[Paper Review] Fast Transient Simulation of High-Speed Channels Using Recurrent Neural Network

Thong Nguyen, Tianjian Lu+2 more|arXiv (Cornell University)|Jan 25, 2019

Electrostatic Discharge in Electronics28 references17 citations

TL;DR

This paper proposes using recurrent neural networks (RNNs), particularly Long Short-Term Memory (LSTM) networks, to accelerate transient simulation of high-speed channels by learning black-box macro-models from short circuit simulator sequences. The trained RNN predicts full eye diagrams with high accuracy and orders-of-magnitude faster computation than traditional SPICE-like simulators, achieving strong agreement with reference simulations while reducing runtime significantly.

ABSTRACT

Generating eye diagrams by using a circuit simulator can be very computationally intensive, especially in the presence of nonlinearities. It often involves multiple Newton-like iterations at every time step when a SPICE-like circuit simulator handles a nonlinear system in the transient regime. In this paper, we leverage machine learning methods, to be specific, the recurrent neural network (RNN), to generate black-box macromodels and achieve significant reduction of computation time. Through the proposed approach, an RNN model is first trained and then validated on a relatively short sequence generated from a circuit simulator. Once the training completes, the RNN can be used to make predictions on the remaining sequence in order to generate an eye diagram. The training cost can also be amortized when the trained RNN starts making predictions. Besides, the proposed approach requires no complex circuit simulations nor substantial domain knowledge. We use two high-speed link examples to demonstrate that the proposed approach provides adequate accuracy while the computation time can be dramatically reduced. In the high-speed link example with a PAM4 driver, the eye diagram generated by RNN models shows good agreement with that obtained from a commercial circuit simulator. This paper also investigates the impacts of various RNN topologies, training schemes, and tunable parameters on both the accuracy and the generalization capability of an RNN model. It is found out that the long short-term memory (LSTM) network outperforms the vanilla RNN in terms of the accuracy in predicting transient waveforms.

Motivation & Objective

• To reduce the computational cost of transient simulation in high-speed channels, especially under nonlinear conditions.
• To replace computationally intensive SPICE-like simulations with machine learning-based models that preserve accuracy.
• To develop a black-box RNN macro-modeling approach requiring minimal domain knowledge or complex circuit simulation.
• To evaluate the impact of RNN architecture, training schemes, and hyperparameters on accuracy and generalization in signal integrity applications.

Proposed method

• Train an RNN on a short transient waveform sequence generated from a SPICE-like circuit simulator.
• Use teacher-forcing with truncated back-propagation through time (TBPTT) to optimize the RNN parameters.
• Employ an Elman RNN (ERNN) topology with shared recurrent weights for efficient sequence modeling.
• Compare different RNN units: vanilla RNN, LSTM, and GRU, focusing on convergence and prediction accuracy.
• Use ReLU activation and Adam optimizer to improve training stability and convergence speed.
• Validate the trained RNN on long pseudo-random bit sequences (PRBS) to generate full eye diagrams.

Experimental results

Research questions

• RQ1 Can RNN-based models accurately predict transient waveforms in high-speed channels without explicit circuit modeling?
• RQ2 How do different RNN architectures (vanilla RNN, LSTM, GRU) compare in predicting nonlinear channel responses?
• RQ3 What is the impact of training sequence length and TBPTT window size on RNN generalization and numerical error accumulation?
• RQ4 Can the RNN model generalize to longer PRBS sequences beyond the training data?
• RQ5 How does the RNN-based approach compare in accuracy and speed to traditional SPICE-like simulation?

Key findings

• The LSTM network outperforms vanilla RNN and GRU in both convergence speed and prediction accuracy due to better handling of vanishing gradients.
• The RNN model achieves eye diagrams that show strong agreement with SPICE simulations, with optimal sampling points matching within 0.001 μs (e.g., 14.662 μs).
• Computation time is reduced by orders of magnitude compared to full SPICE simulation, with inference being significantly faster than iterative Newton-like solvers.
• Numerical error accumulates over long sequences due to TBPTT, degrading performance after hundreds of thousands of bits, indicating a limitation of current training methodology.
• The method requires no complex circuit simulations or domain-specific knowledge after initial training, enabling fast inference and model reuse.