Generative Mapping and Control of Stationary Points in Complex Dynamical Systems

复杂动力系统中驻点的生成映射和控制

• 批准号: EP/X018288/1
• 负责人: Massimiliano Vasile
• 金额: $ 25.79万
• 依托单位: University of Strathclyde
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX018288%2F1
• 关键词: Generative; Mapping; Control; Stationary; Points

Complex dynamical systems, from protein folding to brain dynamics, from complex networks to galaxies, present structures that are key to predicting and controlling their evolution. Among these structures, equilibrium points, periodic and libration solutions and resonances are of paramount importance to understand and control the evolution of these systems.Identifying these structures is fundamental to ensure the resilience of national infrastructures, manufacture effective medication, understand and cure disease, study the evolution of climate on Earth, preserve our ability to access space. Just to name some key applications.However, the identification of these structures in complex high dimensional system is a daunting task with a computational complexity that grows exponentially with the number of dimensions. In this project we propose to use recent advances in generative machine learning to develop a new paradigm to automatically discover these structures and lay down the foundations of Generative Dynamics. The new paradigm, called MAX-net, has the potential to break the curse of dimensionality affecting many problems in scientific computing and provide a game changing enabling technology in all fields of engineering and science.

复杂的动力学系统，从蛋白质折叠到脑动力学，从复杂的网络到星系，呈现出对预测和控制它们的进化至关重要的结构。在这些结构中，平衡点、周期和振动解以及共振对于理解和控制这些系统的演化至关重要。识别这些结构对于确保国家基础设施的弹性、制造有效的药物、了解和治疗疾病、研究地球气候的演变、保持我们进入太空的能力至关重要。然而，在复杂的高维系统中识别这些结构是一项令人望而生畏的任务，其计算复杂性随维的数量呈指数增长。在这个项目中，我们建议利用产生式机器学习的最新进展来开发一种新的范式来自动发现这些结构，并为产生式动力学奠定基础。这种名为Max-Net的新范式有可能打破影响科学计算中许多问题的维度诅咒，并在工程和科学的所有领域提供一种改变游戏规则的使能技术。