No Arabic abstract
Machine learning algorithms have been available since the 1990s, but it is much more recently that they have come into use also in the physical sciences. While these algorithms have already proven to be useful in uncovering new properties of materials and in simplifying experimental protocols, their usage in liquid crystals research is still limited. This is surprising because optical imaging techniques are often applied in this line of research, and it is precisely with images that machine learning algorithms have achieved major breakthroughs in recent years. Here we use convolutional neural networks to probe several properties of liquid crystals directly from their optical images and without using manual feature engineering. By optimizing simple architectures, we find that convolutional neural networks can predict physical properties of liquid crystals with exceptional accuracy. We show that these deep neural networks identify liquid crystal phases and predict the order parameter of simulated nematic liquid crystals almost perfectly. We also show that convolutional neural networks identify the pitch length of simulated samples of cholesteric liquid crystals and the sample temperature of an experimental liquid crystal with very high precision.
We present a new nonlinear mode decomposition method to visualize the decomposed flow fields, named the mode decomposing convolutional neural network autoencoder (MD-CNN-AE). The proposed method is applied to a flow around a circular cylinder at $Re_D=100$ as a test case. The flow attributes are mapped into two modes in the latent space and then these two modes are visualized in the physical space. Because the MD-CNN-AEs with nonlinear activation functions show lower reconstruction errors than the proper orthogonal decomposition (POD), the nonlinearity contained in the activation function is considered the key to improve the capability of the model. It is found by applying POD to each field decomposed using the MD-CNN-AE with hyperbolic tangent activation that a single nonlinear MD-CNN-AE mode contains multiple orthogonal bases, in contrast to the linear methods, i.e., POD and the MD-CNN-AE with linear activation. We further assess the proposed MD-CNN-AE by applying it to a transient process of a circular cylinder wake in order to examine its capability for flows containing high-order spatial modes. The present results suggest a great potential for the nonlinear MD-CNN-AE to be used for feature extraction of flow fields in lower dimension than POD, while retaining interpretable relationships with the conventional POD modes.
The onset of hydrodynamic instabilities is of great importance in both industry and daily life, due to the dramatic mechanical and thermodynamic changes for different types of flow motions. In this paper, modern machine learning techniques, especially the convolutional neural networks (CNN), are applied to identify the transition between different flow motions raised by hydrodynamic instability, as well as critical non-dimensionalized parameters for characterizing this transit. CNN not only correctly predicts the critical transition values for both Taylor-Couette (TC) flow and Rayleigh- Benard (RB) convection under various setups and conditions, but also shows an outstanding performance on robustness and noise-tolerance. In addition, key spatial features used for classifying different flow patterns are revealed by the principal component analysis.
The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to be optimized via unsupervised machine learning methods. Incorporation of physical constraints such as time-reversibility or stochasticity into the dynamical model has been established for a linear, but not for arbitrarily nonlinear (deep learning) representations of the latent space. Here we develop theory and methods for deep learning Markov and Koopman models that can bear such physical constraints. We prove that the model is an universal approximator for reversible Markov processes and that it can be optimized with either maximum likelihood or the variational approach of Markov processes (VAMP). We demonstrate that the model performs equally well for equilibrium and systematically better for biased data compared to existing approaches, thus providing a tool to study the long-timescale processes of dynamical systems.
One of the most crucial tasks in seismic reflection imaging is to identify the salt bodies with high precision. Traditionally, this is accomplished by visually picking the salt/sediment boundaries, which requires a great amount of manual work and may introduce systematic bias. With recent progress of deep learning algorithm and growing computational power, a great deal of efforts have been made to replace human effort with machine power in salt body interpretation. Currently, the method of Convolutional neural networks (CNN) is revolutionizing the computer vision field and has been a hot topic in the image analysis. In this paper, the benefits of CNN-based classification are demonstrated by using a state-of-art network structure U-Net, along with the residual learning framework ResNet, to delineate salt body with high precision. Network adjustments, including the Exponential Linear Units (ELU) activation function, the Lov{a}sz-Softmax loss function, and stratified $K$-fold cross-validation, have been deployed to further improve the prediction accuracy. The preliminary result using SEG Advanced Modeling (SEAM) data shows good agreement between the predicted salt body and manually interpreted salt body, especially in areas with weak reflections. This indicates the great potential of applying CNN for salt-related interpretations.
Plasma tomography consists in reconstructing the 2D radiation profile in a poloidal cross-section of a fusion device, based on line-integrated measurements along several lines of sight. The reconstruction process is computationally intensive and, in practice, only a few reconstructions are usually computed per pulse. In this work, we trained a deep neural network based on a large collection of sample tomograms that have been produced at JET over several years. Once trained, the network is able to reproduce those results with high accuracy. More importantly, it can compute all the tomographic reconstructions for a given pulse in just a few seconds. This makes it possible to visualize several phenomena -- such as plasma heating, disruptions and impurity transport -- over the course of a discharge.