S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912380929179648 |
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| author | Huang, Junlang Chen, Hao Luo, Li Cai, Yong Zhang, Lexin Ma, Tianhao Zhang, Yitian Guan, Zhong |
| author_facet | Huang, Junlang Chen, Hao Luo, Li Cai, Yong Zhang, Lexin Ma, Tianhao Zhang, Yitian Guan, Zhong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_11843 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation Huang, Junlang Chen, Hao Luo, Li Cai, Yong Zhang, Lexin Ma, Tianhao Zhang, Yitian Guan, Zhong Signal Processing Machine Learning 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. |
| title | S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2505.11843 |