This research introduces a new approach that reveals the structural variables of complex systems and restructures the way we model unpredictable behavior in the real world.
Complex systems model dynamic and unpredictable real-world behavior. Simulation is difficult due to nonlinearities, where small changes in conditions can have disproportionately large effects, many interacting variables that complicate computational modeling, and randomness, where outcomes are stochastic. Machine learning is a powerful tool for understanding complex systems. It can be used to find hidden relationships in high-dimensional data and to predict the future state of a system based on previous data.
This research develops a new machine learning approach for complex systems that allows users to extract important information about collective variables in the system, called intrinsic structural variables. The researchers used a type of machine learning tool called an autoencoder to look at snapshots of how atoms are arranged in the system at any given moment (called the instantaneous atomic configuration). We then matched each snapshot to a more stable version of that structure (unique structure) that represents the underlying shape or pattern of the system. Intrinsic structural variables enable analysis of structural transitions and calculation of high-resolution free energy landscapes. These are detailed maps that show how a system’s energy changes as its structure and composition change, helping researchers understand the stability, transitions, and dynamics of complex systems.
This model is versatile, and the authors demonstrate how it can be applied to metal nanoclusters and protein structures. In the case of Au147 nanoclusters, a well-organized structure consisting of 147 gold atoms, the unique structural variables reveal three main types of stable structures that gold nanoclusters can adopt. These are called fcc (face-centered cube), Dh (decahedron), and Ih (icosahedron). These structures represent different stable states that the nanocluster can switch to and appear as valleys in the high-resolution free energy landscape. It is not easy to move from one valley to another. Between the valleys are narrow paths or barriers called kinetic bottlenecks.
The researchers validated the machine learning model using Markov state models, a mathematical tool that helps analyze how systems move between different states over time, and electron microscopy, which can image atomic structures and confirm that the predicted structures exist within the gold nanoclusters. This approach also captures nonequilibrium melting and freezing processes, providing insight into polymorphic selection and metastable states. Demonstrates scalability up to Au309 cluster.
The generality of this method is further demonstrated by applying it to a completely different type of system, the bradykinin peptide, and identifying distinct structural motifs and transitions. Applying this method to biomolecules provides further evidence that machine learning approaches are flexible and powerful techniques for studying different types of complex systems. This work contributes not only to machine learning strategies but also to experimental and theoretical studies of complex systems, with potential applications spanning liquids, glasses, colloids, and biomolecules.
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