Collaborative Research: Differential Equations Motivated Multi-Agent Sequential Deep Learning: Algorithms, Theory, and Validation

从多个主体观察到的顺序数据在人工智能（AI）和科学应用中无处不在，例如，在计算机视觉、自然语言处理、机器人、计算生物学和生物物理学以及知识图谱中。从顺序观察到的数据中学习通常提供对底层系统的全局理解，并且比从非顺序（单次）观察到的数据中学习产生更可靠的预测。序列数据通常在时间和空间上是不规则采样的，当它与代理之间的交互结合在一起时，它给机器学习带来了巨大的挑战。该项目通过开发对这些瓶颈的新的数学理解，并结合用于顺序和图学习的新的数学原则深度学习算法，来解决这些挑战。该项目的预期结果和算法将广泛适用于重要的社会问题，如流行病传播、协作机器人和环境变化。该项目包括研究生的研究培训机会。该项目将常微分方程（ode）和偏微分方程（PDEs）理论与多智能体顺序学习实践相结合。该项目进一步利用ODE和PDE的见解来推进深度顺序和图学习的理论基础算法。该项目协同集成了神经ODE方法的最新进展和机器学习图网络的最新进展。该项目开发并探索建立基于图上波动方程的下一代算法，将二阶连续动力学与图滤波耦合在一起。该研究为克服过度平滑问题的新方法提供了理论保证，以实现对具有深度体系结构的图的顺序学习。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Sequential data observed from multiple agents is ubiquitous in artificial intelligence (AI) and scientific applications, for example, in computer vision, natural language processing, robotics, computational biology and biophysics, and knowledge graphs. Learning from sequentially observed data often provides a global understanding of the underlying system and yields more reliable predictions than learning from a non-sequentially (single-shot) observed data. Sequential data is often irregularly-sampled in time and space and when this is combined with the interaction between agents, it raises tremendous challenges for machine learning. This project addresses these challenges by developing new mathematical understandings of these bottlenecks combined with new mathematically-principled deep learning algorithms for sequential and graph learning. Anticipated results and algorithms from this project will have broad applicability to important societal issues, such as pandemic spread, cooperative robotics, and environmental change. The project includes research training opportunities for graduate students.This project bridges ordinary differential equations (ODEs) and partial differential equations (PDEs) theory with multi-agent sequential learning practice. The project further leverages ODE and PDE insights to advance theoretically-grounded algorithms for deep sequential and graph learning. This project synergistically integrates recent advances in neural ODE methods with recent advances in graph networks for machine learning. The project develops and explores building next-generation algorithms based on wave equations on graphs, coupling second-order continuous dynamics in time with graph filtering. The research includes theoretical guarantees for the new methods in overcoming the over-smoothing issue, to enable sequential learning on graphs with deep architectures.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.