基于算子网络的复杂几何结构瞬态流动预测

摘要

目前仍难以构建能够快速泛化几何形状的非定常流动替代模型。我们提出了一种时间相关的几何感知深度算子网络，可预测参数化与非参数化形状周围中等雷诺数流动的速度场。该模型通过符号距离场主干网络编码几何信息，通过卷积神经网络分支编码流动历史，基于841组高保真仿真数据进行训练。在未见过的几何形状上，模型实现了约5%的相对L2单步误差，计算速度较计算流体力学方法提升高达1000倍。我们提供了以物理量为核心的滚动预测诊断方法（包括测点相位误差和散度范数）来量化长期预测精度。结果表明模型能准确预测短期瞬态流动，但在精细尺度尾流中会出现误差累积，这种效应在尖角几何形体中最为显著。我们分析了失效模式并提出了实用改进方案。代码、数据分割和脚本已开源发布（https://github.com/baskargroup/TimeDependent-DeepONet），以支持可复现性研究与基准测试。

English

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.

基于算子网络的复杂几何结构瞬态流动预测

Predicting Time-Dependent Flow Over Complex Geometries Using Operator Networks

摘要

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