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

arXiv: https://arxiv.org/abs/2505.11843 · HTML: https://mlsanity.com/paper/2505.11843/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 69 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Deep Convolutional Networks in System Identification](https://mlsanity.com/paper/1909.01730/) (2019)
- [A Survey of Deep Learning: From Activations to Transformers](https://mlsanity.com/paper/2302.00722/) (2023)
- [Deep transfer learning for system identification using long short-term memory neural networks](https://mlsanity.com/paper/2204.03125/) (2022)
- [Deep active learning for nonlinear system identification](https://mlsanity.com/paper/2302.12667/) (2023)

## Abstract (arXiv)

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(n3) 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 (R2) accuracy against HSPICE golden waveforms and accelerates simulation by up to 18(X), providing a scalable, physics-aware framework for high-dimensional nonlinear modeling.