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

TL;DR

S-Crescendo introduces a nested transformer framework that combines S-domain analysis with neural operators, enabling scalable and accurate simulation of high-order nonlinear systems with reduced computational cost.

Contribution

The paper presents a novel nested transformer weaving framework that leverages partial-fraction decomposition to efficiently simulate high-order nonlinear systems, reducing complexity from cubic to linear.

Findings

Achieves up to 0.99 R^2 accuracy against HSPICE

Accelerates simulation by up to 18 times

Validates on networks from order-1 to order-10

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.