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

2025-05-17

AI Summary

To address the high computational cost and challenges in modeling chaotic transients in high-order nonlinear circuit simulation, this paper proposes a nested Transformer framework integrating S-domain analytical methods with neural operators. The method introduces a novel Jacobian-free iterative paradigm driven by S-domain partial fraction decomposition, reducing computational complexity from O(n³) to O(n). It further establishes, for the first time, a synergistic architecture comprising an S-domain encoder and a physics-guided attention correction operator, jointly incorporating modal residual modeling and neural differential operators. Evaluated on nonlinear circuits of order 1–10, the approach achieves an R² score of 0.99 relative to HSPICE, with up to 18× speedup. It significantly improves both accuracy and scalability in time-domain response prediction for high-dimensional, strongly nonlinear, and chaos-sensitive systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Hardware-aware ML

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

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.

Problem

• Simulating high-order nonlinear systems with computational efficiency
• Overcoming bifurcation-induced instability in VLSI backend design
• Reducing computational complexity from O(n^3) to O(n)

Innovation

• Nested transformer weaving for scalable nonlinear systems
• Partial-fraction decomposition reduces complexity to linear
• S-domain encoder with attention-based correction operator