AI summaryⓘ
The authors explored a way to design aerodynamic shapes by working backward from limited flow data using Bayesian methods, which also estimate uncertainty. They showed that using neural networks called neural operators as fast stand-ins for expensive fluid simulations allows preserving important statistical details, even in tricky flow conditions like shocks. They found that how you describe the shape matters for reliable results and that their approach speeds up the process dramatically, from hours to under a second. They also tested a quick method to directly predict the shape without uncertainty estimates. Overall, the authors demonstrate a practical way to speed up aerodynamic design while keeping trustworthy uncertainty information.
Bayesian inverse designcomputational fluid dynamicsMarkov chain Monte Carloneural operatorsquasi-one-dimensional nozzle flowcubic B-splinesDeep Operator NetworkNo-U-Turn Samplersurrogate modelinguncertainty quantification
Abstract
Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited by the cost of repeated high-fidelity simulations required for gradient-based Markov chain Monte Carlo (MCMC) sampling. While surrogate models are commonly proposed to reduce this cost, their effect on posterior geometry and uncertainty, especially for shock-dominated flows, remains poorly understood. In this work, we demonstrate that neural operator surrogates can be embedded directly within the MCMC inference loop while preserving posterior structure. Using a fully Bayesian inverse formulation of quasi-one-dimensional nozzle flow, we demonstrate that geometry parameterization plays a decisive role in identifiability and posterior conditioning, with cubic B-splines yielding stable and physically meaningful uncertainty estimates. Building on this formulation, a Deep Operator Network trained on CFD-generated data is substituted for the CFD solver within a No-U-Turn Sampler, while keeping the likelihood model, priors, and sampling configuration unchanged. Across sparse to fully observed regimes, surrogate-based inference reproduces the posterior geometry and uncertainty trends of the CFD reference. As a result of surrogate integration, total inference time is reduced to under one second, corresponding to a speedup exceeding three orders of magnitude. In addition, a direct inverse neural operator is examined as a deterministic alternative for inverse design, enabling single-shot geometry reconstruction without posterior sampling. These results demonstrate that neural operator-accelerated Bayesian inference enables practical, uncertainty-aware inverse design workflows for aerodynamic applications.