Penalization Function Research Articles

A one-field fluid/meso-structure coupling approach for multiscale transport in heterogeneous porous media

Modeling transport phenomena within heterogeneous porous media poses considerable challenges, particularly on account of the complexity of the involved geometries combined with nonlinear transport interactions. In the present study, a novel one-field modeling approach for multiscale fluid–solid interactions is proposed that does not need any a priori information on permeability. This approach implicitly considers the existence of multiscale structures through a penalization function that encompasses merely one single effective parameter. The definition, determination, as well as the response of the effective parameter to influencing factors are elaborated in detail. It is demonstrated that this approach is effective in representing properly the heterogeneity of solids. The method has been successfully applied to both nonlinear porous media flows and Darcian transport problems, exhibiting comparable accuracy but substantial computational savings as opposed to pore-scale simulations. It leads to more accurate interphase mass transfer predictions and lower computational cost in comparison with the Darcy–Brinkmann–Stokes approach. Overall, this method appears to be highly effective in forecasting realistic, industrial-scale porous media transport problems.

Optimization of penalization function in Bayesian penalized likelihood reconstruction algorithm for [18F]flutemetamol amyloid PET images.

Point-spread-function (PSF) correction is not recommended for amyloid PET images due to Gibbs artifacts. Q.Clear™, a Bayesian Penalized Likelihood (BPL) reconstruction method without incorporating PSF correction reduces these artifacts but degrades image contrast by our previous findings. The present study aimed to recover lost contrast by optimizing reconstruction parameters in time-of-flight (TOF) BPL reconstruction of amyloid PET images without PSF correction. We selected candidate conditions based on a phantom study and then determined which were optimal in a clinical study. Phantom images were reconstructed under conditions of 1‒9 iterations, β 300-1000 and γ factors from 2 to 10 in TOF-BPL without PSF correction. We evaluated the %contrast and the coefficients of variation (CV, %). Standardized uptake value ratios (SUVr) and Centiloid scales (CL) were calculated from PET images acquired from 71 participants after an [18F]flutemetamol injection. Both %contrast and CV were independent of iterations, whereas a trade-off was found between γ factors and β. We selected a γ factors of 5 without PSF correction (iterations, 1; β, 500) and of 10 without PSF correction (iterations, 1; β, 800) as candidates for clinical investigation. The SUVr and CL remained stable across various conditions, and CL scales effectively discriminated amyloid PET using measured values. The optimal reconstruction parameters of TOF-BPL for [18F]flutemetamol PET images were γ factor 10, iterations 1 and β 800, without PSF correction.

Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms

Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D-Wave Advantage and D-Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms.

Improved error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems

In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using a variable penalty for second-order elliptic problems. The strategy is to use a penalization function of the form O(1/h1+δ), where h denotes the mesh size and δ is a user-dependent parameter. We then quantify its direct impact on the convergence analysis, namely, the (strong) consistency, discrete coercivity and boundedness (with hδ-dependency), and we derive updated error estimates for both discrete energy- and L2-norms. The originality of the error analysis relies specifically on the use of conforming interpolants of the exact solution. All theoretical results are supported by numerical evidence.

Stress constrained topology optimization simultaneously considering the uncertainty of load positions

AbstractThis study presents a topological optimization method simultaneously considering the stress constraint and the uncertainty of the load positions for practical applications. The phase field design method is used to derive the topologically optimal structure shape. The stress penalization function, which makes intermediate design variable values disproportionately expensive, is employed to ensure numerical stability and avoid the singularity during the optimization process. The adaptive mesh refinement and a modified P‐norm stress with correction factor are also employed to reduce the computational cost. As numerical examples, cantilever beam, L‐shaped, and MBB‐beam are presented to verify the proposed design method. The open‐source code FreeFEM++ is used for the finite element analysis and the design process.

Topology optimization of structures subject to self-weight loading under stress constraints

PurposeThe purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.Design/methodology/approachThe resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.FindingsNumerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.Originality/valueThe novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

An Adaptive Material Interpolation for the Reconstruction of P-Wave Velocity Models with Sharp Interfaces using the Topology Optimization Method

A topology optimization (TO) approach is used to reconstruct P-wave velocity models with sharp interfaces. The concept of material model (interpolation), usually applied in TO to design structures and multi-physics devices, is explored in this work to solve this inverse problem. An adaptive interpolation rule is proposed to deal with the reconstruction problem as a transition from a single- to a multi-material approach combining the Solid Isotropic Material with Penalization (SIMP) and peak function material models. Data collected during the optimization process is used to find material candidates by means of a curve fitting strategy based on generalized simulated annealing (GSA), if this information is not available. The numerical analysis is carried out using a finite element (FE) approach in the frequency domain. Both forward and adjoint problems are solved aided by an open source Domain-Specific Language (DSL) framework and automated derivation tool, while the optimization problem is solved by using a BFGS algorithm. Numerical results for 2D examples demonstrated that proposed material interpolation can lead to solutions with sharper interfaces and improved resolution without including any type of regularization or extra constraint in the optimization problem.

