A Lower-envelope Eikonal Neural Operator
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We propose the Lower-envelope Eikonal Neural Operator (LENO), a physics-informed neural operator for eikonal equations with heterogeneous velocity fields and general source sets. LENO encodes the variational minimum principle of viscosity solutions by constructing source-wise candidate fields and taking their pointwise minimum. This lower-envelope structure enforces the boundary condition exactly and represents nonsmooth multi-source solutions without a soft boundary penalty. The model is trained without precomputed solution data, using a Godunov upwind residual as the sole training signal. Experiments on point and curve sources, piecewise velocity fields, and OpenFWI CurveVel-A and Style-A media show accurate agreement with fast-marching references.
