pinn_heat_conduction

PINN-Based Heat Dispersion Modeling in an Aluminum Disk

This repository contains an undergraduate research project investigating the use of Physics-Informed Neural Networks (PINNs) to model transient heat dispersion in an axisymmetric anodized aluminum disk subject to localized laser heating.

The work focuses on enforcing governing heat-transfer physics through the loss function in order to improve prediction accuracy under sparse sensor data.

Problem Description

A non-modulating laser is applied at the center of a 10-inch diameter, 0.5-inch thick anodized aluminum disk. Temperature sensors are located on the back surface at discrete radial positions, with the perimeter assumed insulated and the initial temperature uniform.

The objective is to predict the transient temperature field on the back surface of the disk using limited measurement data.

Methodology

• Governing system based on the axisymmetric heat equation in cylindrical coordinates
• Physics constraints enforced through PINN loss terms:
  • PDE residual
  • Initial conditions
  • Boundary conditions (Neumann and convective)
  • Data consistency
• Neural network implemented in MATLAB using a custom training loop
• Sparse on-sensor data used for training, with off-sensor data used for validation

Implementation

The model is implemented using MATLAB® and the Deep Learning Toolbox. A custom loss function is constructed to incorporate physical constraints alongside data error. Automatic differentiation is used to compute PDE residuals required for PINN training.

Custom components include:

• Swish activation layer implementation
• Physics-based loss evaluation
• Data normalization and validation pipelines

Results

The trained PINN successfully captures the temporal and radial trends of heat dispersion and demonstrates interpolation capability beyond sensor locations. Model performance degrades gracefully as training data is reduced, highlighting the benefit of physics-informed constraints in sparse-data regimes.

Repository Contents

• report/ — Technical report detailing formulation, assumptions, and results
• src/ — MATLAB source files for data generation, network training, and validation
• figures/ — Selected output plots and visualizations

Status

This repository accompanies a technical research report and is not a formal publication. Portions of the analysis and figures may be refined as the study continues.

Environment

MATLAB R2024a (Deep Learning Toolbox, Statistics and Machine Learning Toolbox)

Author

Cassie Vetrovec
University of Florida — Mechanical & Aerospace Engineering