Predicting Time-Dependent Flow Over Complex Geometries Using Operator Networks

Abstract:Developing neural surrogates for unsteady flow that generalize across complex geometries and maintain accuracy over extended rollouts remains a critical challenge for accelerating flow simulations. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, and is trained using 841 high-fidelity simulations from the FlowBench dataset (this https URL). The model attains $\sim 5\%$ relative L2 single-step error and up to 1000x speedups over CFD on 262 test geometries not used for training. We provide physics-centric rollout diagnostics, including probe-based phase lag and Strouhal frequency analysis, to quantify long-horizon fidelity. These reveal accurate near-term transients but systematic error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigation strategies including physics-informed regularization and diffusion-based refinement. Code, splits, and scripts are openly released at: this https URL to support reproducibility and benchmarking.

Fluid Dynamics (physics.flu-dyn); Machine Learning (cs.LG)

arXiv:2512.04434 [physics.flu-dyn]

(or arXiv:2512.04434v2 [physics.flu-dyn] for this version)

https://doi.org/10.48550/arXiv.2512.04434 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1016/j.cma.2026.118931 Focus to learn more DOI(s) linking to related resources

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