The existence and decay of solitary waves for the Fornberg–Whitham equation

In this paper, we consider the Fornberg-Whitham equation and a family of solitary wave solutions is found by using minimization principle, where a related penalization function and the concentration-compactness lemma play a key role in our proof. Besides, we also prove that the family of solitary solutions is orbital stable and decay exponentially when speed wave c is bigger than 1.

Fastest motion planning for an unmanned vehicle in the presence of accelerating obstacles

Estimating the fastest trajectory is one of the main challenges in autonomous vehicle research. It is fundamental that the vehicle determines its path not only to minimize travel time, but to arrive at the destination safely by avoiding any obstacles that may be in collision route. In this paper, we consider estimating the trajectory and acceleration functions of the trip simultaneously with an optimization objective function. By approximating the trajectory and acceleration function with B-splines, we transform an infinite-dimensional problem into a finite-dimensional one. Obstacle avoidance and kinematic constraints are carried out with the addition of a penalization function that penalizes trajectories and acceleration functions that do not satisfy the vehicles’ constraints or that are in a collision route with other obstacles. Our approach is designed to model observations of the obstacles that contain measurement errors, which incorporates the realistic stochasticity of radars and sensors. We show that, as the number of observations increases, the estimated optimization function converges to the optimal one where the obstacles’ positions are known. Moreover, we show that the estimated optimization function has a minimizer and that its minimizers converge to the minimizers of the optimization function involving the true threat zones.

Semiclassical states for critical Choquard equations

In this paper, by constructing an appropriate Byeon-Wang type penalization function, we consider the critical Choquard equation−ϵ2Δu+V(x)u=1ϵα(Iα⁎|u|N+αN−2)|u|N+αN−2−2u+λg(u)inRN, where N≥3, (N−4)+<α<N, ϵ,λ>0 are parameters, and Iα is the Riesz potential. We obtained the localized semiclassical states concentrating at local minimizers of potential. It is the first time to study Choquard equations using this method as far as we know.

TCox: Correlation-Based Regularization Applied to Colorectal Cancer Survival Data.

Colorectal cancer (CRC) is one of the leading causes of mortality and morbidity in the world. Being a heterogeneous disease, cancer therapy and prognosis represent a significant challenge to medical care. The molecular information improves the accuracy with which patients are classified and treated since similar pathologies may show different clinical outcomes and other responses to treatment. However, the high dimensionality of gene expression data makes the selection of novel genes a problematic task. We propose TCox, a novel penalization function for Cox models, which promotes the selection of genes that have distinct correlation patterns in normal vs. tumor tissues. We compare TCox to other regularized survival models, Elastic Net, HubCox, and OrphanCox. Gene expression and clinical data of CRC and normal (TCGA) patients are used for model evaluation. Each model is tested 100 times. Within a specific run, eighteen of the features selected by TCox are also selected by the other survival regression models tested, therefore undoubtedly being crucial players in the survival of colorectal cancer patients. Moreover, the TCox model exclusively selects genes able to categorize patients into significant risk groups. Our work demonstrates the ability of the proposed weighted regularizer TCox to disclose novel molecular drivers in CRC survival by accounting for correlation-based network information from both tumor and normal tissue. The results presented support the relevance of network information for biomarker identification in high-dimensional gene expression data and foster new directions for the development of network-based feature selection methods in precision oncology.

Sparse signal reconstruction for nonlinear models via piecewise rational optimization

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and a penalization term. In contrast with most previous works which settle for approximated local solutions, we seek for a global solution to the obtained challenging nonconvex problem. Our global approach relies on the so-called Lasserre relaxation of polynomial optimization.We here specifically include in our approach the case of piecewise rational functions, which makes it possible to address a wide class of nonconvex exact and continuous relaxations of the ℓ0 penalization function. Additionally, we study the complexity of the optimization problem. It is shown how to use the structure of the problem to lighten the computational burden efficiently. Finally, numerical simulations illustrate the benefits of our method in terms of both global optimality and signal reconstruction.

