# DeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design

arXiv: https://arxiv.org/abs/2504.03955 · HTML: https://mlsanity.com/paper/2504.03955/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 44 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 18 of 18)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [The Convergence Rate of Neural Networks for Learned Functions of Different Frequencies](https://mlsanity.com/paper/1906.00425/) (2019)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [DeepOHeat: Operator Learning-based Ultra-fast Thermal Simulation in 3D-IC Design](https://mlsanity.com/paper/2302.12949/) (2023)
- [An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient](https://mlsanity.com/paper/2007.09684/) (2020)
- [A Thermal Machine Learning Solver For Chip Simulation](https://mlsanity.com/paper/2209.04741/) (2022)
- [Separable Operator Networks](https://mlsanity.com/paper/2407.11253/) (2024)
- [Towards Real Time Thermal Simulations for Design Optimization using Graph Neural Networks](https://mlsanity.com/paper/2209.13348/) (2022)

## Built on by (most cited first, 2 of 2)

- [DeepOHeat-v2: Self-Improving Operator Learning for Fast and Trustworthy Thermal Optimization in 3D-IC Design](https://mlsanity.com/paper/2608.16080/) (2026)
- [A Composable AI-Accelerated Iterative Solver for 3D-IC Thermal Modeling](https://mlsanity.com/paper/2610.02461/) (2026)

## Abstract (arXiv)

Thermal analysis is crucial in 3D-IC design due to increased power density and complex heat dissipation paths. Although operator learning frameworks such as DeepOHeat~citeliu2023deepoheat have demonstrated promising preliminary results in accelerating thermal simulation, they face critical limitations in prediction capability for multi-scale thermal patterns, training efficiency, and trustworthiness of results during design optimization. This paper presents DeepOHeat-v1, an enhanced physics-informed operator learning framework that addresses these challenges through three key innovations. First, we integrate Kolmogorov-Arnold Networks with learnable activation functions as trunk networks, enabling an adaptive representation of multi-scale thermal patterns. This approach achieves a 1.25x and 6.29x reduction in error in two representative test cases. Second, we introduce a separable training method that decomposes the basis function along the coordinate axes, achieving 62x training speedup and 31x GPU memory reduction in our baseline case, and enabling thermal analysis at resolutions previously infeasible due to GPU memory constraints. Third, we propose a confidence score to evaluate the trustworthiness of the predicted results, and further develop a hybrid optimization workflow that combines operator learning with finite difference (FD) using Generalized Minimal Residual (GMRES) method for incremental solution refinement, enabling efficient and trustworthy thermal optimization. Experimental results demonstrate that DeepOHeat-v1 achieves accuracy comparable to optimization using high-fidelity finite difference solvers, while speeding up the entire optimization process by 70.6× in our test cases, effectively minimizing the peak temperature through optimal placement of heat-generating components. Open source code is available at https://github.com/xlyu0127/DeepOHeat-v1.