Physics-Informed Neural Networks for PCB Parasitic Extraction

Full 3D electromagnetic field solvers (HFSS, CST, Ansys Q3D) are the gold standard for PCB parasitic extraction, but they are prohibitively slow for the inner-loop iterations that modern AI-driven design requires. A single via simulation can take minutes; a full design verification can take days.

Physics-Informed Neural Networks

A Physics-Informed Neural Network (PINN) embeds the governing Maxwell's equations as soft constraints in the loss function. Rather than learning from data alone, the network is penalized for solutions that violate the underlying physics. This means the model generalizes reliably to geometries and operating frequencies outside the training set — a critical requirement for PCB design where the parameter space is effectively infinite.

Our PINN architecture takes as input the geometric parameters of a PCB structure (trace width, height, dielectric constant, loss tangent, frequency) and outputs the S-parameters across the relevant band. The network is trained on a dataset of 500,000 full-wave simulations generated over 18 months.

Performance

On a held-out test set of 50,000 structures not seen during training, our PINN achieves a mean S-parameter error of 0.15 dB magnitude and 1.2° phase across 0.1–50 GHz. Inference takes 0.8 ms on a standard CPU — roughly 1,000× faster than a comparable HFSS simulation.

Integration with FlowSim

In FlowSim, the PINN extractor runs continuously as the designer modifies the layout, providing real-time S-parameter feedback on all critical nets. When the designer requests a high-accuracy verification, the full field solver is invoked only on flagged structures — reducing total verification time by 90% without sacrificing accuracy where it matters.

This hybrid approach — PINN for exploration, field solver for sign-off — is the architecture underlying FlowSim's real-time simulation capability.