PINNs

This course is designed to provide a deep understanding of Physics-Informed Neural Networks (PINNs) and their applications in the Transportation & Logistics industries. Participants will learn how to integrate physical laws and domain knowledge into neural network models, enabling them to solve complex problems in transportation systems, traffic flow, supply chain optimization, and logistics management. The course covers the theoretical foundations of PINNs, as well as practical implementation strategies and case studies tailored to the specific challenges and requirements of the Transportation & Logistics industries.

• Understand the theoretical foundations and advantages of Physics-Informed Neural Networks in the context of Transportation & Logistics

• Formulate and implement PINNs for solving PDEs relevant to transportation and logistics problems

• Incorporate domain knowledge and physical constraints into neural network architectures for transportation and logistics applications

• Apply PINNs to solve forward and inverse problems in traffic flow prediction, supply chain optimization, and logistics management

• Evaluate and interpret the performance of PINN models using appropriate metrics and visualization techniques

• Develop and deploy PINN-based solutions for real-world problems in the Transportation & Logistics industries

1.  Introduction to PINNs for Transportation & Logistics

• Overview of PINNs and their advantages over traditional numerical methods in transportation and logistics

• Mathematical formulation of PINNs for solving PDEs in transportation and logistics systems

• Comparison of PINNs with other machine learning approaches used in Transportation & Logistics

• Hands-on exercises: Implementing a basic PINN for solving a simple transportation or logistics-related PDE

2. PINNs for Traffic Flow Prediction and Management

• Governing equations in traffic flow theory (e.g., Lighthill-Whitham-Richards, Payne-Whitham)

• Formulating PINNs for problems in traffic flow prediction, congestion detection, and control

• Applying PINNs to optimize traffic signal timing and ramp metering

• Hands-on exercises: Developing PINN models for specific traffic flow case studies

3. PINNs for Supply Chain Optimization and Logistics Management

• Formulating PINNs for supply chain optimization problems (e.g., inventory management, facility location)

• Applying PINNs to solve vehicle routing and scheduling problems

• Integrating PINNs with traditional optimization techniques (e.g., linear programming, heuristics)

• Hands-on exercises: Implementing PINN models for specific supply chain optimization and logistics management case studies

4. PINNs for Multimodal Transportation and Intelligent Transportation Systems

• Formulating PINNs for multimodal transportation problems (e.g., mode choice, intermodal freight transport)

• Applying PINNs to intelligent transportation systems (e.g., autonomous vehicles, connected vehicles)

• Integrating PINNs with real-time data sources (e.g., GPS, sensors) for transportation system monitoring and control

• Hands-on exercises: Developing a PINN-based multimodal transportation optimization system

5. Deployment and Future Directions in Transportation & Logistics

• Deploying PINN models in production environments for transportation and logistics applications

• Strategies for model validation, testing, and maintenance in Transportation & Logistics

• Scalability and computational efficiency considerations for large-scale transportation networks and logistics systems

• Future research directions and open challenges in PINNs for Transportation & Logistics industries

• Hands-on exercises: Deploying a PINN model for a transportation or logistics use case and discussing deployment strategies

• Strong understanding of partial differential equations (PDEs) and numerical methods

• Proficiency in programming with Python and deep learning frameworks (e.g., TensorFlow, PyTorch)

• Familiarity with transportation and logistics concepts (e.g., traffic flow theory, supply chain management, operations research)