A physics-constrained AI framework enables accurate thermal field inversion for chiplet-based packaging with sparse data

Researchers at Shanghai University have developed a physics-constrained, data-efficient artificial intelligence framework that enables accurate thermal field inversion in chiplet-based packaging systems using only limited temperature measurements. The approach addresses a critical challenge in advanced heterogeneous integration, where increasing power density and material heterogeneity complicate thermal monitoring and reliability assessment.

Chiplet-based packaging integrates multiple heterogeneous chiplets into a single system, offering improved flexibility, yield, and cost efficiency compared to traditional system-on-chip designs. However, the resulting increase in power density and deterioration of heat dissipation conditions can lead to localized overheating, threatening system stability and long-term reliability. Accurately reconstructing the temperature field of such systems from sparse sensor data is therefore essential, yet remains a difficult inverse problem in practical engineering applications.

What's New?

Thermal field inversion typically relies either on dense temperature measurements or on complete knowledge of boundary conditions and heat sources. In chiplet-based systems, however, sensor placement is constrained by wiring and packaging design, and key thermal information—such as heat generation within interconnects or passive components—is often unavailable. Conventional numerical methods struggle under these conditions, while purely data-driven machine learning approaches generally require large datasets and lack physical interpretability.

To address these challenges, Yupeng Qi and colleagues propose a Region-Coupled Physics-Informed Neural Network (RC-PINN) framework that explicitly integrates physical laws with sparse observational data. The method combines domain decomposition based on material boundaries with physics-informed learning, enabling stable and physically consistent thermal field reconstruction even under severe data scarcity.

How It Works

The RC-PINN framework divides the chiplet packaging domain into multiple regions according to material properties, such as silicon chiplets and organic substrates. Each region is modeled by an independent neural network that embeds the governing heat conduction equation and relevant boundary conditions into its loss function. Physical coupling between regions is enforced through temperature and heat-flux continuity constraints at material interfaces, ensuring global physical consistency.

To further improve performance when observational data are extremely limited, the authors introduce a Gaussian Process Uncertainty-Guided Sampling (GP-UGS) strategy. This approach augments the training dataset by selectively generating additional data points based on predictive uncertainty estimated from Gaussian process regression. By balancing high-confidence reinforcement with targeted exploration of uncertain regions, GP-UGS enhances both accuracy and generalization without introducing excessive noise.

Validation and Results

The proposed framework was evaluated on representative two-dimensional thermal inversion scenarios for chiplet-based packaging, covering cases with known boundary conditions and unknown heat sources, as well as the reverse situation. Numerical simulations were used as reference solutions, while only sparse temperature observations were provided to the models.

Results show that RC-PINN achieves an average relative error below 0.4% under limited data conditions and improves prediction accuracy by approximately 40% compared to conventional neural networks. When combined with GP-UGS, the framework reaches coefficients of determination (R²) exceeding 0.99 using as few as 64 temperature observations. Importantly, the method accurately captures sharp temperature gradients at material interfaces, a task where standard single-network models typically fail.

Why It Matters

Reliable thermal field reconstruction is essential for monitoring hotspots, diagnosing anomalies, and improving the reliability and lifespan of advanced chiplet systems. By jointly enforcing physical laws, material interface continuity, and data-driven learning, the RC-PINN framework offers a practical solution for thermal characterization when sensor deployment and data availability are severely constrained.

Beyond chiplet packaging, the authors note that the proposed methodology is broadly applicable to other inverse heat transfer and multi-material engineering problems where data are scarce and physical consistency is critical.

What's Next?

Future work will focus on extending the framework to multi-property thermal–mechanical coupling, uncertainty-aware prediction, and more complex three-dimensional packaging architectures. These developments aim to further support cost-effective and reliable thermal management in next-generation heterogeneous integration technologies.

Journal Information
This research, titled “A physics-constrained and data-driven approach for thermal field inversion in chiplet-based packaging,” was published in AI & Materials.
DOI: 10.55092/aimat20250016

Qi Y, Wu Y, Xiong , Hu , Pan D. A physics-constrained and data-driven approach for thermal field inversion in chiplet-based packaging. AI Mater. 2025(2):0016, https://doi.org/10.55092/aimat20250016.