Model-free short-term fluid dynamics estimator with a deep 3D-convolutional neural network

Abstract

Deep learning models are not yet fully applied to fluid dynamics predictions, while they are the state-of-the-art solution in many other areas i.e. video and language processing, finance, robotics . Prediction problems on high-dimensional, complex dynamical systems require deep learning models devised to avoid overfitting while maintaining the required model complexity. In this work we present a deep learning prediction model based on a combination of 3D convolutional layers and a low-dimensional intermediate representation that is specifically designed to forecast the future states of this type of dynamical systems. The model predicts p future velocity-field time-slices (samples) based on k past samples from a training dataset consisting of a synthetic jet in transitional regime. The complexity of this flow is characterized by two topology patterns that are periodically changing, making this flow as a suitable example to test the performance of deep learning models to predict time states in complex flows. Moreover, the wide number of applications of synthetic jets (i.e.: fluid mixing, heat transfer enhancement, flow control), points out this example as a reference for future applications, where modeling synthetic jet flows with a reduced computational effort is needed. This work additionally opens up research opportunities for other areas that also operate with complex and high-dimensional time-series data: future frame video prediction, network traffic forecasting, network intrusion detection . The proposed model is presented in detail. A comprehensive analysis of the results is provided. The results are based on a strict validation strategy to ensure its generalization. The model offers an average symmetric mean absolute error (sMAPE) and a relative root mean square error (RRMSE) of 1.068 and 0.026 respectively (one order of magnitude improvement over low-rank approximation tools), using 10 past samples and predicting 6 future samples of a two-dimensional velocity field on a 70x50 point matrix associated to a synthetic jet dataset.