Physics-supervised Convergent Born Neural Operators for Full Waveform Modeling and Inversion

Full Waveform Inversion (FWI) is vital for subsurface resource exploration and geological hazard monitoring, but remains computationally prohibitive. Deep learning-based acceleration faces three core obstacles: scarce supervised labels, unstable physics-constrained training, and difficulty in enforcing accurate open-boundary modeling under broadband settings. We propose Physics-supervised Convergent Born Neural Operators (CBNO), a framework whose central mechanism learns wavefield mappings without paired wavefield labels by minimizing a Convergent Born Series (CBS) fixed-point discrepancy. CBS updates with Perfectly Matched Layers (PML) provide the physical training signal, avoiding the need for precomputed target wavefields. To support broadband prediction, frequency-partitioned Axial-AFNO experts combine shared low-rank projections with axis- and wavenumber-aware gates. The trained surrogate is then frozen and used in differentiable inversion, where upgoing-wave separation emphasizes weak reflection signals. Empirically, CBNO achieves highly accurate forward modeling on OpenFWI with a 10× speedup over the CBS reference solver, enables zero-shot transfer of the frozen forward surrogate to inversion on 2D Marmousi and Overthrust benchmarks, and demonstrates extensibility through separately trained 3D forward models.