Convergence of the direct limit analysis design method for discrete topology optimization

The present paper addresses the robustness and convergence behavior of the direct limit analysis (LA) based methodology developed for the topology design of continuum structures subject to prescribed statically and plastically admissible loads. The design methodology, based on a direct method formulation of the static LA problem, has recently been proposed for continuous topology optimization and its merits were highlighted. One of its remarkable features is the outstanding similarity of the topology design mathematical problem with its underlying direct static form of the LA problem. Subsequently, it has been extended to solve two dimensional discrete, i.e. black-and-white, topology design problems by modifying the objective function into a square root form in a way to penalize the intermediate densities and solving a sequence of conic quadratic programming problems of identical scale and algebraic structure as the continuous design problem, leaving a number of issues to be investigated, pertaining to convergence. In the present work different families of penalization function forms are proposed and assessed as alternatives to the original square root function. The performance is evaluated in terms of robustness, accuracy in the sense of closeness of the final design to a 0–1 topology and efficiency or number of approximate problems required for convergence. Convergence of the discrete topology design is shown to be improved using higher order power functions as well as trigonometric and exponential type penalty functions. The performance of the design method in solving example problems using the various penalization schemes is compared and the factors that affect it are analyzed.

An Inverse Approach for Ultrasonic Imaging From Full Matrix Capture Data: Application to Resolution Enhancement in NDT.

In the context of nondestructive testing (NDT), this article proposes an inverse problem approach for the reconstruction of high-resolution ultrasonic images from full matrix capture (FMC) data sets. We build a linear model that links the FMC data, i.e., the signals collected from all transmitter-receiver pairs of an ultrasonic array, to the discretized reflectivity map of the inspected object. In particular, this model includes the ultrasonic waveform corresponding to the response of transducers. Despite a large amount of data, the inversion problem is ill-posed. Therefore, a regularization strategy is proposed, where the reconstructed image is defined as the minimizer of a penalized least-squares cost function. A mixed penalization function is considered, which simultaneously enhances the sparsity of the image (in NDT, the reflectivity map is mostly zero except at the flaw locations) and its spatial smoothness (flaws may have some spatial extension). The proposed method is shown to outperform two well-known imaging methods: the total focusing method (TFM) and Excitelet. Numerical simulations with two close reflectors show that the proposed method improves the resolution limit defined by the Rayleigh criterion by a factor of four. Such high-resolution imaging capability is confirmed by experimental results obtained with side-drilled holes in an aluminum sample.

Topology optimization of heat and mass transfer problems in two fluids—one solid domains

Among various topology optimization methods used in fluid flow problems, density approach has gained more interest compared to other techniques as level set approach, topological derivative technique, and phase field method. The key part of density approach is the penalized interpolation function, which forces progressively porous cells made of fluid and solid simultaneously to belong discretely to fluid or solid sub-domains. However this type of problem was only solved in mono-fluid domains, in which the method accounts for the distribution of a single fluid and a single solid. The actual work aims to extend topology optimization in fluid flow problems to bi-fluid domain. A new interpolation function was developed for this purpose. Furthermore a penalization function was integrated in the multiobjective function, which ensure that each fluid takes its own path in the device, while maintaining a minimal required solid thickness between the channels of different fluids. The results showed the capacity of the proposed method to deal with multiple fluid phases in minimizing the pressure drop while maximizing heat exchange between different flows. The main conclusion is the potential of density approach to be applied on optimization of heat exchangers.

Spatial Multilevel Optical Flow Architecture-based Dynamic Motion Estimation in Vehicular Traffic Scenarios

Pedestrian detection is a challenging area in the intelligent vehicles domain. During the last years, many works have been proposed to efficiently detect motion in images. However, the problem becomes more complex when it comes to detecting moving areas while the vehicle is also moving. This paper presents a variational optical flow-based method for motion estimation in vehicular traffic scenarios. We introduce a framework for detecting motion areas with small and large displacements by computing optical flow using a multilevel architecture. The flow field is estimated at the shortest level and then successively computed until the largest level. We include a filtering parameter and a warping process using bicubic interpolation to combine the intermediate flow fields computed at each level during optimization to gain better performance. Furthermore, we find that by including a penalization function, our system is able to effectively reduce the presence of outliers and deal with all expected circumstances in real scenes. Experimental results are performed on various image sequences from Daimler Pedestrian Dataset that includes urban traffic scenarios. Our evaluation demonstrates that despite the complexity of the evaluated scenes, the motion areas with both moving and static camera can be effectively identified.

