Minimization Scheme Research Articles

Solving phase‐field fracture problems in the tensor train format

AbstractPhase‐field models for the quasi‐static simulation of brittle fracture where the crack is approximated by a damage phase‐field are limited by the necessary memory and computation time. In this contribution, we study the applicability of low‐rank methods to phase‐field fracture models, specifically the tensor train (TT) format. To this end, we investigate the low‐rank structure of the crack phase‐field. Additionally, we present an implementation of an alternating minimization scheme to solve the coupled displacement and damage problem in the TT format. We show the evolution of the TT ranks of the displacement and damage fields for a specific example.

Nonasymptotic analysis of robust regression with modified Huber's loss

To achieve robustness against the outliers or heavy-tailed sampling distribution, we consider an Ivanov regularized empirical risk minimization scheme associated with a modified Huber's loss for nonparametric regression in reproducing kernel Hilbert space. By tuning the scaling and regularization parameters in accordance with the sample size, we develop nonasymptotic concentration results for such an adaptive estimator. Specifically, we establish the best convergence rates for prediction error when the conditional distribution satisfies a weak moment condition.

Five loop minimal MOM scheme field and quark mass anomalous dimensions in QCD

We determine the anomalous dimensions of the gluon, Faddeev–Popov ghost and quark in the minimal momentum subtraction scheme to five loops for a general colour group when quantum chromodynamics is fixed in a linear covariant gauge. The quark mass anomalous dimension is also constructed in the same scheme.

Enhancement of natural convection of a nanofluid by stress-free patches in an L-shaped enclosure

Purpose This study aims at investigating the heat transfer characteristics of a nonsquare enclosure when hydrodynamic resistance is altered discontinuously along its inner surface. Particularly, it focuses on investigating how several essential factors collaboratively influence the natural convection, including the Rayleigh number (Ra), the aspect ratio (AR), the nanoparticle volume fraction (ϕ) and the locations of changing hydrodynamic resistance. Design/methodology/approach To achieve these objectives, an L-shaped enclosure of various AR is adopted, while zero local shear resistance is applied and modeled by stress-free (SF) patches of four distinct arrangements (corresponding to Cases 1–4). The nanofluid is modeled by Buongiorno’s two-phase model. The effects are explored using an in-house numerical framework based on a hybrid lattice Boltzmann-finite difference method with the total variation minimization scheme. Findings The results show that when Ra is sufficiently large, i.e. Ra = 105, SF patches can generally enhance the heat transfer performance regardless of other factors. However, the ways of achieving those enhancements are different, which mainly depend on the arrangement of the SF patches and AR but are nearly independent of ϕ. The maximum improvement of heat transfer can be achieved in Case 3 with AR = 0.6, Ra = 105 and ϕ = 0.04, where the averaged Nusselt number is enhanced by 8.89%. Originality/value This study presents a new scenario where the SF patches of various arrangements are applied to enhance the nanofluid natural convection of a nonsquared enclosure, and it reveals how the improvement is achieved and cooperatively affected by several important factors.

Practical data-driven modeling and robust predictive control of mammalian cell fed-batch process

Even if the performances of bioprocesses can be significantly improved by model-based control, there often remains a tradeoff between model complexity and control robustness. This paper proposes an original data-driven strategy for fast design of dynamic bioprocess models with minimal complexity (i.e., minimal number of bioreactions). Maximum likelihood principal component analysis (MLPCA) is applied to infer the minimal reaction scheme from a 25-state mammalian cell culture database. Then, a systematic algorithm is used to provide a continuous kinetic model formulation assuming all rates to occur simultaneously, which may be far from true cell metabolic conditions sometimes presenting discontinuous metabolic switches. A robust model predictive formulation is therefore adopted to reduce the impact of model structural uncertainty on the process performances. Additional numerical results show that the proposed strategy presents excellent performances in presence of unexpected metabolic switches.

