The pattern formation and spatial–temporal chaos are interesting issues in nonlinear dynamics. A novel model based on machine learning methods is designed to learn and imitate the pattern evolution in Bénard–Marangoni convection (BM convection). There is a supercritical process, which is an inevitable and unique experimental phenomenon, on the way to chaos in BM convection. A single layer of fluid uniformly heated at the bottom is used as the experimental system. During the experiment, the temperature difference between top and bottom of the liquid layer is increased first to make the system enter the supercritical convection state and then decreased after a while; surface temperature distribution of the liquid layer is measured in real time with an infrared thermal imager, which visualized the formation and re-organization of cellular convection during the supercritical state. The temperature data are used as the material that meets the conditions of machine learning and then the machine learning method in charge of predicting the picture of temperature distribution that it never has seen before in two steps. The experimental data are used to train an auto-encoder model based on convolutional neural networks and an RNN–CNN joint model, in which the former is used for extracting low-dimensional features of the temperature field, and the latter is used for predicting evolution results of the low-dimensional features and recovering them back to the temperature field. The models have finally achieved the objectives of supplementing the missing experimental data and correcting actual experimental data by comparing the actual experimental results with the prediction results of the machine learning approach and theoretical analysis results. On the other hand, active exploration has been undertaken in predicting physical experimental results that have never happened before.
Stability control of the convection flow field has always been a focal issue. The annular flow discussed in this work is extracted from the industrial crystal growth by the Czochralski method. It is believed that the instability of thermal convection is the key factor affecting the quality of crystal growth. Combining the reinforcement learning algorithm with the neural network, this paper proposed a control policy that makes forced convection compete with thermocapillary convection by changing the dynamic boundary conditions of the system. This control policy is successfully applied to the control of the quasi-equilibrium state of annular flow, and the global stability of the flow field is well maintained. It first experimentally makes the annular flow field under low and medium Ma numbers achieve a quasi-equilibrium state which is different from that before the onset of flow oscillations. Then a simulation environment is created to imitate the experimental conditions. After training in the simulation environment, with the self-optimized algorithm, the machine learning approach can successfully maintain the simulation environment in a quasi-equilibrium state for a long period of time. Finally, the learning method is validated in the experimental environment, and a quasi-equilibrium state control policy is completely optimized by using the same optimization policy and similar neural network structure. This work demonstrates that the model can understand the physical environment and the author's control objectives through reinforcement learning. It is an important application of reinforcement learning algorithms and a clear demonstration of the research value of microgravity fluid physics.
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