Physics-Informed Neural Networks for High-Fidelity Electromagnetic Field Approximation in VLSI and RF EDA Applications

The increasing complexity of Very Large Scale Integration (VLSI) circuits and Radio Frequency (RF) systems demands sophisticated electromagnetic field analysis capabilities that traditional Electronic Design Automation (EDA) tools struggle to provide efficiently. This research presents a novel Physics-Informed Neural Network (PINN) framework specifically tailored for high-fidelity electromagnetic field approximation in VLSI and RF Electronic Design Automation applications. The proposed methodology integrates Maxwell's equations with advanced neural network architectures to enable accurate field prediction across diverse frequency ranges from DC to millimeter-wave operations while maintaining computational efficiency suitable for interactive design workflows. Through comprehensive validation across representative VLSI interconnect structures, RF passive components, and millimeter-wave integrated circuits, our PINN framework demonstrates superior accuracy compared to conventional moment-based methods while achieving computational speedup factors of 45-150× for typical design scenarios. The framework successfully captures complex electromagnetic phenomena including substrate coupling, crosstalk mechanisms, and frequency-dependent losses with mean absolute errors below 3.8% across frequency ranges spanning DC to 300 GHz. The adaptive mesh-free formulation eliminates geometric discretization constraints that limit traditional EDA tools, enabling seamless analysis of irregular conductor geometries and multi-layer dielectric stackups common in advanced semiconductor processes. Real-time field visualization capabilities facilitate intuitive understanding of electromagnetic coupling mechanisms, supporting design optimization workflows that were previously computationally prohibitive. The framework incorporates specialized handling of conductor loss mechanisms, dielectric dispersion effects, and substrate characteristics specific to semiconductor manufacturing processes, ensuring practical relevance for modern VLSI and RF design challenges. Validation against commercial EDA software demonstrates comparable accuracy for standard benchmarks while providing substantial performance advantages for parametric analysis and optimization applications critical to contemporary circuit design methodologies.