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

Lead Research Organisation: Imperial College London
Department Name: Chemical Engineering

Abstract

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.

Publications

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Malpica-Morales A (2024) Forecasting with an N-dimensional Langevin equation and a neural-ordinary differential equation. in Chaos (Woodbury, N.Y.)

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Nold A (2024) Hydrodynamic density-functional theory for the moving contact-line problem reveals fluid structure and emergence of a spatially distinct pattern in Physical Review Fluids

 
Title Statistical Mechanics and Machine Learning of Nonequilbrium Processes 
Description The work undertaken by the project so far is centred on the following two themes: Statistical Mechanics of Nonequilibrium Processes The overarching objective is the development of a generic theoretical-numerical framework aided by machine learning that 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 and efficient analysis of classical fluids, and complex multiscale systems (CMS) in general, far from equilibrium conditions. This work is primarily theoretical aiming at the development of new models from first principles and exploring the mathematical structure of the theory. But the work also takes place closely with the parallel computational effort on the project involving physics-informed machine learning (ML), in particular coupling the theoretical developments with ML. ML of Nonequilibrium Processes The overarching objective here is the development of a generic theoretical-numerical framework aided by machine learning that 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 and efficient analysis of classical fluids, and complex multiscale systems (CMS) in general, far from equilibrium conditions. This work is primarily computational focusing on physics-informed machine learning (ML), in particular coupling the parallel theoretical developments in the project with ML. 
Type Of Material Improvements to research infrastructure 
Year Produced 2025 
Provided To Others? No  
Impact It is far too early in the project to have notable impacts. But the long term, the theoretical framework developed could potentially shift the paradigm in a number of fields, while targeted applications planned as part of the project will ultimately establish it as a useful and versatile toolbox for the mathematical and computational scrutiny of CMS. I also note that the project started on 01/09/2023, but this was with my time. Research staff to carry out the individual tasks and undertake the work were not in place until 20/03/2024 and 01/06/2024 when two post-doctoral research associates joined the group. 
 
Title Machine Learning of Nonequilibrium Processes 
Description As noted in the Section "Research Tools & Methods" the project has a significant computational component focusing on physics-informed ML, in particular coupling the parallel theoretical developments in the project with ML. For this purpose progress is being made on a number of directions: numerical solution of integral-differential equations, in particular equations of the density-functional-theory (DFT) type, which play a central role and are key components of the project, and continuation methods for DFT equations; numerical solution of deterministic and stochastic partial differential equations; deep learning from molecular dynamics (MD) and optimal models from nonequilibrium. 
Type Of Material Computer model/algorithm 
Year Produced 2025 
Provided To Others? No  
Impact Again, it is too early for any notable impact to be realised. Nevertheless, the work on data-driven and deep learning from MD will offer new ways of utilising MD and as such we expect it to impact statistical physics, but also data science and fields where MD is crucial, such as computational chemical physics, and ultimately achieve cross-fertilization between these fields. It could also potentially stimulate the development of new algorithms and computational approaches for non-equilibrium phenomena, thus influencing areas such as nonlinear dynamics and numerical analysis. Our generic computational-theoretical framework will be applied directly to a number of real-world problems, from wetting to cloud formation and social dynamics. This in turn will seed further studies with our framework, potentially shifting the paradigm in a number of fields. Successful applications will also play an important role in widely adopting our framework and ultimately establishing it as a useful and versatile toolbox for the mathematical and computational scrutiny of CMS.