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

• URL: http://arxiv.org/abs/2505.11843v1
• Date: Sat, 17 May 2025 05:06:58 GMT
• Title: S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation
• Authors: Junlang Huang, Hao Chen, Li Luo, Yong Cai, Lexin Zhang, Tianhao Ma, Yitian Zhang, Zhong Guan,
• Abstract summary: S-Crescendo is a nested transformer weaving framework that synergizes S-domain with neural operators for scalable time-domain prediction.<n>Our method achieves up to 0.99 test-set ($R2$) accuracy against HSPICE golden waveforms and simulation accelerates by up to 18(X)
• Score: 4.945568106952893
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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