Predicting Time-Dependent Flow Over Complex Geometries Using Operator Networks

2025-12-03

AI Summary

To address the challenge of efficiently and accurately predicting unsteady flow fields over complex geometries, this paper proposes a time-dependent, geometry-aware deep operator network. Methodologically, it pioneers the integration of signed distance field (SDF) encoding with convolutional neural network (CNN)-based temporal modeling to construct an end-to-end geometry-to-flow-field mapping architecture. Trained on 841 high-fidelity CFD simulations, the model incorporates physics-informed diagnostic metrics to assess long-term prediction reliability. Experiments demonstrate that, on both unseen parametric and non-parametric geometries, the method achieves approximately 5% single-step relative L² error while accelerating inference by up to 1000× compared to conventional CFD solvers—substantially outperforming existing data-driven approaches. To foster reproducibility and community benchmarking, the source code, dataset splits, and evaluation scripts are publicly released.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Predict unsteady fluid flows around complex parametric shapes
• Achieve fast surrogate modeling with geometry generalization capability
• Address error accumulation in long-term flow predictions

Innovation

• Geometry-aware Deep Operator Network for flow prediction
• Uses signed distance field and CNN for encoding
• Achieves 1000X speedup over traditional CFD simulations