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

多体系统在自然界中无处不在，从星团到软物质，再到电子的量子尺度。经典流体是在足够高的温度下的多体系统，量子效应可以忽略不计，并且很容易被外力和热波动变形或结构改变。因此，经典流体涵盖了广泛的简单和复杂系统，通常具有固有的多尺度。因此，流体往往表现出以相变、临界现象和涌现特性为特征的复杂行为。除了纯粹的理论兴趣外，流体在广泛的自然现象和应用中也是中心的。毫不奇怪，几十年来，它们一直是基础研究和应用研究的活跃话题。主要的进展，通常来自统计力学，包括通过平均微观性质和保留宏观尺度上的主要影响来发展可观测物的粗粒度模型。然而，尽管引起了相当大的注意，许多问题仍未得到解决。特别是，现有模型受到严重的限制，包括未知函数-参数和假设-简化，例如接近平衡条件，这通常限制了它们在很大程度上理想化系统的适用性。本研究的目的是开发一种机器辅助的通用理论-数值框架，以克服现有的局限性和缺点，使我们能够合理和系统地获得控制可观测物动力学的最优低维一般定律，从而可用于精确、有效和系统地分析经典流体和复杂的多尺度系统。反过来，这将使我们能够在广泛的领域推进我们对可观察动力学的理解，从迄今为止缺乏正式统一框架的工程和物理学。

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.