Towards Physics-informed Deep Learning for Turbulent Flow Prediction (1911.08655v4)

Abstract: While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatiotemporal velocity fields of large-scale fluid flow simulations of relevance to turbulence modeling and climate modeling. We adopt a hybrid approach by marrying two well-established turbulent flow simulation techniques with deep learning. Specifically, we introduce trainable spectral filters in a coupled model of Reynolds-averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES), followed by a specialized U-net for prediction. Our approach, which we call turbulent-Flow Net (TF-Net), is grounded in a principled physics model, yet offers the flexibility of learned representations. We compare our model, TF-Net, with state-of-the-art baselines and observe significant reductions in error for predictions 60 frames ahead. Most importantly, our method predicts physical fields that obey desirable physical characteristics, such as conservation of mass, whilst faithfully emulating the turbulent kinetic energy field and spectrum, which are critical for accurate prediction of turbulent flows.

• The paper introduces TF-Net, which integrates trainable spectral filters with a U-Net architecture to achieve an 11.1% reduction in RMSE for turbulent flow predictions.
• The model produces physically coherent predictions that respect conservation laws and accurately capture the turbulent kinetic energy spectrum.
• It offers a scalable, efficient framework that dynamically adjusts to multi-scale turbulence, promising significant impacts in industrial CFD and climate modeling.

Analysis of "Towards physics-informed deep learning for turbulent flow prediction"

The paper "Towards physics-informed deep learning for turbulent flow prediction" presents an innovative approach to addressing the computational challenges associated with predicting turbulent flows. This research uniquely combines deep learning techniques with well-established methods from computational fluid dynamics (CFD) to propose a new framework, Turbulent-Flow Net (TF-Net), designed to enhance the accuracy and efficiency of predicting turbulent flow dynamics.

Summary of the Approach

TF-Net leverages the principles of hybrid CFD techniques such as Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES), which traditionally model different scales within turbulent flows. These scales encompass large eddies that carry most of the energy and smaller turbulent motions that are resolved to varying extents depending on computational resources. The model introduces trainable spectral filters for these components, effectively merging them with a deep learning framework anchored by a specialized U-Net architecture. This setup enables the prediction of turbulent flows over 60 frames ahead, demonstrating TF-Net’s capability to capture the non-linear dynamics of turbulent systems.

Key Findings and Contributions

1. Reduction in Prediction Error: The TF-Net model achieves an 11.1% reduction in RMSE for prediction accuracy and significant improvements in capturing the energy spectrum and turbulence kinetic energy compared to state-of-the-art baselines, showcasing its ability to accurately forecast turbulent flow fields.
2. Physically Coherent Predictions: Critical to any model predicting turbulent flow is its ability to respect physical laws, such as the conservation of mass and the accurate representation of the turbulent kinetic energy field and spectrum. TF-Net predictions align closely with these physical characteristics, reinforcing its potential applicability in real-world scenarios where such fidelity is paramount.
3. Scalable Framework: The approach is not contingent on preset filter specifications but instead uses trainable filters, allowing TF-Net to adjust to various scales within the turbulent flow data dynamically.
4. Computational Efficiency: Despite the complexity of modeling turbulent flows, TF-Net demonstrates improved computation time over traditional methods, particularly highlighted in its ability to generate accurate simulations faster than some numerical methods traditionally used in CFD.

Implications and Future Directions

The integration of physics-informed strategies into deep learning models like TF-Net sets a precedent for future research in areas demanding high fidelity and efficiency, such as climate modeling and industrial fluid dynamics. By pioneering a method that respects the underlying physical laws while utilizing the data-driven power of deep learning, this paper opens new avenues for research into hybrid models that can efficiently tackle multi-scale problems inherent in natural and engineered systems.

Looking forward, extending the TF-Net approach to three-dimensional problems and incorporating additional physical variables such as pressure or temperature could further enhance its applicability. Moreover, refining the model’s scalability could potentially bring about vast improvements in industrial and environmental applications where computational resources are a limiting factor.

In conclusion, "Towards physics-informed deep learning for turbulent flow prediction" presents a meaningful advancement in the confluence of deep learning and fluid dynamics. By addressing some of the inherent complexities and computational demands of turbulence prediction, this work lays foundational insights that may inspire future innovations in AI-powered solutions for complex physical phenomena.