Stochastic force inference via density estimation

TL;DR

This paper introduces a method to infer nonlinear force fields from low-resolution, cross-sectional data in biophysics by leveraging density estimation and score-matching, effectively handling noise and non-stationary conditions.

Contribution

It presents a novel approach combining density estimation and score-matching to infer diffusion-based force fields from limited biophysical data, accommodating various noise models.

Findings

Successfully extracts non-conservative forces from non-stationary data

Learns equilibrium dynamics from steady-state data

Handles both additive and multiplicative noise models

Abstract

Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We explore a common scenario in which we have access to an adequate amount of cross-sectional samples at a few time-points, and assume that our samples are generated from a latent diffusion process. We propose an approach that relies on the probability flow associated with an underlying diffusion process to infer an autonomous, nonlinear force field interpolating between the distributions. Given a prior on the noise model, we employ score-matching to differentiate the force field from the intrinsic noise. Using relevant biophysical examples, we demonstrate that our approach can extract non-conservative forces from non-stationary data, that it learns equilibrium dynamics when applied to steady-state data, and that it can do so with both additive and multiplicative noise models.