A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent L\'evy Jumps
arXiv:2606.01122v1 Announce Type: new Abstract: We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent L\'evy jumps, targeting a general failure mode of neural PDE methods: a learned solution can match headline scalar diagnostics while miscomputing an operator inside its training loss. The protocol pairs each neural solve with at least one from-scratch independent reference, decomposes the Hamiltonian into drift, diffusion, compensator, and nonlocal-integral components across a u-grid, and compares the value function and its low-order derivatives over a (t,x) grid before any argmax comparison. Applied to a standard CRRA-Merton-Variance-Gamma benchmark, it isolates a missing 1/2-mixture factor in the neural method's importance-proposal density that scaled the nonlocal integral by exactly half - a textbook signature of a constant proposal scale error, invisible to longer training, grid refinement, and truncation sweeps. With the bug

