A single mathematical framework could replace dozens of ad-hoc models used to describe how fluids—from cooling systems to blood flow—behave under real-world conditions. Classical fluids are everywhere, but the equations that predict their behaviour break down when systems are far from equilibrium, such as during turbulence or rapid phase changes. Existing models rely on unknown parameters or oversimplified assumptions, limiting their use to idealised laboratory conditions. This project aims to build a machine-aided theoretical framework that systematically derives accurate, low-dimensional laws for fluid dynamics, removing the need for guesswork. If successful, the framework could transform how engineers and physicists simulate complex fluids in pipelines, chemical reactors, or biological systems. It may improve the design of cooling systems, drug delivery mechanisms, or manufacturing processes that depend on precise fluid control. The work is fundamental science—it does not promise an immediate product—but it addresses a long-standing gap in statistical mechanics. Past advances in this field have underpinned everything from weather forecasting to microchip fabrication.
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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.
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