ϕ4 theory at seven loops

We give a detailed account of the theory of position space renormalization using graphical functions in the case of dimensionally regularized ${\ensuremath{\phi}}^{4}$ theory in four dimensions. In this theory we calculate the beta function, the mass gamma function, and the self-energy to seven loops in the minimal subtraction scheme. The anomalous dimension $\ensuremath{\gamma}$ is calculated to loop order eight. When possible, we generalize to even dimensions $\ensuremath{\ge}4$ with particular focus on ${\ensuremath{\phi}}^{3}$ theory in six dimensions. In this theory we calculate the anomalous dimension $\ensuremath{\gamma}$ to loop order six.

Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations

This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE.

Tensor-DAAD: When tensor meets online early fault detection with transfer learning

This paper tries to address the concerns about online early fault detection in non-stop scenarios: (1) no information of running status and operating condition is available for online data; (2) False alarms are raised by irregular noise. This paper proposes a new self-supervised deep tensor domain-adversarial anomaly detection model, named Tensor-DAAD. A contrastive learning network is first built to generate pre-trained features and pseudo-labels for online data. Second, a new tensor hypersphere-adversarial network is designed. By calculating core tensors of two domains’ features, this network builds hypersphere-based one-class detection rules from noisy data, and then realizes rule adaptation between the domains through adversarial training. Finally, a training algorithm with alternating minimization scheme is proposed to seek the optimal tensor decomposition and domain-invariant feature representation. Results on the two widely-used bearing datasets demonstrate that Tensor-DAAD can find early fault occurrence in an earlier location with a much lower false alarm rate.

An Efficient Flows Dispatching Scheme for Tardiness Minimization of Data-Intensive Applications in Heterogeneous Systems

Next-generation computer networks are expected to support a wide plethora of novel applications, demanding to handle a huge number of different computation tasks, typically data-intensive. As a consequence, the tasks raw data are pre-processed on Intermediate Processing Nodes (IPNs) before being sent toward the destination server. However, despite the IPNs are constrained in pre-processing capability, usually their influence on the resulting flow computing models is not taken into account. Aiming to fill this gap, this paper applies matching theory in defining a suitable flows dispatching scheme with the aim at maximizing the system utility in a capacity-constrained network. As a consequence, a novel matching algorithm with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">externalities</i> is proposed, and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">two-sided exchange</i> stability is theoretically analyzed and properly discussed. We proved that the considered problem is NP-hard to solve and we verified the convergence of the proposed algorithm to a stable matching outcome, usually representing a severe challenge in the class of the matching games with externalities, due to the mutual dependence among the preferences lists of the players. Finally, simulation results evidence the validity of the proposed algorithm, highlighting remarkable advantages in comparison to different alternative schemes.

Interference Alignment for Physical Layer Security in Multi-User Networks With Passive Eavesdroppers

We investigate the physical layer security (PLS) in multi-user interference networks. In particular, we consider secure transmission from a legitimate source (Alice) to a legitimate destination (Bob), coexisting with multiple passive eavesdroppers (Eves), as well as multiple legitimate transceivers. By assuming that only statistical channel state informations (CSIs) of Eves and local CSIs of legitimate users are available, we propose an artificial noise (AN) assisted interference alignment (IA) for security enhancement. Unlike traditional IA based security approaches which may result in secret signal cancellation, we design a modified alternating minimization (AM) scheme to overcome this threat, by incorporating the max-eigenmode beamforming (MEB) for secure transmission. Moreover, by partitioning the IA equation into three independent subsets and their combinations, a much tighter necessary condition for IA feasibility is established. We also provide guiding insights into the practical system designs, including useful guidelines for the selection of the dimension of AN. Furthermore, the power allocation ratio between the secret signal and the AN signal is optimized to minimize the secrecy outage probability (SOP), subject to a minimum secrecy rate constraint. Numerical results demonstrate that our design can enhance both quality and security of the secret signal, and thus is suitable and reliable for PLS in interference networks.

