A Foundation Model for Time-Harmonic Electromagnetic Behavior

3D electromagnetic (EM) systems underpin semiconductor packaging, conformal antennas, and consumer devices such as phones and wearables. Full-wave simulations are necessary to model these systems but remain costly across large design and frequency spaces, while existing surrogates typically specialize in a narrow design family and predict either fields or aggregate responses. We introduce the first EM foundation model for complex 3D systems, predicting both electromagnetic fields and scattering parameters for unseen devices. Our contribution is threefold. First, we generate a corpus of approximately 250k simulations spanning 25 template families of 3D printed-circuit-board and package structures. Second, we train a 340M-parameter model that predicts complex-valued electric and magnetic fields at arbitrary locations and S-parameters across frequencies and port pairs. Finally, we introduce $\text{EMVal}$, the first public evaluation suite for EM foundation models covering both data modalities. We find that joint field and S-parameter supervision preserves in-distribution S-parameter accuracy while reducing out-of-distribution error relative to S-parameter-only training, suggesting that field supervision encourages representations that generalize more effectively across geometry families. Also, ablations identify impedance-aware target scaling, a robust field objective, and relative spatial encoding as critical to accurate complex-field prediction. Ultimately, our model's full EM vector-field predictions provide a rich physical description of unseen devices that enables design-critical downstream calculations and visual debugging, opening a path toward general-purpose learned models of EM systems.