Predicting time-dependent flow over complex geometries using operator networks

Ali Rabeh

doi:10.1016/j.cma.2026.118931

Predicting time-dependent flow over complex geometries using operator networks

2026-03-26

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PRE

AI

Adarsh Krishnamurthy *

B

Baskar Ganapathysubramanian *

DOI：10.1016/j.cma.2026.118931

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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. The model attains  ∼ 5% relative L2 single-step error and up to 1000 ×  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 here to support reproducibility and benchmarking.

Keywords:

Deep Operator Network

Unsteady Flow Prediction

Geometry-aware Neural Networks

Signed Distance Field

Flow Simulation Acceleration

Predicting time-dependent flow over complex geometries using operator networks

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