PRISM-UDE：通过通用微分方程对3nm FinFET进行物理正则化迭代符号建模

中文摘要 AI 辅助

紧凑型晶体管模型是电路仿真的数学基础。然而，在3nm等先进节点上，输运物理变得过于复杂，传统手工推导的方程难以精确捕捉。另一方面，纯数据驱动的神经替代模型在电路求解器内部数值不稳定，且对其自身预测无法提供物理洞察。我们提出PRISM-UDE（通过通用微分方程进行物理正则化迭代符号建模），这是一个将小型神经网络嵌入基于物理的晶体管模型中的框架，仅利用网络学习解析基线未能捕捉的输运行为，而非完全取代物理。训练完成后，该神经校正通过符号回归蒸馏为单一、可解释的闭式表达式，使最终模型完全解析且可直接用于仿真器。应用于3nm FinFET基准数据集时，与标准纯物理基线相比，PRISM-UDE将预测误差降低六倍以上（从70.33%降至11.01%）。蒸馏后的表达式几乎精确地保持了这一精度，同时完全消除了神经网络。我们进一步在SPICE电路仿真器内部直接验证提取的表达式，确认在静态偏置扫描和动态开关条件下均具有稳定、物理一致的行为。

英文摘要

Compact transistor models are the mathematical backbone of circuit simulation. However, at advanced nodes such as 3nm, transport physics becomes too complex for traditional hand-derived equations to capture accurately. Purely data-driven neural surrogates, on the other hand, are numerically unstable inside circuit solvers and offer no physical insight into their own predictions. We introduce PRISM-UDE (Physics-Regularized Iterative Symbolic Modeling via Universal Differential Equations), a framework that embeds a small neural network inside a physics-based transistor model, using the network only to learn the transport behavior that the analytical baseline misses, rather than replacing the physics altogether. Once trained, this neural correction is distilled into a single, interpretable closed-form expression via symbolic regression, making the final model fully analytical and simulator-ready. Applied to a 3nm FinFET benchmark dataset, PRISM-UDE reduces prediction error more than sixfold (70.33% to 11.01%) relative to the standard physics-only baseline. The distilled expression preserves this accuracy almost exactly while eliminating the neural network entirely. We further validate the extracted expression directly inside a SPICE circuit simulator, confirming stable, physically consistent behavior under both static bias sweeps and dynamic switching conditions.

发表机构

• The University of Texas at Austin（德克萨斯大学奥斯汀分校）
• Vizuara AI Labs（Vizuara人工智能实验室）

机构由 AI 辅助整理，请以论文原文为准。