Thermal Field Reconstruction on Microcontrollers: A Physics-Informed Digital Twin Using Laplace Equation and Real-Time Sensor Data

This paper presents a physics-informed digital twin designed for real-time thermal monitoring and visualization of a metallic plate. The system comprises a physical layer consisting of an aluminum plate equipped with thermistors to capture boundary conditions, a computational layer that implements the steady-state Laplace equation using the finite difference method, and an embedded execution framework deployed on a microcontroller that utilizes Direct Memory Access-driven ADC for efficient concurrent acquisition. The computed thermal field is transmitted through a serial interface and displayed in real time using a Python-based visualization interface. The Steinhart-Hart model was used to experimentally characterize the sensors, ensuring accuracy in the boundary condition acquisition. While the current formulation is restricted to steady-state conditions, it enables accurate spatial reconstructions with acceptable error margins and demonstrates operational concurrency with the physical system. The compact and modular architecture allows adaptation to other physical domains governed by elliptic PDEs, making it suitable for educational applications, diagnostic prototyping, and embedded edge deployments.