Phase Synchronization for Helix Enhanced Wake Mixing in Downstream Wind Turbines

Wind farm controllers such as the Helix approach have shown potential in increasing plant power production through wake mixing. The concept suggests that actuating the upstream turbines’ blade pitching with a specific periodic signal can induce a helix-shaped wake, thereby alleviating wind velocity deficit on downstream turbines. Wake mixing initiation by downstream turbines may also be shown advantageous for power production; however, little to no attention has been given to such an approach. Similar wake mixing is expected to be achievable at lower control costs if the downstream turbine can benefit from the periodic component already present in the wake of the upstream turbine. Such a hypothesis is studied in this work by designing a minimal control scheme where the wake acting on the downstream turbine is simulated by a periodic input disturbance. A Kalman filter is proposed for incoming input disturbance phase estimation using SCADA data. The reconstructed phase information allows synchronization of the downstream control action with the periodic input disturbance by means of a phase synchronization wake mixing controller. The periodic component was estimated with a minimal root-mean-square error and the resulting control action was in phase with the input disturbance and demonstrated satisfactory performance even with a small phase perturbation. Future work will include applications in a high-fidelity wind turbine model and wind tunnel studies.

A New Deep Tensor Autoencoder Network for Unsupervised Health Indicator Construction and Degradation State Evaluation of Metro Wheel

For metro vehicles, wheel performance degradation is inevitable due to the continuous wear of tread and rim. It is of significant value to apply machine learning techniques to evaluate the wheel’s degradation state with vibration signals, as it can lessen expert dependence and optimize repair strategy. In the real metro operation process, however, the wheels’ vibration signal is easily disturbed by irregular noise from many factors, such as load, road condition, and temperature, etc., and lacks essential tendency characteristics for the intelligent state evaluation. To solve this problem, this paper proposes a new unsupervised degradation state evaluation method for metro wheels against irregular noise disturbance. First, a new deep tensor autoencoder (TAE) network is proposed based on the merit of tensor representation in exploring the intrinsic information from raw signals. By extracting the core tensor from hidden features via Tucker decomposition, a new decoding process is rebuilt and a tensorized tendency regularizer is designed with the core tensor. Moreover, a new training algorithm with alternating minimization scheme is constructed to seek the optimal tensor representation and unsupervised feature extraction. Second, a health indicator (HI) of the degradation process is built with the extracted features. A HI-based state assessment algorithm is further proposed to adaptively determine the interval of state change in order to substitute the first/second warning in the current maintenance strategy. A set of comparative experiments are conducted using the wheel data from Beijing Subway. The results demonstrate that TAE can extract features with good monotonicity and tendency from the raw signals under irregular noise disturbance. More importantly, the obtained warning positions can precisely match the wheel diameter’s change in the actual repair record, which offers an easy-to-deploy and intelligent solution for the health management of metro wheels.

Nonlinear matrix recovery using optimization on the Grassmann manifold

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the rank minimization of a nonlinear feature map applied to the original matrix, which is then further approximated by a constrained non-convex optimization problem involving the Grassmann manifold. We propose two sets of algorithms, one arising from Riemannian optimization and the other as an alternating minimization scheme, both of which include first- and second-order variants. Both sets of algorithms have theoretical guarantees. In particular, for the alternating minimization, we establish global convergence and worst-case complexity bounds. Additionally, using the Kurdyka-Lojasiewicz property, we show that the alternating minimization converges to a unique limit point. We provide extensive numerical results for the recovery of union of subspaces and clustering under entry sampling and dense Gaussian sampling. Our methods are competitive with existing approaches and, in particular, high accuracy is achieved in the recovery using Riemannian second-order methods.

