2020/10/31 by Peter Yatsyshin, Serafim Kalliadasis, A. Duncan +1
Biochemistry, Genetics and Molecular Biology · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Bayesian inference #Bayesian probability #Computer science #Inference #Machine Learning in Materials Science #Machine learning #Mathematics #Parametric statistics #Phase Equilibria and Thermodynamics #Protein Structure and Dynamics #Statistical inference #cond-mat.stat-mech #physics.data-an #stat.ML
paper · pdf · doi:10.1063/5.0071629
published as J. Chem. Phys. (2022)
arxiv created 2021/06/23 · openalex publication_date 2022/02/16 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that system? By combining non-parametric Bayesian inference with physically-motivated constraints, we develop an efficient learning algorithm which automates the construction of approximate free energy functionals. In contrast to optimisation-based machine learning approaches, which seek to minimise a cost function, the central idea of the proposed Bayesian inference is to propagate a set of prior assumptions through the model, derived from physical principles. The experimental data is used to probabilistically weigh the possible model predictions. This naturally leads to humanly interpretable algorithms with full uncertainty quantification of predictions. In our case, the output of the learning algorithm is a probability distribution over a family of free energy functionals, consistent with the observed particle data. We find that surprisingly small data samples contain sufficient information for inferring highly accurate analytic expressions of the underlying free energy functionals, making our algorithm highly data efficient. We consider excluded volume particle interactions, which are ubiquitous in nature, whilst being highly challenging for modelling in terms of free energy. To validate our approach we consider the paradigmatic case of one-dimensional fluid and develop inference algorithms for the canonical and grand-canonical statistical-mechanical ensembles. Extensions to higher-dimensional systems are conceptually straightforward, whilst standard coarse-graining techniques allow one to easily incorporate attractive interactions.