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We present a physics-constrained neural network (PCNN) approach to solvingMaxwell's equations for the electromagnetic fields of intense relativisticcharged particle beams. We create a 3D convolutional PCNN to map time-varyingcurrent and charge densities J(r,t) and p(r,t) to vector and scalar potentialsA(r,t) and V(r,t) from which we generate electromagnetic fields according toMaxwell's equations: B=curl(A), E=-div(V)-dA/dt. Our PCNNs satisfy hardconstraints, such as div(B)=0, by construction. Soft constraints push A and Vtowards satisfying the Lorenz gauge.

Physics-constrained 3D Convolutional Neural Networks for Electrodynamics