Stochastic force inference via density estimation
This addresses the problem of separating molecular programs from noise in transcriptomics for biophysicists, representing an incremental improvement in force inference techniques.
The paper tackled the challenge of inferring dynamical models from low-resolution temporal data in biophysics by proposing a method that uses probability flow and score-matching to infer nonlinear force fields from cross-sectional samples, demonstrating its ability to extract non-conservative forces and handle various noise models in biophysical examples.
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.