Coarse-Graining Self-Assembly by the Stochastic Landscape Method

Inferring the dynamics of many-body stochastic systems from data remains a fundamental challenge in statistical physics, particularly when models must provide both predictive power and physical interpretability. Nonequilibrium self-assembly, where molecular components are driven to form ordered structures from disordered building blocks, is a prime example, central to nanotechnology, material science, and biology. Markov state models (MSMs) have emerged as a powerful framework for representing and understanding the dynamic behavior of such complex systems by discretizing their high-dimensional phase space into a network of metastable states and transition probabilities. Yet, constructing accurate and interpretable MSMs for nonequilibrium self-assembly remains challenging, often requiring extensive, multidimensional data sets or system-specific assumptions. Here, we introduce a novel framework for constructing MSMs of nonequilibrium self-assembly based on the stochastic landscape method (SLM), a physically grounded approach previously shown to enable predictive control of assembly dynamics. Using a tractable amount of simulation data, our method effectively coarse-grains the vast state space into a low-dimensional model that accurately reproduces key dynamic observables, including yield and first assembly times, under both equilibrium and driven conditions. Furthermore, we show that the resulting MSM generalizes beyond the conditions used for their construction, enabling accurate predictions in previously unexplored physical parameter regimes, while reducing the computational cost of baseline simulation by several orders of magnitude. While developed in the context of nonequilibrium self-assembly, this approach is broadly applicable to many-body systems governed by stochastic dynamics, offering a general strategy for constructing interpretable, efficient models of complex processes.