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Phase transitions are ubiquitous across life, yet hard to quantify anddescribe accurately. In this work, we develop an approach for characterizinggeneric attributes of phase transitions from very limited observations madedeep within different phases' domains of stability. Our approach is calledThermodynamic Maps, which combines statistical mechanics and molecularsimulations with score-based generative models. Thermodynamic Maps enablelearning the temperature dependence of arbitrary thermodynamic observablesacross a wide range of temperatures. We show its usefulness by calculatingphase transition attributes such as melting temperature, temperature-dependentheat capacities, and critical exponents. For instance, we demonstrate theability of thermodynamic maps to infer the ferromagnetic phase transition ofthe Ising model, including temperature-dependent heat capacity and criticalexponents, despite never having seen samples from the transition region. Inaddition, we efficiently characterize the temperature-dependent conformationalensemble and compute melting curves of the two RNA systems GCAA tetraloop andHIV-TAR, which are notoriously hard to sample due to glassy-like landscapes.

Inferring phase transitions and critical exponents from limited observations with Thermodynamic Maps