Conformal Uncertainty-Aware Physics-Informed Neural Networks for Reliable Electromagnetic Field Prediction in VLSI Interconnects
DOI:
https://doi.org/10.54097/56shkz94Keywords:
Physics-informed neural networks, conformal prediction, uncertainty quantification, VLSI interconnects, electromagnetic field prediction, parasitic extraction, EDAAbstract
Electromagnetic field prediction in very-large-scale integration (VLSI) interconnects is increasingly constrained by two competing requirements: field solvers must remain physically faithful near conductor edges and material interfaces, yet they must also provide calibrated reliability indicators for fast design-space exploration. This paper proposes a conformal uncertainty-aware physics-informed neural network (UQ-PINN) for quasi-static electromagnetic field approximation in a two-layer interconnect cross-section. The method combines a random-feature neural representation with boundary, sparse observation, and electroquasistatic residual constraints, and then converts ensemble uncertainty into finite-sample prediction intervals using split conformal calibration. The scope is deliberately reproducible: no measured silicon data are claimed. A deterministic finite-difference solution of div (epsilon grad phi)=0 is used as the reference benchmark, and all reported values are generated by the accompanying code. On the benchmark, the physics-informed ensemble obtains a potential MAE of 0.02057 V and an electric-field magnitude relative L2 error of 17.69%, improving the sparse data-only neural baseline. The conformalized interval achieves 90.60% empirical coverage for a 90% target, whereas the uncalibrated ensemble interval reaches only 66.63%. These results indicate that physics constraints and conformal calibration can jointly support reliable electromagnetic surrogates for early-stage EDA analysis without overstating the substitute for sign-off full-wave verification.
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