Sequence-to-Sequence Neural Surrogate Modeling of Transient Responses in High-Speed Links with Variable Design Parameters

Signal integrity (SI) analysis in printed circuit board (PCB) interconnects faces increasing complexity due to diverse integrated circuit (IC) buffer technologies, varying operating conditions, and manufacturing tolerances. Existing machine learning (ML) surrogate models for the prediction of SI metrics such as the inner eye contour, eye-height (EH), eye-width (EW), and transient waveform features often rely on fixed buffer parameters, limiting the adaptability across design and technology variations. This paper introduces a buffer-parameterized ML surrogate modeling methodology capable of handling cross-technology variations without retraining by treating IC buffer characteristics, e.g., clock frequency, supply voltage, rise/fall times, jitter, and internal resistors and capacitors, as model inputs in addition to the PCB parameters. To identify the optimal surrogate architecture for this high-dimensional space, tree-based methods (RFR/GBM), kernel methods (SVR/KRR), Gaussian process regression (GPR), and neural networks are compared. The buffer-parameterized approach is validated using a complex interconnect with a total of 44 design parameters. In addition to demonstrating strong generalization, the results show that neural networks outperform other ML models on large datasets, while the anisotropic GPR excels in low-data regimes. Finally, the practical value of the ML surrogate models is demonstrated through a cross-technology design space exploration and optimization scenario, which indicates large computational speedups for eye mask compliance checking compared to simulation.

This paper proposes a Mamba surrogate model with mixture-of-experts (MoE) routing to represent the transient dynamics of inverter-based resources. A Mamba surrogate model is a predictive machine learning model built on the Mamba architecture. MoE routing uses a router network to assign data-dependent weights to specialized subnetworks (experts). The resulting Mamba--MoE surrogate can perform two tasks: (i) closed-loop simulation and (ii) measurement-window forecasting of inverter transients. A single Mamba backbone with task conditioning and expert routing serves both tasks, replacing two separate specialists. Task-matched objectives fit each prediction form, and an adaptive conformal layer provides prediction intervals for both tasks. For the considered grid-following inverter, the unified surrogate model remains in the same low-error regime as a Mamba specialist pair while using 13% fewer parameters. The prediction intervals achieve 94--96% empirical mean marginal coverage across the two tasks. For transient dynamics---that is, beyond the vicinity of an equilibrium point---our surrogate model with MoE routing yields lower errors across all outputs in both tasks compared to a shared Mamba backbone without expert routing. A controller hardware-in-the-loop simulation validates our results and shows that adapting only the shared output head with limited measured data reduces held-out forecasting error.

Pre-layout design space exploration (DSE) for high-speed signal integrity (SI) analysis is often limited by the computational cost of simulations and iterative optimization algorithms within modern electronic design automation (EDA) workflows. While machine learning surrogate models accelerate the simulation step, optimizing designs still requires utilizing iterative black-box search methods. This iterative nature scales poorly, making multi-corner sweeps computationally expensive. As a solution, this paper proposes amortized neural optimization (ANO) for pre-layout SI design. ANO entirely eliminates iterative black-box inference by utilizing fully differentiable neural network surrogate models. ANO extracts analytical gradients from the surrogate to train a global optimization policy. Instead of solving the optimization problem repeatedly at inference, the optimization process is learned offline and therefore amortized. Once the ANO policy is trained, it maps different channel contexts directly to near-optimal design parameters in a single deterministic forward pass. The efficiency and accuracy of the ANO framework are demonstrated based on three complex SI design scenarios, including DDR5 decision feedback equalization (DFE), 9-dimensional SerDes Tx/Rx co-equalization, and DDR3 DQS differential pair routing to optimize eye diagram metrics under intra-pair skew constraints. By trading roughly 10% in optimality compared to instance-specific black-box algorithms, it realizes speedups of three to four orders of magnitude. For a large-scale 320,000-instance multi-corner SerDes sweep optimization, ANO collapses what would have taken days of computation using iterative search algorithms into a single batched forward pass that completes in milliseconds. This transforms computationally expensive SI optimization into real-time and interactive pre-layout DSE.