Thermal Field Reconstruction on Microcontrollers: A Physics-Informed Digital Twin Using Laplace Equation and...

Area of Science:

• Physics
• Engineering
• Computer Science

Background:

• Real-time thermal monitoring is crucial for diagnostics and control.
• Digital twins offer a powerful approach for simulating and visualizing physical systems.
• Accurate boundary condition acquisition is essential for reliable thermal field reconstruction.

Purpose of the Study:

• To develop and demonstrate a physics-informed digital twin for real-time thermal monitoring of a metallic plate.
• To implement an efficient embedded system for concurrent data acquisition and computation.
• To validate the accuracy and operational concurrency of the digital twin system.

Main Methods:

• A physical layer with an aluminum plate and thermistors for boundary condition measurement.
• A computational layer solving the steady-state Laplace equation via the finite difference method.
• An embedded system using Direct Memory Access (DMA)-driven Analog-to-Digital Converter (ADC) for data acquisition.
• A Python-based interface for real-time visualization of the computed thermal field.
• The Steinhart-Hart model for experimental sensor characterization.

Main Results:

• Accurate spatial reconstruction of the thermal field with acceptable error margins under steady-state conditions.
• Demonstrated operational concurrency between the physical system and the digital twin.
• Successful real-time visualization of the thermal field via a serial interface.
• Experimental characterization of thermistors using the Steinhart-Hart model ensured accurate boundary data.

Conclusions:

• The developed physics-informed digital twin provides effective real-time thermal monitoring and visualization.
• The compact and modular architecture is adaptable to other physical domains governed by elliptic partial differential equations (PDEs).
• The system is suitable for educational purposes, diagnostic prototyping, and embedded edge computing applications.