Self-Supervised Deep Tensor Domain-Adversarial Regression Adaptation for Online Remaining Useful Life Prediction Across Machines

With deep transfer learning techniques, this paper focuses on the online remaining useful life (RUL) prediction problem across different machines, and tries to address the following concerns: 1) The effect of transfer learning decreases significantly due to considerable divergence of degradation characteristic; 2) A high computational cost is raised by re-training whole model with online data; 3) Error accumulation occurs because of lacking label information of online data. In this paper, a self-supervised deep tensor domain-adversarial regression adaptation approach is proposed. In the pre-training stage, a novel tensor domain-adversarial network, with a tensorized domain discriminator, is constructed using the offline whole-life degradation data and early fault data of the target machine. A new training algorithm with an alternating minimization scheme is then built to seek the optimal core tensor and domain-invariant feature representation. In the online stage, a new self-supervised fine-tuning strategy is designed for the target network initialized from the pre-trained network. The core tensor-formed self-supervised information, extracted from the monotonicity of online degradation process, and the pseudo-supervised information from the pre-trained network are integrated to realize fast and adaptive RUL prediction. This paper takes rolling bearing as an example, and runs both cross-conditions and cross-machines experiments on three rolling bearings datasets, i.e., IEEE PHM Challenge 2012, XJTU-SY and our test rig. The results verify the use of tensor representation can facilitate regression adversarial training, and demonstrate the proposed approach can effectively improve predictive accuracy and stability under unknown online conditions.

Semi-Sparsity for Smoothing Filters.

In this paper, we propose a semi-sparsity smoothing method based on a new sparsity-induced minimization scheme. The model is derived from the observations that semi-sparsity prior knowledge is universally applicable in situations where sparsity is not fully admitted such as in the polynomial-smoothing surfaces. We illustrate that such priors can be identified into a generalized L0-norm minimization problem in higher-order gradient domains, giving rise to a new "feature-aware" filter with a powerful simultaneous-fitting ability in both sparse singularities (corners and salient edges) and polynomial-smoothing surfaces. Notice that a direct solver to the proposed model is not available due to the non-convexity and combinatorial nature of L0-norm minimization. Instead, we propose to solve it approximately based on an efficient half-quadratic splitting technique. We demonstrate its versatility and many benefits to a series of signal/image processing and computer vision applications.

Speckle Removal Using Dictionary Learning and PnP-Based Fast Iterative Shrinkage Threshold Algorithm

Speckle is a multiplicative granular noise that naturally occurs in the images captured by coherent imaging sensors such as synthetic aperture radar (SAR). It visually degrades the underlying image information and has an impact on subsequent image analysis. This problem is addressed here by developing a sparse representation model and applying an alternating minimization scheme for SAR image despeckling. The proposed method directly deals with the multiplicative noise and the data model is formed by utilizing the speckle statistics. The similar patches are clustered together to adaptively learn the dictionary, and the sparse coefficients are updated using plug-and-play based fast iterative shrinkage threshold algorithm (PnP-FISTA). Finally, the clean image is estimated using Newton’s method. Experiments on simulated and practical SAR images signify that the proposed method performs better compared to the state-of-the-art methods in terms of performance metrics and visual assessment.

Algorithms for audio inpainting based on probabilistic nonnegative matrix factorization

Audio inpainting, i.e., the task of restoring missing or occluded audio signal samples, usually relies on sparse representations or autoregressive modeling. In this paper, we propose to structure the spectrogram with nonnegative matrix factorization (NMF) in a probabilistic framework. First, we treat the missing samples as latent variables, and derive two expectation–maximization algorithms for estimating the parameters of the model, depending on whether we formulate the problem in the time- or time-frequency domain. Then, we treat the missing samples as parameters, and we address this novel problem by deriving an alternating minimization scheme. We assess the potential of these algorithms for the task of restoring short- to middle-length gaps in music signals. Experiments reveal great convergence properties of the proposed methods, as well as competitive performance when compared to state-of-the-art audio inpainting techniques.

