Machine Learning Models for SI/PI Analysis with Meshed Planes

As data rates continue to scale into the multi-tens of gigabits per second, the tolerance for uncertainty in interconnect behavior has significantly diminished. At the same time, packaging and board-level technologies are evolving toward higher density, heterogeneous integration, and greater compliance with standards. These trends have driven widespread adoption of meshed reference planes, including cross-hatch ground planes in flexible and rigid-flex designs (Figure 1), and perforated planes with degassing holes in 3D-IC packages (Figure 2).

An article featured in the April issue of Signal Integrity Journal, "Machine Learning Models for SI/PI Analysis with Meshed Planes" by Cadence"s Jiyue Zhu, Regina Thahir, Xiaoyan Xiong, Gang Kang, and Jian Liu, presents machine learning (ML)-based modeling approaches that efficiently characterize signal integrity (SI) and power integrity (PI) behavior in systems with meshed planes.

Conventional approaches to modeling meshed planes rely on 3D full-wave EM solvers. However, a single metal layer may contain thousands to millions of apertures, making direct simulation computationally expensive and often impractical for iterative design flows. Furthermore, SI and PI effects must often be evaluated simultaneously, further increasing model complexity. The article presents ML-based modeling approaches that efficiently characterize SI and PI behavior in systems with meshed planes.

ANN Architecture and Hyperparameter Optimization

Artificial neural network (ANN) models are developed for pre-layout SI analysis of traces referenced to meshed ground planes. These models offer sufficient flexibility to approximate the nonlinear relationships between meshed-plane geometry and EM response. However, model performance is strongly influenced by hyperparameter selection, including hidden layer count, hidden dimension, learning rate, and training epochs.

Rather than relying on manual tuning or grid search, Gaussian process-based Bayesian optimization is employed to identify optimal ANN hyperparameters.

ML Models for Pre-Layout SI Analysis

To address these challenges, ML models are being introduced as surrogate models for EM-based SI analysis. They focus on traces referenced to meshed ground planes, particularly cross-hatch structures commonly used in flexible and rigid-flex boards. The outputs of the model include per-unit-length inductance and capacitance, single-ended trace impedance, propagation delay, and velocity, differential and common-mode impedance for coupled traces, and differential delay and delay mismatch. These outputs directly support pre-layout SI analysis and constraint definition.

The methods proposed in the article demonstrate high accuracy compared with 3D full-wave EM simulations, while achieving orders-of-magnitude reduction in computation time. The advantages are:

• Systematic exploration of the hyperparameter space
• Flexible search domains, allowing continuous parameter ranges rather than discretized values
• Efficient convergence, achieving improved accuracy with fewer training iterations

Notably, the hidden layer dimensions are not constrained to traditional powers-of-two conventions, enabling more efficient network configurations.

The results suggest that ML-enabled modeling can serve as a practical and scalable solution for SI/PI analysis of complex meshed-plane structures.

Conclusion

Meshed planes are becoming indispensable in modern electronic systems, yet they pose significant challenges for conventional SI and PI analysis methodologies. This article has discussed how ML-based modeling, combined with systematic hyperparameter optimization, offers a practical and accurate alternative to brute-force EM simulation. By enabling fast and reliable prediction of key SI metrics for traces referenced to meshed planes, the proposed approach supports efficient design-space exploration and informed engineering decision-making.

View the complete article and learn more about the Cadence Clarity 3D EM Solver, employed for the analysis of the models discussed in the article.