This article presents an original methodology for the prediction of steady turbulent aerodynamic fields. Due to the important computational cost of high-fidelity aerodynamic simulations, a surrogate model is employed to cope with the significant variations of several inflow conditions. Specifically, the Local Decomposition Method presented in this paper has been derived to capture nonlinear behaviors resulting from the presence of continuous and discontinuous signals. A combination of unsupervised and supervised learning algorithms is coupled with a physical criterion. It decomposes automatically the input parameter space, from a limited number of high-fidelity simulations, into subspaces. These latter correspond to different flow regimes. A measure of entropy identifies the subspace with the expected strongest non-linear behavior allowing to perform an active resampling on this low-dimensional structure. Local reduced-order models are built on each subspace using Proper Orthogonal Decomposition coupled with a multivariate interpolation tool. The methodology is assessed on the turbulent two-dimensional flow around the RAE2822 transonic airfoil. It exhibits a significant improvement in term of prediction accuracy for the Local Decomposition Method compared with the classical method of surrogate modeling for cases with different flow regimes. Nomenclature A= matrix of the reduced coordinates a k = k-th reduced coordinate B = matrix of the reduced coordinates of the sensor b k = k-th reduced coordinate of the sensorthe quantity of interest E = averaged normalized error f = high fidelity model g = acceleration due to the gravity or normal distribution H = global entropy h = altitude L = temperature lapse rate l = latent function matrix l = latent function M = Mach number m = number of predictions N = Gaussian probability distribution * PhD. Student, Embedded Systems Department, 118 route de Narbonne, Toulouse. n = number of training samples p = dimension of an input parameter or static pressure Q 2 = predictivity coefficient q = number of clusters r = specific gaz constant or correlation function S = matrix of the snapshots s i = quantity of interet at node i T = temperature U = velocity w = weight of the Gaussian Mixture Model X = horizontal coordinate along the chord Y = vertical coordinate y = target value α = angle of attack Γ = spatial domain δ = Kronecker symbol = energy ratio θ = hyperparameters λ = eigenvalues matrix λ = eigenvalues µ = mean of the Gaussian Process ρ = density Σ = covariance matrix σ 2 0 = prior covariance σ = sigmoid function τ w = wall shear stress Φ = mixture coefficient φ = proper orthogonal decomposition matrix χ = input parameter 1 C = hard splitting function = Subscripts = t = training p = prediction 0 = sea level ∞ = freestream = Superscripts = (k) = k-th component or element = fluctuating part = Operators= · = surrogate model · = mean | · | = absolute value · 2 = Euclidian norm (· , · ) = canonical inner product
We present a new method based on unsupervised machine learning to identify regions of interest using particle velocity distributions as a signature pattern. An automatic density estimation technique is applied to particle distributions provided by PIC simulations to study magnetic reconnection. The key components of the method involve: i) a Gaussian mixture model determining the presence of a given number of subpopulations within an overall population, and ii) a model selection technique with Bayesian Information Criterion to estimate the appropriate number of subpopulations. Thus, this method identifies automatically the presence of complex distributions, such as beams or other non-Maxwellian features, and can be used as a detection algorithm able to identify reconnection regions. The approach is demonstrated for a specific double Harris sheet simulations but it can in principle be applied to any other type of simulation and observational data on the particle distribution function.
One of the goals of machine learning is to eliminate tedious and arduous repetitive work. The manual and semi-automatic classification of millions of hours of solar wind data from multiple missions can be replaced by automatic algorithms that can discover, in mountains of multi-dimensional data, the real differences in the solar wind properties. In this paper we present how unsupervised clustering techniques can be used to segregate different types of solar wind. We propose the use of advanced data reduction methods to pre-process the data, and we introduce the use of Self-Organizing Maps to visualize and interpret 14 years of ACE data. Finally, we show how these techniques can potentially be used to uncover hidden information, and how they compare with previous empirical categorizations.
Abstract. In magnetospheric missions, burst-mode data sampling should be triggered in the presence of processes of scientific or operational interest. We present an unsupervised classification method for magnetospheric regions that could constitute the first step of a multistep method for the automatic identification of magnetospheric processes of interest. Our method is based on self-organizing maps (SOMs), and we test it preliminarily on data points from global magnetospheric simulations obtained with the OpenGGCM-CTIM-RCM code. The dimensionality of the data is reduced with principal component analysis before classification. The classification relies exclusively on local plasma properties at the selected data points, without information on their neighborhood or on their temporal evolution. We classify the SOM nodes into an automatically selected number of classes, and we obtain clusters that map to well-defined magnetospheric regions. We validate our classification results by plotting the classified data in the simulated space and by comparing with k-means classification. For the sake of result interpretability, we examine the SOM feature maps (magnetospheric variables are called features in the context of classification), and we use them to unlock information on the clusters. We repeat the classification experiments using different sets of features, we quantitatively compare different classification results, and we obtain insights on which magnetospheric variables make more effective features for unsupervised classification.
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