Topological Methods for Learning to Steer Self-Organised Growth

自组织和自组装，即实体自发地组织成模式，是自然界中增长和结构形成的核心。这是生产用于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。一种很有前途的方法是逆统计力学方法，它从所需的模式开始，在2D自组装中‘设计’组件之间的最佳相互作用势。将这种逆设计方法直接从应用感兴趣的介观和块状性质映射到真实纳米颗粒的特定性质是一个重大的开放挑战。将这种方法自动化将是从今天高度手动的设计过程向前迈出的重要一步，这些设计过程将研究限制在小实验室规模。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成本，其中进一步包括昂贵的多尺度动力学从头计算模拟。我们设想了三个主要创新来解决这些问题。首先，我们将开发新的生成性建模方法，以取代昂贵的跨尺度自组装的从头计算模拟。利用已被成功地用于描述复杂系统的图神经网络的范例，我们将开发新的结构化模型，该模型准确地捕捉自组装中结构变化动力学的拓扑结构，结合归纳偏向图文法和连接动力学层次的多尺度抽象。其次，我们将开发新的方法来描述自组织表面的拓扑特征，并将这些方法用于校准模拟器的数据，以及设计新的搜索和设计优化算法。最后，一项主要的创新将是将它们结合起来，不仅在硅胶中进行优化，而且通过校准的模型和它们在拓扑驱动的、因此受控较弱的干预中的使用来引导自组装过程的运行，从而在物理组装的运行上进行直接和有效的采样。这是通过多尺度结构-属性图的有效拓扑特征来实现的，这反过来又导致基于模拟的快速推理，以实现对可以生成的模式类型的灵活控制。通过人工智能和机器人专家PI和工程部软物质物理学家Co-I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颗粒的实验，利用最先进的实验设施，包括原子力显微镜和扫描电子显微镜(将用于验证模型)，以及分子级别的计算模型(以生成大规模数据集)，来端到端地演示这一方法。

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).