标题： DeepOHeat-v1：高效算子学习在3D-IC设计中快速且可信赖的热模拟与优化 显示英文标题

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

摘要： 热分析在三维集成电路（3D-IC）设计中至关重要，因为其功率密度增加且热量耗散路径复杂。 尽管操作学习框架如DeepOHeat在加速热模拟方面展示了有希望的初步结果，但在多尺度热模式的预测能力、训练效率以及设计优化期间结果的可信度方面仍面临关键限制。 本文提出了DeepOHeat-v1，这是一种增强的基于物理信息的操作学习框架，通过三项关键技术革新解决了这些挑战。 首先，我们将具有可学习激活函数的Kolmogorov-Arnold网络作为主干网络集成，实现了多尺度热模式的自适应表示。 这种方法在两个代表性测试案例中分别实现了$1.25\times$和$6.29\times$的误差减少。 其次，我们引入了一种可分离的训练方法，沿坐标轴分解基函数，从而在我们的基准案例中实现了$62\times$的训练速度提升和$31\times$的GPU内存减少，并使分辨率受限于GPU内存的热分析成为可能。 第三，我们提出了一种置信度评分来评估预测结果的可信度，并进一步开发了一种混合优化工作流，结合了操作学习与有限差分（FD）使用广义最小残量（GMRES）方法进行增量解细化，实现了高效且可信的热优化。 实验结果表明， DeepOHeat-v1 在准确性上与高保真有限差分求解器的优化结果相当，同时在我们的测试用例中将整个优化过程加快了$70.6\times$，通过热源组件的最佳布局有效降低了峰值温度。 显示英文摘要

摘要： Thermal analysis is crucial in three-dimensional integrated circuit (3D-IC) design due to increased power density and complex heat dissipation paths. Although operator learning frameworks such as DeepOHeat 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 $1.25\times$ and $6.29\times$ 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 $62\times$ training speedup and $31\times$ 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 $70.6\times$ in our test cases, effectively minimizing the peak temperature through optimal placement of heat-generating components.