Discovering and decoding latent mean-field structure with variational autoencoders

Generative models are increasingly used to capture correlations in many-body systems, but the representations they learn remain largely opaque to physical interpretation. Here, we establish an intuitive criterion that quantifies the capacity of a variational autoencoder (VAE) to faithfully reconstruct the joint probability distribution of a many body system. In a nutshell, a bound on the VAE capacity is obtained by comparing the rate of the latent channel to the bipartite mutual information of the data. Using this bound, we show that the conditionally independent decoder of any successful VAE is structurally identical to a finite-size mean-field factorization. Hence, a successful reconstruction is direct evidence for a latent mean-field theory and the microscopic parameters of that theory can be read off the trained decoder. We validate these conclusions on a hierarchy of solvable models with scalar (Curie-Weiss), vector (Hopfield) and tensor (Maier-Saupe) order parameters, recovering the full Hopfield pattern matrix from equilibrium samples alone. We find that, when applied to Salamander retinal recordings, a two-latent VAE reproduces the population statistics with only two effective collective variables allowing us to recover the `stored patterns' of the neural population and write a generalized Hopfield model which correctly models the experimental data.

Learning noisy tissue dynamics across time scales

Tissue dynamics play a crucial role in biological processes ranging from wound healing to morphogenesis. However, these noisy multicellular dynamics are notoriously hard to predict. Here, we introduce a biomimetic machine learning framework capable of inferring noisy multicellular dynamics directly from experimental movies. This generative model combines graph neural networks, normalizing flows and WaveNet algorithms to represent tissues as neural stochastic differential equations where cells are edges of an evolving graph. This machine learning architecture reflects the architecture of the underlying biological tissues, substantially reducing the amount of data needed to train it compared to convolutional or fully-connected neural networks. Taking epithelial tissue experiments as a case study, we show that our model not only captures stochastic cell motion but also predicts the evolution of cell states in their division cycle. Finally, we demonstrate that our method can accurately generate the experimental dynamics of developmental systems, such as the fly wing, and cell signaling processes mediated by stochastic ERK waves, paving the way for its use as a digital twin in bioengineering and clinical contexts.

Information theory for model reduction in stochastic dynamical systems

Model reduction is the construction of simple yet predictive descriptions of the dynamics of many-body systems in terms of a few relevant variables. A prerequisite to model reduction is the identification of these relevant variables, a task for which no general method exists. Here, we develop a systematic approach based on the information bottleneck to identify the relevant variables, defined as those most predictive of the future. We elucidate analytically the relation between these relevant variables and the eigenfunctions of the transfer operator describing the dynamics. Further, we show that in the limit of high compression, the relevant variables are directly determined by the slowest-decaying eigenfunctions. Our information-based approach indicates when to optimally stop increasing the complexity of the reduced model. Further, it provides a firm foundation to construct interpretable deep learning tools that perform model reduction. We illustrate how these tools work on benchmark dynamical systems and deploy them on uncurated datasets, such as satellite movies of atmospheric flows downloaded directly from YouTube.

Zyxin is all you need: machine learning adherent cell mechanics

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. No systematic strategy currently exists to infer large-scale physical properties of a cell from its many molecular components. This is a significant obstacle to understanding biophysical processes such as cell adhesion and migration. Here, we develop a data-driven biophysical modeling approach to learn the mechanical behavior of adherent cells. We first train neural networks to predict forces generated by adherent cells from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion protein, such as zyxin, are sufficient to predict forces and generalize to unseen biological regimes. This protein field alone contains enough information to yield accurate predictions even if forces themselves are generated by many interacting proteins. We next develop two approaches - one explicitly constrained by physics, the other more agnostic - that help construct data-driven continuum models of cellular forces using this single focal adhesion field. Both strategies consistently reveal that cellular forces are encoded by two different length scales in adhesion protein distributions. Beyond adherent cell mechanics, our work serves as a case study for how to integrate neural networks in the construction of predictive phenomenological models in cell biology, even when little knowledge of the underlying microscopic mechanisms exist.