Comparison of the modified unbounded penalty and the LASSO to select predictive genes of response to chemotherapy in breast cancer

Covariate selection is a fundamental step when building sparse prediction models in order to avoid overfitting and to gain a better interpretation of the classifier without losing its predictive accuracy. In practice the LASSO regression of Tibshirani, which penalizes the likelihood of the model by the L1 norm of the regression coefficients, has become the gold-standard to reach these objectives. Recently Lee and Oh developed a novel random-effect covariate selection method called the modified unbounded penalty (MUB) regression, whose penalization function can equal minus infinity at 0 in order to produce very sparse models. We sought to compare the predictive accuracy and the number of covariates selected by these two methods in several high-dimensional datasets, consisting in genes expressions measured to predict response to chemotherapy in breast cancer patients. These comparisons were performed by building the Receiver Operating Characteristics (ROC) curves of the classifiers obtained with the selected genes and by comparing their area under the ROC curve (AUC) corrected for optimism using several variants of bootstrap internal validation and cross-validation. We found consistently in all datasets that the MUB penalization selected a remarkably smaller number of covariates than the LASSO while offering a similar—and encouraging—predictive accuracy. The models selected by the MUB were actually nested in the ones obtained with the LASSO. Similar findings were observed when comparing these results to those obtained in their first publication by other authors or when using the area under the Precision-Recall curve (AUCPR) as another measure of predictive performance. In conclusion, the MUB penalization seems therefore to be one of the best options when sparsity is required in high-dimension. Further investigation in other datasets is however required to validate these findings.

Topology Optimization of Conical-Beam Antennas Exploiting Rotational Symmetry

Microstrip conical-beam antennas are designed by the topology optimization of metallic patches combining the discrete optimization of vias. The antennas are designed to be angular-periodic structures with eight identical sectors, which makes the rotational symmetric radiation pattern more easily to be achieved and the optimization problem much easier to be solved. A restarting technique is introduced for the circular polarization design case, where the high cross-polarization discrimination (XPD) is hard to be realized. By increasing the weight of cross-polarization penalization function after the optimization restarts, much higher XPD is achieved compared to that of the antennas optimized with fixed subobjective weighting factors. By this method, two conical-beam antennas, which are linearly polarized and left-handed circularly polarized antennas, respectively, are designed. Simulated and measured results show that the antennas have expected conical shape radiation patterns, good matching, and high polarization purities.

Unlocking the Deployment of Spectrum Sharing With a Policy Enforcement Framework

Spectrum sharing has been proposed as a promising way to increase the efficiency of spectrum usage by allowing incumbent operators (IOs) to share their allocated radio resources with licensee operators (LOs), under a set of agreed rules. The goal is to maximize a common utility, such as the sum rate throughput, while maintaining the level of service required by the IOs. However, this is only guaranteed under the assumption that all “players” respect the agreed sharing rules. In this paper, we propose a comprehensive framework for licensed shared access (LSA) networks that discourages LO misbehavior. Our framework is built around three core functions: misbehavior detection via the employment of a dedicated sensing network; a penalization function; and, a behavior-driven resource allocation. To the best of our knowledge, this is the first time that these components are combined for the monitoring/policing of the spectrum under the LSA framework. Moreover, a novel simulator for LSA is provided as an open access tool, serving the purpose of testing and validating our proposed techniques via a set of extensive system-level simulations in the context of mobile network operators, where IOs and several competing LOs are considered. The results demonstrate that violation of the agreed sharing rules can lead to a great loss of resources for the misbehaving LOs, the amount of which is controlled by the system. Finally, we promote that including a policy enforcement function as part of the spectrum sharing system can be beneficial for the LSA system, since it can guarantee compliance with the spectrum sharing rules and limit the short-term benefits arising from misbehavior.

A new method for 3-D magnetic data inversion with physical bound

Inversion of magnetic data is an important step towards interpretation of the practical data. Smooth inversion is a common technique for the inversion of data. Physical bound constraint can improve the solution to the magnetic inverse problem. However, how to introduce the bound constraint into the inversion procedure is important. Imposing bound constraint makes the magnetic data inversion a non-linear inverse problem. In this work, a new algorithm is developed for the 3D inversion of magnetic data, which uses an efficient penalization function for imposing the bound constraint and Gauss Newton method to achieve the solution. An adaptive regularization method is used in order to choose the regularization parameter in this inversion approach. The inversion results of synthetic data show that the new method can produce models that adequately match the real location and shape of the synthetic bodies. The test carried out on the field data from Mt. Milligan copper-gold porphyry deposit shows that the new inversion approach can produce the magnetic susceptibility models consistent with the true structures.