EAGER: Exploration of topological self-organizing non-linear dynamical systems with memory as efficient scalable computing fabric

与我们的传统计算机工作方式有很大不同的非传统计算模型正在成为基础科学和技术领域的一个重要研究方向。量子计算是最著名的例子，一种被称为纠缠的现象是量子力学系统特有的，预计将有助于解决一些困难问题，如素因式分解。然而，除了纠缠，人们还可以利用各种各样的物理现象，这些现象不需要极端的技术条件就能运行。这意味着，在我们的传统计算机和量子计算之间，还有一个广阔的研究领域有待探索。该项目将研究一种全新的计算结构，它属于这一未知领域，并能够通过非量子动力学系统有效地解决难题。这种计算结构被称为记忆计算，因为它利用了任何物理系统与生俱来的时间非局部性，即对它们过去动态的记忆。如果成功，该项目预计将迎来计算模式的转变，几乎将影响到技术的方方面面。拟议的活动将有助于高技能人员的专业发展，这些人员的专业知识贯穿于该项目涉及的不同学科。为了证明这种非von-Neumann计算结构的基本价值，该奖项将支持开发一种用于数字记忆计算器的模拟器，该模拟器基于适当的具有记忆的非量子、非线性动力系统的微分方程的数值积分。为了便于独立验证，模拟器将被用于解决具有挑战性的组合问题，例如素因数分解，其解可以很容易地检查。因此，该奖项将成为在硬件中实现这种数字记忆计算器的最终目标的垫脚石。这个项目还将通过调查计算、拓扑和物理系统集体行为之间的深层关系来提高我们对有效计算的物理要求的知识。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Unconventional computing models that depart substantially from how our traditional computers work are emerging as an important research direction in both fundamental science and technology. Quantum computing is the most celebrated example, where a phenomenon known as entanglement and unique to quantum mechanical systems, is expected to help in the solution of some difficult problems, such as prime factorization. However, there is a wide range of physical phenomena one can exploit other than entanglement, and that do not require extreme technological conditions to operate. This means that there is a vast area of research yet to explore between our traditional computers and quantum computing. This project will investigate a radically novel computing fabric that falls within this uncharted territory, and is able to solve difficult problems efficiently by means of non-quantum dynamical systems. Such a computing fabric is called memcomputing because it exploits the innate time non-locality of any physical system, namely memory of their past dynamics. If successful, this project is expected to usher in a paradigm shift in computing that will reverberate across practically all aspects of technology. The proposed activities will contribute to the professional development of highly skilled personnel with expertise that cuts across different disciplines involved in this project. To prove the fundamental value of such a non-von-Neumann computing fabric, this award will support the development of a simulator for digital memcomputing machines based on the numerical integration of the differential equations of appropriate non-quantum, non-linear dynamical systems with memory. To facilitate an independent verification, the simulator will then be employed to tackle challenging combinatorial problems, such as prime factorization, whose solution can be easily checked. This award will thus serve as the stepping stone towards the ultimate goal of realizing such digital memcomputing machines in hardware. This project will also advance our knowledge of the physical requirements to compute efficiently by investigating the deep relation between computing, topology, and collective behavior of physical systems.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.