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COOL: A Cooling-Aware Point Transformer Framework for Thermal Prediction in Advanced 3D/3.5D IC Packaging

This paper introduces COOL, a cooling-aware point transformer framework that represents 3D/3.5D IC packaging as annotated point clouds with physics-informed boundary conditions to achieve high-accuracy thermal prediction with significant speedup over traditional solvers while effectively addressing inter-die coupling and dynamic cooling structures.

Original authors: Yao Lu, Zhicheng Guo, Qijun Zhang, Shang Liu, Wenji Fang, Wenkai Li, Zhiyao Xie

Published 2026-08-18

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CC BY 4.0

Original authors: Yao Lu, Zhicheng Guo, Qijun Zhang, Shang Liu, Wenji Fang, Wenkai Li, Zhiyao Xie

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Modern electronics are becoming incredibly dense, packing more computing power into smaller spaces than ever before. To achieve this, engineers now stack multiple layers of computer chips on top of one another, creating complex three-dimensional structures. While this stacking boosts performance, it creates a significant physical problem: heat. When these tiny layers operate, they generate intense warmth that must escape quickly, or the device will fail. In the past, engineers could rely on standard computer programs to simulate how heat moves through these layers, but these simulations are painfully slow. They often require hours to model a single design, making it impossible to test thousands of variations quickly. As chip designs have grown more intricate, with different materials and cooling systems stacked together, the old methods have become too sluggish to keep up with the pace of innovation.

A team of researchers at the Hong Kong University of Science and Technology has developed a new approach to solve this bottleneck. They created a system called COOL, which uses a type of artificial intelligence to predict temperature patterns in these advanced chip packages almost instantly. Instead of breaking the chip down into a rigid grid of tiny squares, as traditional software does, COOL treats the entire structure as a cloud of individual points. Imagine looking at a sculpture not as a solid block, but as a collection of millions of tiny dots, where each dot knows exactly what material it is made of, how much heat it is generating, and what kind of surface it touches. By feeding this cloud of information into a specialized learning model, the system can understand how heat flows across different materials and layers without needing to build a slow, detailed mesh first.

The researchers found that this method is not only fast but also remarkably accurate. In their tests, the system predicted temperature distributions with an error rate of just 2.4 percent, a level of precision that matches the best traditional simulation tools. More importantly, it achieved this in a fraction of the time. While a standard commercial simulation program took nearly three minutes to analyze a single design, the new system completed the same task in less than twelve seconds. This represents a speedup of more than fifteen times, allowing engineers to explore many more design options in the time it used to take to test just one. The system is particularly effective because it was designed to understand the specific challenges of modern packaging, such as how heat moves between different stacked chips and how cooling structures like heat spreaders interact with the layers below.

Previous attempts to use artificial intelligence for this task often fell short because they treated the chip as a single flat layer or assumed the cooling systems were fixed and unchanging. These older models struggled when faced with the complex, variable reality of modern 3D and 3.5D chip stacks, where the thickness of materials and the arrangement of layers can change frequently during the design process. The new framework, however, explicitly learns to recognize these variations. It understands that the boundary between two different materials, or the surface where air cools the chip, follows specific physical rules. By training the system to respect these physical boundaries, the researchers ensured that the predictions remain realistic even when the design changes.

The team validated their findings by creating a large dataset of diverse chip designs, varying everything from the number of stacked layers to the thickness of the cooling materials. They tested the system against designs it had never seen before, and it consistently outperformed other learning-based methods that relied on simpler grid structures. The results suggest that this point-based approach can handle the geometric complexity of real-world packaging, where heat must travel through silicon, copper, and various adhesives in irregular patterns. By replacing the slow, manual steps of traditional simulation with a fast, automated learning process, this work offers a practical path forward for designing the next generation of high-performance electronics. It allows engineers to verify that their chips will not overheat before they are even built, potentially saving time and resources in the race to create faster, more powerful devices.

Technical Summary: COOL – A Cooling-Aware Point Transformer Framework for Thermal Prediction in Advanced 3D/3.5D IC Packaging

Problem Statement
Advanced 3D and 3.5D Integrated Circuit (IC) packaging technologies enable high integration density but introduce severe thermal management challenges. These include complex cross-layer heat coupling, heterogeneous material compositions (e.g., silicon, TIMs, interposers), and dynamic cooling structures. Traditional thermal analysis relies on Finite Element Method (FEM) or Finite Difference Method (FDM) solvers (e.g., COMSOL, ANSYS Icepak). While accurate, these methods are computationally expensive, often requiring hours to simulate a single power trace, and demand significant manual effort for geometry modeling and meshing. This makes them impractical for iterative design space exploration.

