用于半导体热机械可靠性的递归Transformer
Recursive transformers for semiconductor thermo-mechanical reliability
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中文总结 AI 辅助
本文针对小数据工程代理建模的过拟合与资源开销问题，评估三种递归Transformer架构，验证其在两项任务中可实现预测精度、参数效率与计算成本的有效权衡。
中文摘要 AI 辅助
基于Transformer的代理模型正越来越多地用于替代工程设计中昂贵的第一性原理模拟。但传统Transformer架构对于工程设计空间中典型的小型低维数据集而言，往往参数冗余，而这类大型模拟数据的生成成本高昂。在此情况下，过剩的参数容量会导致过拟合而非精度提升，同时还会产生不必要的内存与计算开销。这促使人们转向关注额外计算而非额外可学习参数的架构。本文对三种用于先进封装热机械分析的递归Transformer范式开展了硬件感知评估：a)微型递归模型、b)本文提出的深度递归Transformer、c)简单递归Transformer。我们系统比较了它们的预测性能（召回率、平均倒数排名）、参数数量、计算复杂度（浮点运算数），为资源受限场景下选择递归Transformer架构提供实用设计准则。我们在两项低维工程预测任务上验证了该原理：1)先进半导体封装的热机械可靠性分析，其中热循环产生的应力与翘曲需在昂贵的有限元分析（FEA）下，在实验设计扫描中反复评估；2)电容场的拉普拉斯偏微分方程迭代数值求解器。总体而言，递归权重共享Transformer为小数据工程代理建模提供了预测精度、参数效率与计算成本间有效且可泛化的权衡。
英文摘要
Transformer-based surrogate models are increasingly used to replace expensive first-principles simulation in engineering design. But conventional transformer architectures are often over parameterized for the small, low-dimensional datasets typical of engineering design spaces, where large simulation data is expensive to generate. Under these conditions, excess parameter capacity leads to overfitting rather than improved accuracy, while also incurring unnecessary memory and compute overhead. This motivates a shift towards architectures that focus on additional compute rather than additional learnable parameters. This paper presents a hardware-aware evaluation of three recursive transformer paradigms for surrogate thermo-mechanical analysis of advanced packages: a)Tiny Recursive Model, b) our proposed Depth Recursive transformer, c) and a simple recursive transformer. We systematically compare their predictive performance (Recall, Mean Reciprocal Rank), parameter count, computational complexity (FLOPs), providing practical design guidelines for selecting recursive transformer architectures under resource-constrained scenarios. We validate this principle on two low-dimensional engineering prediction tasks: 1) thermo-mechanical reliability analysis of advanced semiconductor packages, where stress and warpage from thermal cycling must be evaluated repeatedly across a design-of-experiments sweep under costly finite element analysis (FEA). 2) Laplace PDE iterative numerical solver for capacitance field. Overall, recursive weight-sharing transformers provide an effective and generalizable trade-off between prediction accuracy, parameter efficiency, and computational cost for small data engineering surrogate modeling.
