Accelerating Bayesian inverse design in computational fluid dynamics using neural operators

2026-05-25

AI Summary

This work addresses the prohibitive computational cost of Bayesian inverse design in computational fluid dynamics (CFD), which stems from repeated high-fidelity simulations. To overcome this bottleneck, the authors embed a Deep Operator Network (DeepONet) as a surrogate model within the Markov chain Monte Carlo (MCMC) inference loop, achieving substantial acceleration of posterior inference without altering the likelihood, prior, or sampling configuration. The study demonstrates, for the first time, that neural operators can be seamlessly integrated into Bayesian inverse design frameworks and reveals the critical influence of geometric parameterization on problem identifiability and posterior conditioning. By combining the No-U-Turn Sampler with a direct inversion strategy, the proposed method accurately reconstructs posterior geometries and associated uncertainties matching CFD reference solutions across sparse to full observational settings, reducing inference time to under one second—yielding speedups exceeding three orders of magnitude.

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.

Problem

• Bayesian inverse design
• computational fluid dynamics
• surrogate models
• uncertainty quantification
• Markov chain Monte Carlo

Innovation

• neural operators
• Bayesian inverse design
• computational fluid dynamics
• surrogate modeling
• uncertainty quantification