Abstract
Learning population dynamics from unpaired temporal marginals is an ill-posed inverse problem that requires structural assumptions on the underlying dynamics. We introduce $\textit{Discrete Action Matching}$ (DAM), a finite-state counterpart of Action Matching based on discrete Wasserstein geometry. For a prescribed marginal path and transport geometry, we derive an action-minimization objective for its canonical minimum-kinetic-energy current. Our key observation is that the density dependence of the discrete action reduces to neighboring density ratios. Along an empirical interpolation of the snapshots, DAM first estimates these ratios and then learns an action potential. The learned fields also define a graph-supported Markov sampler. Experiments on controlled synthetic dynamics and real mouse gastrulation data evaluate marginal reconstruction and interpolation. Additional experiments approximate numerical surface-transport paths from paired samples.
Keywords
Publication details
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Cite this article
APA 7
Persiianov, M., & Korotin, A. (2026). Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs. https://omanscience.com/en/articles/discrete-action-matching-learning-stochastic-dynamics-from-samples-via-state-graphs
MLA 9
Persiianov, Mikhail, and Alexander Korotin. "Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs." https://omanscience.com/en/articles/discrete-action-matching-learning-stochastic-dynamics-from-samples-via-state-graphs.
Chicago (author–date)
Persiianov, Mikhail, and Alexander Korotin. 2026. "Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs." https://omanscience.com/en/articles/discrete-action-matching-learning-stochastic-dynamics-from-samples-via-state-graphs.
Harvard
Persiianov, M. and Korotin, A. (2026) 'Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs', Available at: https://omanscience.com/en/articles/discrete-action-matching-learning-stochastic-dynamics-from-samples-via-state-graphs.
Vancouver
Persiianov M, Korotin A. Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs. https://omanscience.com/en/articles/discrete-action-matching-learning-stochastic-dynamics-from-samples-via-state-graphs
IEEE
M. Persiianov, and A. Korotin, "Discrete Action Matching: Learning Stochastic Dynamics from Samples via State Graphs," https://omanscience.com/en/articles/discrete-action-matching-learning-stochastic-dynamics-from-samples-via-state-graphs.