Berkeley researchers have developed a proven mathematical framework for the compression of large reversible Markov chains—probabilistic models used to describe how systems change over time, such as proteins folding for drug discovery, molecular reactions for materials science, or AI algorithms making decisions—while preserving their output probabilities (likelihoods of events) and spectral properties (key dynamical patterns that govern the system’s long-term behavior).

While describing the dynamics of ubiquitous physical systems, Markov chains also allow for rich theoretical and computational investigation. By exploiting the special mathematical structure behind these dynamics, the researchers’ new theory delivers models that are quicker to compute, equally accurate, and easier to interpret, enabling scientists to efficiently explore and understand complex systems. This advance sets a new benchmark for efficient simulation, opening the door to scientific explorations once thought computationally out of reach.

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