Stiff Circuit System Modeling via Transformer

TL;DR

The paper tackles the difficulty of accurately simulating stiff circuits with physics-based SPICE models, which are costly and risk IP leakage, by introducing a transformer-based black-box surrogate that combines Crossformer with Kolmogorov-Arnold Networks. The approach leverages DS-W embeddings and a KAN-augmented decoder to capture multi-scale temporal and input-output relationships, achieving superior fidelity on SPICE-generated ADC data. Empirical results show the proposed model reduces the Normalized RMSE and converges faster than state-of-the-art CTRNN baselines, demonstrating practical speedups for large-scale circuit validation. This work suggests that attention-based, physics-informed transformers can significantly accelerate circuit design workflows while preserving accuracy and robustness under stiff dynamics.

Abstract

Accurate and efficient circuit behavior modeling is a cornerstone of modern electronic design automation. Among different types of circuits, stiff circuits are challenging to model using previous frameworks. In this work, we propose a new approach using Crossformer, which is a current state-of-the-art Transformer model for time-series prediction tasks, combined with Kolmogorov-Arnold Networks (KANs), to model stiff circuit transient behavior. By leveraging the Crossformer's temporal representation capabilities and the enhanced feature extraction of KANs, our method achieves improved fidelity in predicting circuit responses to a wide range of input conditions. Experimental evaluations on datasets generated through SPICE simulations of analog-to-digital converter (ADC) circuits demonstrate the effectiveness of our approach, with significant reductions in training time and error rates.

Figures (7)

• Figure 1: Our model leverages Crossformer crossformer and KAN KAN for time-series forecasting. Specifically, Crossformer is used to incorporate input time-series information. Then, KAN is added to the decoder layer to project outputs to the desired forecasting dimensions.
• Figure 2: Schematic of our 1.5-Bit stage sub ADC.
• Figure 3: One example data record taken from our generated dataset. The top three columns are input signals with low and high frequencies. The bottom two columns are the ground truth outputs the model predictions want to fit. The stiffness in the output signals are challenging for time-series prediction models.
• Figure 4: Fitting result comparison on one example data record. Crossformer + KAN prediction has a more stable prediction for output 1 (Vout1) as it captures well the stiffness and the plateau. For output 2 (Vout2), Crossformer + KAN has a more accurate prediction on stiff signal changes and it reduces the fluctuations shown in the CTRNN.
• Figure 5: Learning curves comparison for all models. CTRNN has requires more epochs to converge than Crossformer only and Crossformer + KAN. By adding KAN with increased neurons to Crossformer, the model becomes more powerful in learning the training data, leading to the minimum validation loss among all models.