Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models

Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting ill-posed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.

We study nonlinear inverse problems of the form F ( x ) = y , and their stable solution via iterative regularization methods, in particular by Newton-type methods, which are well-known for their fast convergence for well-posed problems. A basic step of Newton’s method consists of calculating the update Δ x k via solution of a linearized equation , which will in general be ill-posed if the nonlinear problem is. Thus, for ill-posed problems, the linearized equations have to be solved by some regularization method. In particular for large scale problems, e.g., inverse problems in partial differential equations, where F ( x ) is only defined implicitly via the solution of a PDE, iterative methods have to be used for this purpose. In order to keep the overall effort, i.e., the overall number of iterations, as small as possible, appropriate preconditioning has to be applied. We propose and analyse a general preconditioning strategy in Hilbert scales, and show that the overall number of iterations can be reduced to about the square root by preconditioning. Moreover, in many examples differential operators can be used as preconditioners, and thus preconditioning is almost for free. The theoretical results are illustrated in numerical examples. A comparison with preconditioned Landweber iteration shows that the iteration numbers can be further reduced, if fast iterative methods, e.g., the v -methods, are used for the solution of the linearized problems.

This study investigates the applicability of an emergent learning algorithm called Gaussian process regression (GPR) algorithm to predict damage in plate-like structures as an inverse problem. The presented method is based on static responses and static strain energy as input parameters to GPR model. The performance of the presented methods has been evaluated using two numerical examples, namely, four fixed and cantilever plates. Also, an examination has been performed in which only translational DOFs are selected as measured DOFs. In another work, the effect of noise in static data has been investigated. The model results were compared using mean square errors. The obtained results show the effectiveness of GPR in damage detection and estimation of plate-like structures using static data which may be noisy.

Some matrix-splitting iterative methods for solving systems of linear equations contain parameters that need to be specified in advance, and the choice of these parameters directly affects the efficiency of the corresponding iterative methods. This paper uses a Bayesian inference-based Gaussian process regression (GPR) method to predict the relatively optimal parameters of some HSS-type iteration methods and provide extensive numerical experiments to compare the prediction performance of the GPR method with other existing methods. Numerical results show that using GPR to predict the parameters of the matrix-splitting iterative methods has the advantage of smaller computational effort, predicting more optimal parameters and universality compared to the currently available methods for finding the parameters of the HSS-type iteration methods.

Accurate prediction of performance indices using impeller parameters is of great importance for the initial and optimal design of centrifugal pump. In this study, a kernel-based non-parametric machine learning method named with Gaussian process regression (GPR) was proposed, with the purpose of predicting the performance of centrifugal pump with less effort based on available impeller parameters. Nine impeller parameters were defined as model inputs, and the pump performance indices, that is, the head and efficiency, were determined as model outputs. The applicability of three widely used nonlinear kernel functions of GPR including squared exponential (SE), rational quadratic (RQ) and Matern5/2 was investigated, and it was found by comparing with the experimental data that the SE kernel function is more suitable to capture the relationship between impeller parameters and performance indices because of the highest R square and the lowest values of max absolute relative error (MARE), mean absolute proportional error (MAPE), and root mean square error (RMSE). In addition, the results predicted by GPR with SE kernel function were compared with the results given by other three machine learning models. The comparison shows that the GPR with SE kernel function is more accurate and robust than other models in centrifugal pump performance prediction, and its prediction errors and uncertainties are both acceptable in terms of engineering applications. The GPR method is less costly in the performance prediction of centrifugal pump with sufficient accuracy, which can be further used to effectively assist the design and manufacture of centrifugal pump and to speed up the optimization design process of impeller coupled with stochastic optimization methods.

In this article, a novel power decoupling method for multiport resonant converters (MRCs) is proposed. Due to the natural coupling of resonant impedances and phase-shift angles between each port, the transient performance of MRC is usually poor. To mitigate this issue, a power decoupling method based on the gray wolf optimization (GWO) algorithm is proposed. This algorithm can iterate and find the optimum value of phase-shift angles quickly and accurately compared to other iteration methods. Furthermore, the proposed method does not require linearization and parameter estimation algorithms, which makes it robust to operate at all operating points and parameter mismatch. In addition, a simple online implementation with a digital signal processor is also given. The performance of the proposed method is compared with several existing methods and validated using results from both simulations and laboratory-scaled experimental hardware. The results show that the maximum overshoots during step changes in load and power reference can be significantly reduced from 20% to 27% to only 7%–9%.

