Reduction of Interface-Induced Order Degradation via a Conditional Hybrid Neural-IMEX Framework

High-order implicit-explicit (IMEX) schemes are effective for stiff parabolic partial differential equations when temporal regularity is compatible with the active multistep stencil. In moving-interface problems, a fixed Eulerian node may undergo a rapid transition as a diffuse interface crosses the grid, allowing stored multistep history to mix incompatible local regimes. This paper develops a conditional hybrid Deep Neural Galerkin-IMEX (DNG-IMEX) framework for this order-degradation mechanism. A classical IMEX-BDF3 backbone is retained on smooth intervals, whereas flagged event windows are treated by a localized neural/subcycle bridge followed by restart-consistent history reconstruction. The formulation separates the weak parabolic setting from the additional smoothness used for pointwise interface kinematics and proves a Sobolev-level transport estimate, a weak energy estimate, and a conditional propagation result under explicit flagged/restart defect bounds. Numerical tests on a manufactured Allen–Cahn benchmark show that event-aligned restarting suppresses the dominant history-contamination defect. A benchmark diagnostic realization localizes corrections with available event information and improves the baseline when event windows are resolved and the detector remains selective. Interface-thickness and cost tests indicate that sharper interfaces require stronger event resolution and that the present correction pipeline has non-negligible overhead. These findings support selective interface-aware enhancement of classical IMEX time integration.