Machine-Aided General Framework for Fluctuating Dynamic Density Functional Theory (MAGFFDDFT)

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Many-body systems are ubiquitous in nature, ranging from stellar clusters to soft matter and down to the quantum scale of electrons. Classical fluids are many-body systems at sufficiently high temperatures that quantum effects can be neglected, and which can be easily deformed or structurally altered by external forces and thermal fluctuations. Hence, classical fluids encompass a wide spectrum of simple and complex systems often inherently multiscale. As a result, fluids often exhibit complex behaviour characterised by phase transitions, critical phenomena and emergent properties. Apart from the purely theoretical interest, fluids are central in a wide spectrum of natural phenomena and applications. Not surprisingly, they have been an active topic of both fundamental and applied research for several decades. Major advances, often from statistical mechanics, include the development of coarse-grained models for the evolution of observables by averaging out the microscopic properties and retaining the main effects at the macroscale. However, despite the considerable attention a large number of problems remain unresolved. In particular, existing models suffer from serious limitations including unknown functions-parameters and assumptions-simplifications, e.g. close-to-equilibrium conditions, which often restrict their applicability to largely idealised systems. The aim of the proposed research is to develop a machine-aided generic theoretical-numerical framework that would overcome existing limitations and shortcomings and would allow us to obtain rationally and systematically optimal low-dimensional general laws governing the dynamics of observables, which in turn can be used for the accurate, efficient and systematic analysis of classical fluids and complex multiscale systems in general. This in turn would allow us to advance our understanding of observable dynamics in a wide spectrum of areas, from engineering and physics which so far lack a formal unified framework.