Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through summary statistics, which sacrifice complexity and interdependent structure intrinsic to these data in favor of parameter identifiability. This imposes a fundamental constraint on reliably extracting mechanistic insights from spatiotemporal data, highlighting the need for analytical frameworks that preserve the full richness of these dynamical systems. To address this, we developed a simulation-based inference framework that employs vision transformer-driven variational encoding to generate compact representations of the data, exploiting the inherent contextual dependencies. These representations are subsequently integrated into a likelihood-free Bayesian approach for parameter inference. The central idea is to construct a fine-grained, structured mesh of latent representations from simulated dynamics through systematic exploration of the parameter space. This encoded mesh of latent embeddings then serves as a reference map for retrieving parameter values that correspond to observed data. By integrating generative modeling with Bayesian principles, our approach provides a unified inference framework to identify both spatial and temporal patterns that manifest in multivariate dynamical systems.
Park et al. (Tue,) studied this question.