S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation

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.

Fusing Global and Local: Transformer-CNN Synergy for Next-Gen Current Estimation

This paper presents a hybrid model combining Transformer and CNN for predicting the current waveform in signal lines. Unlike traditional approaches such as current source models, driver linear representations, waveform functional fitting, or equivalent load capacitance methods, our model does not rely on fixed simplified models of standard-cell drivers or RC loads. Instead, it replaces the complex Newton iteration process used in traditional SPICE simulations, leveraging the powerful sequence modeling capabilities of the Transformer framework to directly predict current responses without iterative solving steps. The hybrid architecture effectively integrates the global feature-capturing ability of Transformers with the local feature extraction advantages of CNNs, significantly improving the accuracy of current waveform predictions. Experimental results demonstrate that, compared to traditional SPICE simulations, the proposed algorithm achieves an error of only 0.0098. These results highlight the algorithm's superior capabilities in predicting signal line current waveforms, timing analysis, and power evaluation, making it suitable for a wide range of technology nodes, from 40nm to 3nm.