A Framework of Data Assimilation for Wind Flow Field by Physics-informed Neural Networks

This repository contains the source code for the research presented in the paper A Framework of Data Assimilation for Wind Flow Field by Physics-informed Neural Networks

1. Overview

The main program, main.py, is the training process, in which the wandb is included to search the optimized hyperparameter automatically. Physics-informed Neural Network (PINN) is defined in pinn_model.py under the framework of PyTorch. Four commonly available types of measurement data are supported: LoS wind speed, velocity vector, velocity component, and pressure. Given the turbulent nature of atmospheric boundary layer flow, the Reynolds-Averaged Navier-Stokes (RANS) equations are employed as the flow governing equations. The turbulence eddy viscosity, ${\nu _t}$, is directly predicted as an output variable of the PINN. The pred_write.py is used to reconstruct the wind flow field by a trained PINN. The reconstructed flow field data is written into .h5 files. The script transfer.py is used for online deployment of the pre-trained PINN, assimilating real-time measured data. All the requirements are included in requirement.txt.

2. Test case

The test wind flow field is an atmospheric boundary layer flow simulated by SOWFA (Simulator fOr Wind Farm Applications). The flow field within the horizontal plane upstream of the wind turbine site is chosen to be the test area of the proposed framework.

Section 3.1 of the paper investigates the accuracy of assimilating different types of measurement data. The flow field reconstructed by the trained model in Case 8, as well as the error compared to the actual values, are presented as follows.

The comparison of the spatial extrapolated wind flow field by the PINN trained in Case 8 with the ground truth within the region $x \in [-6D,2D]$, $y \in [-2D,2D]$. The dotted rectangular frame represents the range of equation points.

Since detailed flow field information is reconstructed, other flow field characteristics such as effective wind speed and instantaneous speed at a specific location can also be obtained. Effective wind speed is defined as the average of the wind speed projected onto the rotor plane:

$${\overline u_{eff} (x,t)} = \frac{1}{{{N_y}}}\sum\limits_{i = 1}^{{N_y}} {u(x,{y_i},t)},\quad {y_i} \in \left( { - D/2,D/2} \right)$$

3. Transfer learning

Section 3.4 of the paper examines the feasibility of deploying this framework online using transfer learning. The incorporation of transfer learning enables PINN to predict flow fields over extended periods. Historically, PINN has operated exclusively in an offline mode. This work presents a potential solution for online deployment. The pre-trained PINN is deployed online and then trained on the dataset of real-time measurement data over a certain period. The transfer learning duration required is less than the actual physical flow time, yet the model achieves acceptable accuracy in reconstructing the flow field for this period. At the wind turbine site, the maximum error between the effective wind speed predicted online and the actual wind speed is only 3.7%. This represents a significant improvement compared to models that have not undergone transfer learning.

It must be acknowledged that the prediction of velocity fluctuations is not as accurate as the fully trained PINN. The predicted flow fields displayed following also confirm this observation. The wind speed distribution and direction predicted by the PINN with transfer learning are broadly akin to the ground truth. However, there are some differences in the high-speed areas. It is observed that the intricate details of the wind flow field are not well predicted. The whole predicted wind flow field exhibits smoothness. In contrast, the wind speed distribution predicted by the PINN model without transfer learning shows significant deviations. The results have demonstrated the capability of the PINN, after transfer learning, to predict the evolution of the flow field over a longer period. Considering the scenario of online deployment, the network cannot be fully trained within the constraint of a time frame shorter than the physical flow duration. Despite this, transfer learning remains a promising application, with the potential to solve the long-term prediction weakness of PINN.

4. License

To further promote the utilization of renewable energy, the framework is fully open-sourced under the MIT License, and collaborative development is also encouraged.

5. Acknowledgments

Special thanks to Raissi Maziar for the inspiration and foundational work in the field of Physics-Informed Neural Networks. Thanks to Jincheng Zhang for his pioneering research of introducing PINN to wind energy, and for providing the simulation cases in the folder ./SOWFA.script.