Physics consistent conditional flow matching model as a plasma physics surrogate model

Abstract

Physics-informed surrogate modeling for steady-state systems often struggles with data scarcity and optimization instabilities from soft penalty losses. Unlike prevailing physics-informed generative methods that rely on explicit, differentiable PDE residuals during training, our framework targets systems where closed-form governing equations are unavailable or non-differentiable. We introduce a unified continuous-time conditional flow matching (CFM) framework for surrogate modeling and sparse data assimilation, evaluated on low-temperature plasma dynamics. By combining data-dependent interpolants with dynamic masking, our approach handles unconditioned prediction and missing-data imputation within a single architecture. We replace standard velocity matching with a direct state-prediction ( y-prediction) objective, eliminating variance-induced sampling inefficiencies in deterministic regimes. For inference, the formulation supports both time-dependent ODE integration (CFM- t) and an autonomous regime (CFM- 0) that enables measurement conditioning via anchor substitution. Global conservation laws are enforced via post-hoc geometric projections rather than loss regularizers. Results show that both CFM variants achieve superior accuracy, sample efficiency under data scarcity, and raw physical consistency over standard regressors. Furthermore, macroscopic constraints alone yield negligible reductions in test error, confirming the necessity of a data-driven generative prior over the physical manifold.