用Transformer架构加速高阶非线性电路仿真，提升18倍速度
S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation
- 将传递函数分解为一阶模态项，跳过传统迭代求解
- 计算复杂度从O(n³)降至O(n)，测试准确率达0.99 R²
- 适合需要高速高精度电路仿真的工程师与研究人员
高阶非线性系统仿真需大量计算资源，尤其在现代VLSI后端设计中，分岔引起的不稳定性和类混沌瞬态行为带来挑战。本文提出S-Crescendo——一种嵌套Transformer编织框架，融合S域表示与神经算子，实现高阶非线性网络的可扩展时域预测，通过牛顿-拉夫逊法缓解传统求解器的计算瓶颈。利用n阶传递函数的部分分式分解，将其化为具有重极点和残差的一阶模态项，避免基于雅可比矩阵的迭代，将计算复杂度从立方级O(n³)降至线性O(n)。所提架构将S域编码器与基于注意力的修正算子无缝集成，同时分离主导响应并自适应捕捉高阶非线性特性。在1至10阶网络上验证，方法对HSPICE基准波形的测试集R²最高达0.99，仿真加速最高达18倍，为高维非线性建模提供可扩展、物理感知的解决方案。
原文摘要 · Abstract (English)
Simulation of high-order nonlinear system requires extensive computational resources, especially in modern VLSI backend design where bifurcation-induced instability and chaos-like transient behaviors pose challenges. We present S-Crescendo - a nested transformer weaving framework that synergizes S-domain with neural operators for scalable time-domain prediction in high-order nonlinear networks, alleviating the computational bottlenecks of conventional solvers via Newton-Raphson method. By leveraging the partial-fraction decomposition of an n-th order transfer function into first-order modal terms with repeated poles and residues, our method bypasses the conventional Jacobian matrix-based iterations and efficiently reduces computational complexity from cubic $O(n^3)$ to linear $O(n)$.The proposed architecture seamlessly integrates an S-domain encoder with an attention-based correction operator to simultaneously isolate dominant response and adaptively capture higher-order non-linearities. Validated on order-1 to order-10 networks, our method achieves up to 0.99 test-set ($R^2$) accuracy against HSPICE golden waveforms and accelerates simulation by up to 18(X), providing a scalable, physics-aware framework for high-dimensional nonlinear modeling.
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