Artificial diffusion for convective and acoustic low Mach number flows I: Analysis of the modified equations, and application to Roe-type schemes

Three asymptotic limits exist for the Euler equations at low Mach number - purely convective, purely acoustic, and mixed convective-acoustic. Standard collocated density-based numerical schemes for compressible flow are known to fail at low Mach number due to the incorrect asymptotic scaling of the artificial diffusion. Previous studies of this class of schemes have shown a variety of behaviours across the different limits and proposed guidelines for the design of low-Mach schemes. However, these studies have primarily focused on specific discretisations and/or only the convective limit.In this paper, we review the low-Mach behaviour using the modified equations - the continuous Euler equations augmented with artificial diffusion terms - which are representative of a wide range of schemes in this class. By considering both convective and acoustic effects, we show that three diffusion scalings naturally arise. Single- and multiple-scale asymptotic analysis of these scalings shows that many of the important low-Mach features of this class of schemes can be reproduced in a straightforward manner in the continuous setting.As an example, we show that many existing low-Mach Roe-type finite-volume schemes match one of these three scalings. Our analysis corroborates previous analysis of these schemes, and we are able to refine previous guidelines on the design of low-Mach schemes by including both convective and acoustic effects. Discrete analysis and numerical examples demonstrate the behaviour of minimal Roe-type schemes with each of the three scalings for convective, acoustic, and mixed flows.

Hyperparameter selection for Discrete Mumford–Shah

This work focuses on a parameter-free joint piecewise smooth image denoising and contour detection. Formulated as the minimization of a discrete Mumford-Shah functional and estimated via a theoretically grounded alternating minimization scheme, the bottleneck of such a variational approach lies in the need to fine-tune their hyperparameters, while not having access to ground truth data. To that aim, a Stein-like strategy providing optimal hyperparameters is designed, based on the minimization of an unbiased estimate of the quadratic risk. Efficient and automated minimization of the estimate of the risk crucially relies on an unbiased estimate of the gradient of the risk with respect to hyperparameters. Its practical implementation is performed using a forward differentiation of the alternating scheme minimizing the Mumford-Shah functional, requiring exact differentiation of the proximity operators involved. Intensive numerical experiments are performed on synthetic images with different geometry and noise levels, assessing the accuracy and the robustness of the proposed procedure. The resulting parameter-free piecewise-smooth estimation and contour detection procedure, not requiring prior image processing expertise nor annotated data, can then be applied to real-world images.

Automatic 3D CT liver segmentation based on fast global minimization of probabilistic active contour.

Automatic liver segmentation from computed tomography (CT) images is an essential preprocessing step for computer-aided diagnosis of liver diseases. However, due to the large differences in liver shapes, low-contrast to adjacent tissues, and existence of tumors or other abnormalities, liver segmentation has been very challenging. This study presents an accurate and fast liver segmentation method based on a novel probabilistic active contour (PAC) model and its fast global minimization scheme (3D-FGMPAC), which is explainable as compared with deep learningmethods. The proposed method first constructs a slice-indexed-histogram to localize the volume of interest (VOI) and estimate the probability that a voxel belongs to the liver according its intensity. The probabilistic image would be used to initialize the 3D PAC model. Secondly, a new contour indicator function, which is a component of the model, is produced by combining the gradient-based edge detection and Hessian-matrix-based surface detection. Then, a fast numerical scheme derived for the 3D PAC model is performed to evolve the initial probabilistic image into the global minimizer of the model, which is a smoothed probabilistic image showing a distinctly highlighted liver. Next, a simple region-growing strategy is applied to extract the whole liver mask from the smoothed probabilistic image. Finally, a B-spline surface is constructed to fit the patch of the rib cage to prevent possible leakage into adjacent intercostaltissues. The proposed method is evaluated on two public datasets. The average Dice score, volume overlap error, volume difference, symmetric surface distance and volume processing time are 0.96, 7.35%, 0.02%, 1.17 mm and 19.8 s for the Sliver07 dataset, and 0.95, 8.89%, , 1.45 mm and 23.08 s for the 3Dircadb dataset,respectively. The proposed fully-automatic approach can effectively segment the liver from low-contrast and complex backgrounds. The quantitative and qualitative results demonstrate that the proposed segmentation method outperforms state-of-the-art traditional automatic liver segmentation algorithms and achieves very competitive performance compared with recent deep leaning-basedmethods.