Overview of Cyber-Physical Systems (CPS) and Digital Twins

A Cyber-Physical System (CPS) is a mechanism that integrates, analyzes, processes, and optimizes diverse data collected from the physical world via sensors and IoT devices within cyberspace. It aims to create valuable insights and knowledge. Central to this concept is the "Digital Twin."

What is a Digital Twin?

A Digital Twin is a highly accurate digital representation (or "twin") of physical entities such as machines, facilities, and environments existing in the real world.

Using real-time data collected from physical objects, digital twins enable simulations, predictions, and optimizations in a virtual environment. The results can then be reflected back into real-world operations. Digital twins have broad applications across industries such as manufacturing, logistics, energy, and mobility (transportation), significantly contributing to smarter and more efficient industrial practices.

Technical Elements for Building a CPS

• Internet of Things (IoT): Real-time data collection through various sensors

• Artificial Intelligence (AI) and Deep Learning: Advanced data analysis and pattern recognition

• Big Data: Accumulation, processing, and optimization of large-scale data

• Cloud Integration: Aggregation, sharing, and utilization of distributed data

• Factory Automation (FA): Automatic control systems providing real-world feedback

By integrating these elements, CPS establishes a continuous cycle between the physical and cyber spaces, generating new value for industries and society as a whole.

Cyber-Physical System Mobility Optimization Engine (CPS-MOE)

Towards a Super-Smart Society

In recent years, numerous global initiatives have sought to create a super-smart society—characterized by enhanced safety, security, and convenience—through the integration and fusion of advanced technologies. Although there have been various research collaborations between academia and industry, few projects have successfully bridged theoretical mathematics and practical ecosystem development into real-world services.

Our Vision and Contribution

Our research addresses this gap by establishing and validating integrated frameworks across multiple disciplines. Specifically, our project team has developed the Cyber-Physical System Mobility Optimization Engine (CPS-MOE), an advanced platform designed to foster new industrial opportunities, minimize costs and industrial waste, and provide optimized scheduling solutions for transportation systems.

Core Functionalities of CPS-MOE

CPS-MOE incorporates state-of-the-art techniques such as:

• Graph Analysis: Deep insights into complex relationships within data.

• Optimization Algorithms: Advanced computational methods to achieve optimal performance.

The following sections outline our dedicated work and innovations within these key areas, demonstrating our commitment to driving practical, transformative changes in society and industry.

Recent Trends in Large-Scale Graph Processing in High-Performance Computing (HPC)

While traditional High-Performance Computing (HPC) has primarily focused on numerical computation, recent trends have seen an increase in data-intensive applications, emphasizing large-scale data processing.

What is the Graph500 Benchmark?

Graph500 is an international benchmarking standard that evaluates and ranks computing system performance using multiple graph analysis techniques, including parallel search, shortest-path optimization, and maximal independent set problems. Graph analysis is recognized as an essential computational method across diverse fields such as cybersecurity, drug discovery, data mining, and network analysis.

In particular, the "Huge Class" of Graph500 Benchmark involves handling extremely large graphs exceeding one trillion nodes, necessitating the distribution of data across multiple computing nodes.

Achievements of the JST CREST Team (Fujisawa et al.)

From 2011 to 2017, the JST CREST research team led by Fujisawa developed software for high-speed, large-scale graph traversal on next-generation supercomputers. By integrating advanced software technologies, the team achieved world-leading performance in graph exploration software:

• Efficient partitioning of graph adjacency matrices across multiple computing nodes.

• Optimization algorithms to reduce redundant graph traversal.

• Communication performance optimization in massively parallel computing environments (thousands to tens of thousands of nodes).

• Memory access optimization tailored for multi-core processors.

World Records Set by Supercomputers "K" and "Fugaku"

Thanks to these technological advancements, the "K" supercomputer achieved the world's top position in the Graph500 benchmark consecutively for nine terms (ten terms total) between 2014 and 2019. Notably, in 2015, the "K" supercomputer completed a breadth-first search (BFS) on a massive Kronecker graph consisting of one trillion nodes and 17.59 trillion edges in just 0.56 seconds, achieving a world record performance of 31,302.4 GTEPS (approximately 31.3 trillion TEPS). This result underscored the significant dominance of communication time in large-scale graph analytics.

