Stratified Conformal Prediction for Neural Fluid Surrogates: Spatially Adaptive Uncertainty Quantification via Vorticity

Abstract

Deep learning models, particularly neural operators, are revolutionizing computational fluid dynamics (CFD) by delivering rapid surrogate simulations that mitigate the significant computational costs linked to traditional numerical solvers. Nonetheless, a significant limitation of these AI-driven models is their inherent nature as statistical approximators, which do not inherently ensure adherence to physical conservation laws, thereby leading to a credibility gap in safety-critical engineering applications. Robust Uncertainty Quantification (UQ) is essential to bridge this gap and deploy these models reliably. Although conformal prediction offers distribution-free statistical assurances, conventional global calibration techniques fail when utilized in multiregime fluid systems, treating all flow states uniformly and leading to significantly exaggerated, overly conservative bounds. To address this issue, we propose a regime stratification conformal prediction framework where, instead of using a single global threshold, a regime-aware threshold will be used to compensate for the over or under-coverage. We used two traditional fluid flow datasets, the Lid-Driven Cavity and Cylinder datasets, and divided each into three regimes based on their Reynolds numbers. For the cavity dataset, three regimes achieve 89.7%, 90.4%, and 89.5% coverage with 88.78% tighter, 5.07% wider, and 86.19% tighter bounds, respectively. In terms of cylinder dataset, three regimes accomplished 87.6%, 89.8%, and 92.0% coverage alongside 99.65% tighter, 5.03% wider, and 99.69% tighter safety bounds. But the limitation of this approach is that it neglects the localized and significantly variable attributes of fluid dynamics by leveraging a uniform scalar constraint across the entire spatial domain. So to resolve this issue, a vorticity-adaptive spatial framework is introduced to transition from a uniform global bound for the whole domain to a physics-aware uncertainty map. The vorticity adaptive framework for the cavity dataset attained coverage rates of 89.67%, 90.08%, and 89.18%, with bounds that were 63.64% tighter, 22.87% wider, and 67.49% tighter, respectively. In the cylinder dataset, the vorticity adaptive framework attained coverage rates of 92.66%, 90.35%, and 90.72%, with bounds that were 84.77% tighter, 20.56% wider, and 77.88% tighter, respectively. An ancillary analysis of pressure gradients was conducted to assess the effects of pressure variations across the spatial domain, building on the initial vorticity findings.