6 papers
Simulation-Free Learning of Population Dynamics with Wasserstein Lagrangian Residuals
Fedor Sergeev, Markus Heinonen, Daniel Waxman +4
The dynamics of cells, organisms, and fluids are often modeled as probability distributions evolving over time. Reconstructing and extrapolating this evolution from unpaired snapsh…
Wasserstein Residuals: Learning Gradient Flows from Population Dynamics
Markus Heinonen, Yair Shenfeld, Ricardo Baptista +4
Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distribu…
Dynestyx: A Probabilistic Programming Library for Dynamical Systems
Daniel Waxman, Dmitry Batenkov, John Feser +4
State-space models (SSMs) are the standard formalism for Bayesian treatment of dynamical systems, with natural applications in statistics, signal processing, and machine learning.…
Separation-free exponential fitting with structured noise, with applications to inverse problems in parabolic PDEs
Rami Katz, Dmitry Batenkov, Giulia Giordano
We investigate the recovery of exponents and amplitudes of an exponential sum, where the exponents are the first eigenvalues of a Sturm-Liou…
Spectral Properties of Infinitely Smooth Kernel Matrices in the Single Cluster Limit, with Applications to Multivariate Super-Resolution
Nuha Diab, Dmitry Batenkov
We study the spectral properties of infinitely smooth multivariate kernel matrices when the nodes form a single cluster. We show that the geometry of the nodes plays an important r…
Data-driven identification of reaction-diffusion dynamics from finitely many non-local noisy measurements by exponential fitting
Rami Katz, Giulia Giordano, Dmitry Batenkov
Given a reaction-diffusion equation with unknown right-hand side, we consider a nonlinear inverse problem of estimating the associated leading eigenvalues and initial condition mod…