Predicting Time-Dependent Flow Over Complex Geometries Using Operator Networks

TL;DR

This paper introduces a geometry-aware Deep Operator Network that predicts unsteady flow fields efficiently across various shapes, achieving high accuracy and significant speedups over traditional CFD methods, with detailed diagnostics for long-term fidelity.

Contribution

The work presents a novel time-dependent Deep Operator Network that encodes geometry via SDF and flow history, enabling rapid and accurate flow predictions for complex shapes.

Findings

Achieves ~5% relative L2 error on unseen shapes

Provides up to 1000X speedup over CFD simulations

Identifies error accumulation in fine-scale wakes for sharp geometries

Abstract

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. 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, trained on 841 high-fidelity simulations. On held-out shapes, it attains $\sim 5\%$ relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.