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arXiv · 2505.13197

Inferring stochastic dynamics with growth from cross-sectional data

Stephen Zhang·Suryanarayana Maddu·Xiaojie Qiu·Victor Chardès
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Abstract

Time-resolved single-cell omics data offers high-throughput, genome-wide measurements of cellular states, which are instrumental to reverse-engineer the processes underpinning cell fate. Such technologies are inherently destructive, allowing only cross-sectional measurements of the underlying stochastic dynamical system. Furthermore, cells may divide or die in addition to changing their molecular state. Collectively these present a major challenge to inferring realistic biophysical models. We present a novel approach, unbalanced probability flow inference, that addresses this challenge for biological processes modelled as stochastic dynamics with growth. By leveraging a Lagrangian formulation of the Fokker-Planck equation, our method accurately disentangles drift from intrinsic noise and growth. We showcase the applicability of our approach through evaluation on a range of simulated and real single-cell RNA-seq datasets. Comparing to several existing methods, we find our method achieves higher accuracy while enjoying a simple two-step training scheme.

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Stephen Zhang, Suryanarayana Maddu, Xiaojie Qiu, Victor Chardès. 2025-05-19. Inferring stochastic dynamics with growth from cross-sectional data. https://arxiv.org/abs/2505.13197

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