Parallel diagonally implicit Runge-Kutta-Nyström methods

Atmospheric tomography, i.e., the reconstruction of the turbulence profile in the atmosphere, is a challenging task for adaptive optics (AO) systems for the next generation of extremely large telescopes. Within the AO community, the solver of first choice is the so-called Matrix Vector Multiplication (MVM) method, which directly applies the (regularized) generalized inverse of the system operator to the data. For small telescopes this approach is feasible, however, for larger systems such as the European Extremely Large Telescope (ELT), the atmospheric tomography problem is considerably more complex, and the computational efficiency becomes an issue. Iterative methods such as the Finite Element Wavelet Hybrid Algorithm (FEWHA) are a promising alternative. FEWHA is a wavelet-based reconstructor that uses the well-known iterative preconditioned conjugate gradient (PCG) method as a solver. The number of floating point operations and the memory usage are decreased significantly by using a matrix-free representation of the forward operator. A crucial indicator for the real-time performance are the number of PCG iterations. In this paper, we propose an augmented version of FEWHA, where the number of iterations is decreased by 50% using an augmented Krylov subspace method. We demonstrate that a parallel implementation of augmented FEWHA allows the fulfilment of the real-time requirements of the ELT.

Background and Objectives: Numerical iterative methods are widely used to compute reachability probabilities and expected rewards in probabilistic model checking of Markov decision processes. Several approaches have been proposed to improve the performance of these iterative methods. Reducing the total number of iterations is an important goal that is followed by several techniques in this paper.Methods: In this paper, we consider MDPs with different levels of non-determinism. We show that modified policy iteration performs better than the other standard iterative methods when the degree of non-determinism increases. We propose some novel methods to improve the performance of the modified policy iteration method. Our approach is to define several criteria to avoid useless iterations and updates of the modified policy iteration method. The first criterion considers the graphical structure of the model to define the number of iterations after each policy modification. The second criterion is a dynamic one to determine when a policy should be updated. The third proposed approach in this work is to use several priority heaps to select states for value updates.Results: Our proposed methods are implemented in the PRISM model checker and applied on several standard case studies. The results of experiments show that the running times of our approaches are less than the running time of the standard and previous methods for most case studies. The main reason for these results is that the total numbers of iterations and updates are reduced by our approaches, which results in an improvement in the performance of the method. While the running times are reduced by our approaches, the precision of computations are kept in most cases.Conclusion: The proposed techniques are able to reduce the number of iterations and accelerate the convergence to the optimal policies. The also prioritize the commutations to reduce the total number of updates.

Bayesian Optimization Analysis of Containment-Venting Operation in a Boiling Water Reactor Severe Accident

An iterative method is introduced for solving noisy, ill-conditioned inverse problems. Analysis of the semi-convergence behavior identifies three error components iteration error, noise error, and initial guess error. A derived expression explains how the three errors are related to each other relative to the number of iterations. The Standard Tikhonov regularization method is just the first iteration of the iterative method and the derived noise damping filter is a generalization of the Standard Tikhonov filter. The derived filter is a function two parameters, a regularization parameter and the iteration number parameter. The new method is tested on image reconstruction from projections simulated data set.

In this paper, a robust identification method of the system model is proposed. The robustizing process is in the form of a Robbins-Monro stochastic approximation (RMSA) algorithm and is based on the m-interval polynomial approximation (MIPA) method. The resulting algorithm, which estimates the coefficients of the system model, represents a recursive robustized version of the well-known maximum entropy method (MEM) for spectral estimation introduced by Burg, or of the popular Widrow least-mean-square (LMS) adaptive filter adopted widely in engineering. Furthermore, the MIPA robustizing algorithm leads naturally to a robustized Akaike's information criterion (AIC) to determine the order of the system model. The simplicity of implementation and flexibility make applications of the MIPA identification algorithms attractive in practice. The robustness of performance is confirmed by Monte Carlo simulations.

Current total pressure measurement techniques in rotating detonation combustors (RDCs) are based on different assumptions and therefore show different applicability for specific RDC operating conditions, and few studies have directly compared these techniques. Therefore, this study comprehensively tested three total pressure measurement techniques: the direct Kiel probe method, the Mach-corrected capillary tube averaged pressure (CTAP) method, and the equivalent available pressure (EAP) method under different RDC geometries and mass flow rates, and compared them with their corresponding uncertainties considered. The results show that for all tests in this study, the EAP method shows the largest uncertainty range up to 24%, which is mainly contributed by the load cell calibration process, while the direct Kiel probe method has the lowest uncertainty range, which is consistently below 7%. These uncertainties were incorporated into the comparison between the three techniques via Gaussian process regression, showing that the direct Kiel probe method and the Mach-corrected CTAP method can present EAP-like total pressure. In particular, the total pressure of the single wave with counter-rotating components (SWCC) and L modes measured by the three techniques is very comparable. This work shows that the comparability of total pressure techniques depends on the specific RDC environment, and provides the possibility to evaluate the RDC performance with the simplest implementation.