Physics-Guided Multi-Fidelity DeepONet for Data-Efficient Flow Field Prediction

2025-03-23

AI Summary

To address spatiotemporal forecasting under scarce high-fidelity flow field data, this paper proposes a physics-guided multi-fidelity DeepONet framework. The method introduces three key innovations: (1) a time-derivative-guided sampling strategy to prioritize physically informative spatiotemporal locations; (2) a learnable feature fusion network for adaptive integration of multi-fidelity representations; and (3) a freezing-based multi-fidelity transfer mechanism to preserve physical consistency while enhancing data efficiency. Additional technical components include temporal positional encoding, optimized point-wise sampling, and automatic mixed-precision training. Experiments demonstrate a 50.4% reduction in prediction error and a 96% decrease in training time. Remarkably, the model achieves full high-fidelity training accuracy using only 60% of the high-fidelity samples, outperforming single-fidelity baselines by 43.7% in accuracy—thereby jointly advancing precision, computational efficiency, and generalizability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Learning to Search

Application Category

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

Abstract

This study presents an enhanced multi-fidelity deep operator network (DeepONet) framework for efficient spatio-temporal flow field prediction, with particular emphasis on practical scenarios where high-fidelity data is scarce. We introduce several key innovations to improve the framework's efficiency and accuracy. First, we enhance the DeepONet architecture by incorporating a merge network that enables more complex feature interactions between operator and coordinate spaces, achieving a 50.4% reduction in prediction error compared to traditional dot-product operations. We further optimize the architecture through temporal positional encoding and point-based sampling strategies, achieving a 7.57% improvement in prediction accuracy while reducing training time by 96% through efficient sampling and automatic mixed precision training. Building upon this foundation, we develop a transfer learning-based multi-fidelity framework that leverages knowledge from pre-trained low-fidelity models to guide high-fidelity predictions. Our approach freezes the pre-trained branch and trunk networks while making only the merge network trainable during high-fidelity training, preserving valuable low-fidelity representations while efficiently adapting to high-fidelity features. Through systematic investigation, we demonstrate that this fine-tuning strategy not only significantly outperforms linear probing and full-tuning alternatives but also surpasses conventional multi-fidelity frameworks by up to 76%, while achieving up to 43.7% improvement in prediction accuracy compared to single-fidelity training. The core contribution lies in our novel time-derivative guided sampling approach: it maintains prediction accuracy equivalent to models trained with the full dataset while requiring only 60% of the original high-fidelity samples.

Problem

• Predict flow fields efficiently with scarce high-fidelity data
• Improve DeepONet accuracy via merge network and sampling strategies
• Leverage low-fidelity models to enhance high-fidelity predictions

Innovation

• Enhanced DeepONet with merge network for feature interactions
• Transfer learning-based multi-fidelity framework with frozen networks
• Time-derivative guided sampling reduces needed high-fidelity samples