Further, from 2020 to 2024, the Fugaku supercomputer renewed the world record in the Graph500 benchmark:

• June 2020: Approximately 70.9 trillion TEPS

• November 2023: Approximately 138.86 trillion TEPS

• Latest Record (November 2024): Approximately 204.06 trillion TEPS

These achievements highlight the technological superiority of Japan's supercomputers in the field of large-scale and complex data processing.

Mathematical Optimization for Large-Scale Problems

We introduce our advanced parallel implementation designed for solving large-scale mathematical optimization problems. Among these, the Semidefinite Programming (SDP) problem stands out as one of the most critical and challenging areas in mathematical optimization today.

Semidefinite Programming and the Primal-Dual Interior-Point Method (PDIPM)

The Primal-Dual Interior-Point Method (PDIPM) is recognized as one of the most powerful algorithms available for solving SDP problems. It has been widely utilized by various research groups to develop sophisticated software packages. However, two primary computational bottlenecks are well-known in the PDIPM framework:

• Generation of the Schur Complement Matrix (SCM)

• Cholesky Factorization of SCM

SDPARA: Advanced Parallel Implementation

To address these bottlenecks, we have developed an enhanced version of SDPARA, a highly parallelized solver optimized for multiple CPUs and GPUs. SDPARA is specifically engineered to handle extremely large-scale SDP problems with over a million constraints.

Key features of SDPARA include:

• Automatic extraction of unique characteristics from SDP problems.

• Intelligent identification of computational bottlenecks.

When the SCM generation is identified as a bottleneck, SDPARA achieves remarkable scalability through:

• Extensive utilization of CPU cores.

• Processor affinity techniques.

• Memory interleaving methods.

If Cholesky factorization becomes the limiting factor, particularly for SDP problems exceeding two million constraints, SDPARA employs:

• Parallel Cholesky factorization leveraging thousands of GPUs.

• Advanced methods to overlap computation and communication.

Demonstrated Performance

Our numerical experiments conducted on the TSUBAME 2.5 supercomputer illustrate SDPARA’s exceptional performance as a general SDP solver across multiple application domains. Notably:

• Successfully solved the largest SDP problem with over 2.33 million constraints, establishing a new global record.

• Achieved a peak performance of 1.774 PFlops (double precision) for large-scale Cholesky factorization utilizing 2,720 CPUs and 4,080 GPUs.

These results confirm SDPARA's status as a world-leading solution for large-scale SDP challenges, setting a new standard for computational optimization.

Development and Industrial Applications of the CPS Mobility Optimization Engine (CPS-MOE)

In recent years, numerous global initiatives have promoted the realization of a highly safe, secure, and convenient "Super-Smart Society" (Society 5.0) through the integration and combination of advanced technologies. The rapid progress in Information and Communication Technology (ICT) has particularly enabled precise modeling of real-world phenomena, facilitating simulations and optimizations in response to environmental changes. Consequently, Cyber-Physical Systems (CPS) have emerged as innovative and practical business models.

In collaboration with various private enterprises, our team is currently developing the Cyber-Physical System Mobility Optimization Engine (CPS-MOE). This engine utilizes extensive sensor data (e.g., tracking movements of people and objects) and open datasets (such as Wi-Fi-based mobility records) to perform sophisticated optimizations and simulations in cyberspace. The primary objectives of this initiative are to foster new industrial sectors, reduce operational costs and waste, and enhance scheduling efficiency for transportation systems.

CPS-MOE: Three Core Mobility Areas

To fully implement CPS-MOE, we are advancing mathematical and computational technologies in the following three targeted mobility domains:

1. Information Mobility (Human Interests and Intentions)

• User Clustering Techniques: Utilizing web access histories and users' latent interests for effective grouping and prediction.

2. Mobility of People and Objects

• Position Detection and Tracking: Leveraging deep learning for accurate identification and monitoring.

• Congestion Detection and Flow Optimization: Techniques for efficiently managing and visualizing movements.

3. Transportation Mobility (Optimized Operations)

• Route and Logistics Optimization: Streamlining travel routes and logistics operations.

• Mobility as a Service (MaaS): Implementing and optimizing services such as bike-sharing to improve urban mobility.

Through these efforts, CPS-MOE aims to significantly enhance the efficiency, sustainability, and overall effectiveness of future mobility systems.