a gradient-flow perspective, these divergences generate stable and robust dynamics in probability space, enabling the learning of distributions with singular structure, including strange attractors, extreme events, and low-dimensional manifolds, with provable guarantees in sample size. We illustrate how this mathematical structure leads naturally to generative particle flows for reconstructing nonlinear cellular dynamics from snapshot single-cell RNA sequencing data, including real patient datasets, highlighting the role of proximal regularization in stabilizing learning and inference in high dimensions.

Structure-Preserving Construction of Collision Operators for Kinetic Equations from Molecular Dynamics

Huan Lei Michigan State University USA Co-Author(s):

Abstract: We introduce a data-driven approach to learn generalized collision operators from molecular dynamics. Unlike conventional models (e.g., Landau), the present operator takes a symmetry-breaking non-stationary form that depends not only on the relative velocity but also on the average velocity of the collision pair, capturing heterogeneous energy transfer arising from collective interactions with the environment. The constructed model strictly preserves the frame-indifference, conservation laws, and physical constraints such as the H-theorem. To enable efficient numerical evaluation, we develop a fast spectral separation method that represents the kernel as a low-rank tensor product of univariate basis functions. This formulation admits an O(N log N) algorithm and structure-preserving discretization. Numerical results demonstrate that the proposed model accurately captures plasma dynamics in the moderately coupled regime beyond the standard Landau model while maintaining high computational efficiency and structure-preserving properties.

Amortized approximation of probabilistic conditioning by neural operators

Nicholas H Nelsen Cornell University USA Co-Author(s):

Abstract: Probabilistic conditioning concerns the identification of the distribution of a random variable X given a random variable Y. It is a cornerstone of science and engineering applications where modeling uncertainty is key. This problem has traditionally been addressed in machine learning by directly learning the conditional distribution of a fixed joint distribution. Instead, this talk solves the conditioning problem by identifying a single operator that maps any joint density to its conditional, thus amortizing over joint-conditional pairs. The talk establishes that density-to-density conditioning can be approximated to arbitrary accuracy by neural operators. The proof relies on new stability estimates for the conditioning operator over suitable classes of densities. Numerical experiments that train neural operators to condition a class of Gaussian mixtures illustrate the promise of the new framework.

Blood pressure monitoring with biophysics-informed machine learning models

Braxton Osting Dept. Mathematics, University of Utah USA Co-Author(s):

Abstract: Measurement of blood pressure (BP) is essential for early diagnosis and management of hypertension, a condition that 45% of US adults have and a risk factor for development of heart failure, the leading cause of death in the US. Wearable technologies have the potential to transform BP monitoring by providing continuous assessments of cardiovascular health metrics and guiding clinical management. However, existing cuffless wearable devices for BP monitoring often rely on methods lacking theoretical foundations, such as pulse wave analysis or pulse arrival time, making them vulnerable to physiological and experimental confounders that undermine their accuracy and clinical utility. We developed a smartwatch device with real-time electrical bioimpedance (BioZ) sensing for cuffless hemodynamic monitoring. We elucidate the biophysical relationship between BioZ and BP via a multiscale analytical and computational modeling framework, and identify physiological, anatomical, and experimental parameters that influence the pulsatile BioZ signal at the wrist. A signal-tagged physics-informed neural network incorporating fluid dynamics principles enables calibration-free estimation of BP and radial and axial blood velocity. We successfully tested our approach with healthy individuals at rest and after physical activity including physical and autonomic challenges, and with patients with hypertension and cardiovascular disease in outpatient and intensive care settings. Our findings demonstrate the feasibility of BioZ technology for cuffless BP and blood velocity monitoring, addressing critical limitations of existing cuffless technologies.