Existing learning-based thermal prediction methods attempt to accelerate this process but face critical limitations in advanced packaging scenarios:

Failure to capture inter-die coupling: Many models (e.g., DeepOHeat, ASRR-PINN) treat systems as single dies or assume uniform power maps across layers, failing to model vertical heat propagation between stacked chiplets.
Static treatment of cooling structures: Current frameworks often treat cooling components (heat spreaders, TIMs) as fixed, pre-defined boundary conditions rather than flexible design elements with variable thickness and material properties. This rigidity prevents generalization across diverse packaging configurations.

Methodology
The authors propose COOL, a cooling-aware, data-driven framework that models the entire thermal domain (chips, packages, and cooling structures) as a unified, annotated 3D point cloud. The framework consists of three core components:

Point Cloud Representation & Feature Encoding:
- Instead of fixed grids, COOL represents heterogeneous assemblies as a set of 3D points ( $N \approx 3 \times 10^5$ per design).
- Dual-Domain Material Encoding: To distinguish overlapping physical properties, materials are encoded via a one-hot categorical identifier concatenated with continuous physical attributes (thermal conductivity $k_{iso}$ , specific heat $C_p$ , density $\rho$ ).
- Tri-Channel Power Representation: Power dissipation is encoded using raw magnitude, a binary active/passive flag, and log-transformed power to handle sparse, long-tailed distributions.
- Geometric & Boundary Features: Points are annotated with geometry domain IDs and specific flags for convection (Robin) and adiabatic (Neumann) boundaries.
Hierarchical Point Transformer Architecture:
- Encoder: Utilizes a "Transition Down" (TD) strategy. Unlike standard Farthest Point Sampling (FPS), COOL employs Temperature-Aware FPS (TA-FPS), which biases sampling toward thermally critical regions (hotspots, interfaces) based on a composite score of temperature gradients, power density, and boundary indicators.
- Point Transformer Blocks: These blocks use attention mechanisms to aggregate local neighborhood features, allowing the network to prioritize neighbors that significantly influence heat transfer.
- Decoder: Mirrors the encoder with "Transition Up" (TU) stages using distance-weighted interpolation and skip connections to restore full resolution.
Physics-Informed Boundary Conditioning (PI-BC):
- To enforce physical consistency, the training loss function ( $L$ $L$ ) combines a data term (Mean Squared Error) with physics-based regularization terms:
  - Laplacian Regularization ( $L_{phys}$ ): Penalizes non-physical temperature jumps within homogeneous material domains.
  - Boundary Condition Loss ( $L_{BC}$ ): Explicitly enforces Robin (convection) and Neumann (adiabatic) boundary conditions on relevant surface points during training.

Key Contributions

First Cooling-Aware Framework for 3D/3.5D ICs: COOL is the first learning-based method to explicitly model coupled heat transfer across chips, packages, and cooling structures simultaneously, capturing design-dependent effects of TIMs, TSVs, and heat spreaders.
Point-Cloud-Based Learning Methodology: The paper introduces a representation where the entire thermal domain is treated as a collection of spatial points annotated with material, structural, and power attributes, avoiding grid quantization errors.
Physics-Informed Boundary Conditioning (PI-BC): A novel training scheme that injects boundary physics (Robin/Neumann) directly into the loss function to enhance accuracy at material interfaces and hotspot regions.
Comprehensive Benchmarking: The authors constructed a diverse dataset of 740 thermal scenarios covering 74 unique 3D/3.5D packaging configurations with varying structural and cooling parameters.

Experimental Results
Experiments were conducted on a dataset generated via FEM simulation, split into 580 training and 160 testing samples (design-level split to prevent leakage).

Accuracy: COOL achieved a Normalized Mean Absolute Error (NMAE) of 2.4% on the test set. This significantly outperformed point-based baselines (U-Net: 15.6% NMAE; U-Net+SA: 13.7% NMAE).
Convergence: COOL demonstrated faster and more stable convergence, reaching near-convergence by epoch 160 compared to the slower decline of baselines.
Speedup: Compared to commercial FEM solvers (which take ~189 seconds per design), COOL performs inference in 12 seconds, yielding a 15.7× speedup.
Visualization: Qualitative results showed COOL accurately captured spatial thermal gradients and hotspot distributions in both 3D stacked and 3.5D CoWoS-style configurations, with local MAEs of ~0.45°C and ~0.38°C respectively.

Significance and Claims
The paper claims that COOL provides a practical solution for thermal-aware co-design in next-generation IC packaging. By explicitly modeling cooling structures as dynamic design elements rather than static boundaries, and by leveraging point transformers to handle geometric heterogeneity, COOL bridges the gap between the speed of learning-based methods and the fidelity required for complex 3D/3.5D systems. The authors assert that this framework enables rapid, automated thermal analysis suitable for iterative design optimization, overcoming the bottlenecks of traditional solvers and the generalization limits of prior learning-based approaches.

Technical Summary: COOL – A Cooling-Aware Point Transformer Framework for Thermal Prediction in Advanced 3D/3.5D IC Packaging

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