Icarus: Physics-Informed Machine Learning Toolkit for Thermal Field Decomposition and Heat Flux Prediction

Icarus is a Python machine learning library focused on thermal fluid dynamics, offering a complete workflow from infrared thermal imaging data to heat flux prediction models. It implements physics-informed methods based on Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), and artificial neural networks. On a flow boiling dataset with 17 million samples, it achieves a prediction performance of R²=0.729, a 69% improvement over the linear baseline. This open-source project provides a powerful tool for researchers and engineers.

Heat flux prediction is a core problem in thermal fluid dynamics, crucial for energy optimization, electronic heat dissipation, etc. Traditional invasive measurement methods have limitations; infrared thermal imaging provides non-invasive temperature field measurement, but inverting heat flux from temperature fields is an inverse problem challenge. Icarus emerged to implement the research method from Twum-Barima 2025, providing a complete physics-informed toolchain.

Icarus implements three feature strategies:

1. Raw Temperature (Model A)：Directly uses temperature data, ignoring gradient information, leading to limited prediction capability;
2. Gradient Enhancement (Model B)：Incorporates temporal/spatial gradients of temperature, using physical intuition to improve performance;
3. Modal Mapping (Model C, Best)：Decomposes temperature fields into dominant modes via POD, learns modal coefficient mapping, then reconstructs heat flux fields, achieving the best performance of R²=0.729.

Icarus adopts a modular architecture, with key modules including:

• Data Loading: Supports formats like .mat/.h5/.npz, flexibly connecting to experimental data;
• Decomposition Modules: POD (extracts dominant modes), DMD (analyzes dynamic behavior);
• Feature Engineering: Gradient calculation, modal feature construction;
• Model Module: MLP neural network + Optuna hyperparameter optimization;
• Evaluation & Visualization: Provides metrics like R²/RMSE, supports visualization of temperature fields/modes, etc.

On the flow boiling dataset (17 million samples), the performance comparison of the three strategies is as follows:

Strategy	R²	Improvement
Raw Temperature	Baseline	-
Gradient Enhancement	Moderate improvement	Medium
Modal Mapping	0.729	+69%
The significant improvement of Model C verifies the value of physics-informed methods. By extracting physically relevant modes via POD, it more efficiently captures the intrinsic relationship between temperature and heat flux.

Application Scenarios:

• Experimental Thermal Fluid Dynamics: Analyze infrared data to invert heat flux;
• Energy System Optimization: Boiler/heat exchanger design and operation optimization;
• Electronic Heat Dissipation: Heat dissipation design for high-power devices;
• Chemical Processes: Optimization of phase-change heat transfer reactors. Limitations:
• Dataset Dependence: The R²=0.729 result is for a specific dataset and requires independent validation;
• Model Scale: Currently uses scikit-learn MLP; ultra-large-scale data requires deep learning frameworks;
• DMD Limitation: Only applicable for short-term predictions.

Future Directions:

• GPU Acceleration: Add PyTorch support for large-scale training;
• Pre-trained Models: Develop pre-trained models for specific fluids to enhance transferability;
• Improved DMD: Integrate variants like EDMD/KDMD to improve prediction accuracy. Insights:
• Importance of Domain Knowledge: Physics-inspired feature engineering significantly improves performance;
• Value of Open-Source Ecosystem: Built on NumPy/SciPy, demonstrating Python's scientific computing capabilities;
• Reproducible Research: Complete implementation and documentation support result reproduction, promoting open science.