Topological Methods for Learning to Steer Self-Organised Growth

自组织和自组装，即实体自发组织成模式，是自然界生长和结构形成的核心。这是生产功能材料和器件的更大结构的最具成本效益的方法。纳米粒子自组装是制造纳米结构/图案的少数实用策略之一。一种有希望的方法是逆统计力学方法，该方法从期望的模式开始“设计”二维自组装中组件之间的最佳相互作用潜力。将这种逆向设计方法扩展到直接从应用感兴趣的中观尺度和体性质映射到实际纳米颗粒的特定性质是一个主要的公开挑战。自动化这样的方法将是向前迈出的重要一步，从今天的高度手工设计过程，限制研究的小实验室规模。自动化道路上的关键瓶颈是双向映射的拓扑复杂性，以及由此产生的蒙特卡罗方法的巨大费用，其中进一步包括昂贵的多尺度动力学从头开始模拟。我们设想了解决这些问题的三大创新。首先，我们将开发新的生成建模方法，以取代昂贵的跨尺度自组装从头算模拟。利用已成功用于描述复杂系统的图神经网络范式，我们将开发新的结构化模型，准确捕获自组装中结构变化动态的拓扑结构，结合归纳偏差图语法和连接动态级别的多尺度抽象。其次，我们将开发自组织表面拓扑表征的新方法，并将这些方法用于校准模拟器的数据，以及设计用于搜索和设计优化的新算法。最后，一项重大创新将是将这些技术结合起来，不仅可以在计算机上进行优化，还可以通过校准模型直接和有效地对物理组装进行优化，并将其用于拓扑驱动的弱控制干预，以引导自组装过程的运行。这是通过多尺度结构属性映射的高效拓扑特征来实现的，这反过来又导致基于仿真的快速推理，从而实现对可生成的模式类型的灵活控制。通过PI（人工智能和机器人专家）和Co-I（工程部门的软物质物理学家）之间的合作，我们将通过将开发的模型和优化方法应用于实验室中涉及功能化纳米粒子的实验，利用最先进的实验设备，包括原子力显微镜和扫描电子显微镜（将用于验证模型），端到端演示这种方法。以及分子尺度的计算模型（生成大规模数据集）。

Self-organisation and self-assembly, i.e. spontaneous organisation of entities into patterns, are at the heart of growth and structure formation in nature. It is the most cost-effective way to produce larger structures for functional materials and devices. Nanoparticle self-assembly is one of the few practical strategies for making nanostructures/ patterns. One promising approach to this is an inverse statistical-mechanics method which 'designs' the optimal interaction potential between components in 2D self-assembly starting from a desired pattern. It is a major open challenge to extend such an inverse design methodology to map directly from meso-scale and bulk properties of application interest to specific properties of the real nanoparticle. Automating such a methodology would be a major step forward from today's highly manual design processes which restrict research to the small laboratory scale. Key bottlenecks on the path to automation are the topological complexity of the two-way mapping, and the significant expense of resulting Monte Carlo approaches that further include expensive ab initio simulations of the multi-scale dynamics.We envision three major innovations towards solving these problems. Firstly, we will develop new generative modelling approaches that could replace expensive ab-initio simulations of self-assembly across scales. Using the paradigm of Graph Neural Networks which have been successfully used to describe complex systems, we will develop new structured models that accurately capture the topology of structure-change dynamics in self-assembly, incorporating as inductive bias graph grammars, and multi-scale abstractions connecting levels of dynamics. Secondly, we will develop new methods for topological characterisation of the self-organising surface and use these in calibrating simulators to data, as well as to devise new algorithms for search and design optimisation. Finally, a major innovation will be in combining these to conduct optimisation not only in-silico, but directly and sample efficiently over runs of physical assembly through calibrated models and their use in topology-driven hence weakly controlled interventions to steer runs of the self-assembly process. This is enabled by efficient topological characterisation of multi-scale structure-property maps, which in turn leads to fast simulation-based inference to achieve flexible control over types of patterns that can be generated. Through collaboration between the PI, who is an AI and robotics specialist, and Co-I who is a soft matter physicist in an engineering department, we will demonstrate this methodology end-to-end by applying the developed models and optimisation methods in experiments involving functionalised nanoparticles in the laboratory, leveraging access to state-of-the-art experimental facilities including Atomic Force Microscopy and Scanning Electron Microscopy (which will be used to validate models), and to computational models at the molecular scale (to generate large scale datasets).