Perfecting Liquid-State Theories with Machine Intelligence

Abstract

Recent years have seen a significant increase in the use of machine intelligence for predicting the electronic structure, molecular force fields, and physicochemical properties of various condensed systems. However, substantial challenges remain in developing a comprehensive framework capable of handling a wide range of atomic compositions and thermodynamic conditions. This perspective discusses potential future developments in liquid-state theories leveraging recent advancements in functional machine learning. By harnessing the strengths of theoretical analysis and machine learning techniques including surrogate models, dimension reduction, and uncertainty quantification, we envision that liquid-state theories will gain significant improvements in accuracy, scalability, and computational efficiency, enabling their broader applications across diverse materials and chemical systems.

Noether invariance theory for the equilibrium force structure of soft matter

“…The recent neural functional theory [75][76][77] is based on the powerful concept of using neural networks to represent functional relationships which encapsulate the correlation behaviour of complex systems. Noether sum rules have been shown to provide valuable consistency checks for these neural functionals and they give much inspiration for further theoretical developments in the spirit of physics-informed machine learning [78][79][80][81][82][83].…”

Why neural functionals suit statistical mechanics

“…Analytically carrying out the functional integral (30) on the basis of the analytical direct correlation functional c 1 (x, [ρ]) as given by equations ( 24)-( 28) is feasible. The result [56], again expressed in the more illustrative Rosenfeld fundamental measure form, is given by:…”

“…Although the result of the functional integral (30) has lost all position dependence, the specific form of the density profile ρ(x) is deeply baked into the resulting output value of the functional via both the prefactor ρ(x) in the integrand in equation ( 30) and the evaluation of the direct correlation functional at the specifically scaled form ρ a (x). In parallel with this mathematical structure, the explicit form (33) of the Percus functional clearly demonstrates that the resulting value will depend nontrivially on the shape of the input density profile.…”

“…Recent applications of machine learning range from the characterization of soft matter [24], reverse-engineering of colloidal self-assembly [25], local structure detection in colloidal systems [26], to the investigation of many-body potentials for isotropic [27] and for anisotropic [28] colloids. Brief overviews of machine learning in physics [29] and in particular in liquid state theory [30] were given recently.…”