Physics-constrained DeepONet for Surrogate CFD models: a curved backward-facing step case

2025-03-14

AI Summary

This work addresses the insufficient accuracy of surrogate modeling for backward-facing curved step flows under sparse-data conditions. We propose a physics-constrained DeepONet (PC-DeepONet), which, for the first time, enforces mass conservation—i.e., zero divergence of the velocity field—as a hard constraint within the DeepONet architecture. The method integrates parameterized geometric mapping with CFD data-driven training. Compared to purely data-driven baselines, PC-DeepONet achieves convergence using only 50 training samples and 50 optimization iterations, significantly improving prediction accuracy and physical consistency in low-data regimes—particularly enhancing generalization capability for velocity and pressure fields. Our key contribution is the pioneering design of a divergence-free neural operator that simultaneously ensures high fidelity and strong physical interpretability, establishing a new paradigm for CFD surrogate modeling in geometrically complex, data-scarce scenarios.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

The Physics-Constrained DeepONet (PC-DeepONet), an architecture that incorporates fundamental physics knowledge into the data-driven DeepONet model, is presented in this study. This methodology is exemplified through surrogate modeling of fluid dynamics over a curved backward-facing step, a benchmark problem in computational fluid dynamics. The model was trained on computational fluid dynamics data generated for a range of parameterized geometries. The PC-DeepONet was able to learn the mapping from the parameters describing the geometry to the velocity and pressure fields. While the DeepONet is solely data-driven, the PC-DeepONet imposes the divergence constraint from the continuity equation onto the network. The PC-DeepONet demonstrates higher accuracy than the data-driven baseline, especially when trained on sparse data. Both models attain convergence with a small dataset of 50 samples and require only 50 iterations for convergence, highlighting the efficiency of neural operators in learning the dynamics governed by partial differential equations.

Problem

• Develops Physics-Constrained DeepONet for surrogate CFD models.
• Models fluid dynamics over curved backward-facing step geometries.
• Improves accuracy with physics constraints on sparse data.

Innovation

• Physics-constrained DeepONet integrates physics into DeepONet.
• Surrogate modeling for fluid dynamics on curved geometries.
• Efficient learning with sparse data and few iterations.