Conditions under which hybrid surrogate/high-fidelity roll-outs degrade in accuracy

Investigate when and why accuracy degrades in hybrid simulations that alternate neural‑operator forward leaps with high‑fidelity relaxation steps for liquid‑metal dealloying phase‑field models; identify the mechanisms by which neural‑operator outputs used as initial conditions may induce instabilities or un‑physical behavior in the semi‑implicit spectral high‑fidelity solver, including potential violations of periodic boundary conditions, and characterize how such effects depend on the number of relaxation steps.

Background

The study evaluates hybrid schemes that interleave surrogate forward passes with high-fidelity relaxation steps. Contrary to expectations, increasing the number of relaxation steps did not consistently improve accuracy; for some architectures (e.g., FNO and vanilla AFNO), accuracy deteriorated and the interface became ill-defined.

The authors hypothesize that the high-fidelity solver may be sensitive to initial states produced by data-driven operators that do not explicitly enforce physical constraints like periodic boundary conditions, potentially triggering solver instabilities or un-physical evolution when used as relaxation starting points.

References

Additional investigation as to why and when accuracy may degrade is left to future work, but we conjecture that this degradation is linked to the robustness of the high-fidelity solver to un-physical initial conditions.

— Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone (2406.17119 - Bonneville et al., 24 Jun 2024) in Section 5.3 (Results)