Inferring stochastic dynamics with growth from cross-sectional data

2025-05-19

AI Summary

In single-cell omics, reconstructing molecular dynamics from static cross-sectional data is confounded by cell proliferation and death, which distort inferred temporal trajectories. Method: We propose a novel non-equilibrium probabilistic flow inference framework that, for the first time under a Lagrangian formulation, decouples drift, intrinsic noise, and growth effects. It constructs a variational objective grounded in the Fokker–Planck equation and employs a two-stage optimization strategy coupled with multi-scale validation integrating simulations and experimental data. Results: Evaluated on multiple synthetic and real scRNA-seq datasets, our method achieves superior dynamical reconstruction accuracy, enhanced model interpretability, and more concise, robust training compared to state-of-the-art approaches. It provides the first systematic solution for reverse-engineering stochastic biophysical processes—including proliferation and apoptosis—from static snapshots.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Data transparency and provenance

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, emph{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.

Problem

• Infer stochastic dynamics with growth from cross-sectional data
• Disentangle drift, intrinsic noise, and growth in biological processes
• Improve accuracy in modeling single-cell RNA-seq datasets

Innovation

• Unbalanced probability flow inference for stochastic dynamics
• Lagrangian formulation of Fokker-Planck equation
• Disentangles drift, intrinsic noise, and growth