Minimization Of Energy Function Research Articles

A framework for automated reconstruction of communication towers from terrestrial laser scanning point clouds

ABSTRACT Communication towers provide reliable wireless communication services and play a vital role in modern society. This paper presents an automatic 3D reconstruction framework for communication towers based on point clouds. The antenna is reconstructed by a model-driven method, which constructs an energy function including the data and smoothing terms to evaluate the model accuracy. The parameters of the antenna model are obtained by minimizing energy function with hybrid Genetic Algorithm (GA) and Simulated Annealing (SA). And the predefined model is transformed using these parameters to achieve antenna 3D reconstruction. For tower body reconstruction, the point cloud of the tower body is finely extracted with the region growing followed by piecewise fitting to obtain the model. The performance of the proposed method is evaluated on point clouds from six scenes. The average root-mean-square error (RMSE) of antenna reconstruction is 1.3 cm. The average precision, recall, and F1-score values of the tower body point extraction are 99.9%, 93.5%, and 96.6%, respectively. The average RMSE of tower body reconstruction is 1.2 cm. The experimental results indicate that the method can effectively reconstruct the antenna and tower body with point clouds, providing a feasible framework for the 3D reconstruction of communication towers.

SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR IN SLIDING MODE

The paper examines a series of speed control algorithms for a synchronous permanent magnet motor in sliding mode, providing asymptotic stability of the first, second, and third order. In the sliding mode, the control system exhibits properties that are unattainable with classical continuous control algorithms. The control algorithms are developed based on the inverse dynamics method combined with the minimization of local instantaneous energy functionals. The key idea of the method lies in the reversibility of the direct Lyapunov method for stability analysis. The closed-loop control system has a predefined Lyapunov function, represented by the instantaneous energy. Notably, the control algorithms do not require knowledge of the object's parameters or differentiation operations, which facilitates their practical implementation. The regulator parameters consist solely of coefficients used to specify the desired duration and shape of current and motor speed transient processes. The vector speed control system comprises two controllers for the stator current components and the motor speed controller. All regulators operate in sliding mode. The output signals of the stator current component controllers and speed vary discontinuously from maximum to minimum values. Simulation results demonstrate the effectiveness and high-quality performance of the control algorithms. To determine the control performance indicators for the three synthesized speed controllers, the motor startup trajectory is formed from characteristic segments of constant, linearly increasing, and parabolic signals. The speed control algorithm with a first-order asymptote ensures zero tracking error only for a constant reference signal. With a linearly increasing reference signal, the steady-state relative tracking error is 2,5 %, while for a parabolic reference signal, the error varies between zero and 2,5 %. The second-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant and linearly increasing reference signals, and for a parabolic reference signal, the steady-state relative tracking error is 0,125 %. The third-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant, linearly increasing, and parabolic reference signals, with a maximum dynamic relative tracking error of 0,05 %.

Minimizers of fractional NLS energy functionals in $$\mathbb {R}^{2}$$

Minimizers of fractional NLS energy functionals in $$\mathbb {R}^{2}$$

Fundamental Theory and R-linear Convergence of Stretch Energy Minimization for Spherical Equiareal Parameterization

Abstract Here, we extend the finite distortion problem from bounded domains in ℝ2 to closed genus-zero surfaces in ℝ3 by a stereographic projection. Then, we derive a theoretical foundation for spherical equiareal parameterization between a simply connected closed surface M and a unit sphere 𝕊2 by minimizing the total area distortion energy on ̅ℂ. After the minimizer of the total area distortion energy is determined, it is combined with an initial conformal map to determine the equiareal map between the extended planes. From the inverse stereographic projection, we derive the equiareal map between M and 𝕊2. The total area distortion energy is rewritten into the sum of Dirichlet energies associated with the southern and northern hemispheres and is decreased by alternatingly solving the corresponding Laplacian equations. Based on this foundational theory, we develop a modified stretch energy minimization function for the computation of spherical equiareal parameterization between M and 𝕊2. In addition, under relatively mild conditions, we verify that our proposed algorithm has asymptotic R-linear convergence or forms a quasi-periodic solution. Numerical experiments on various benchmarks validate that the assumptions for convergence always hold and indicate the efficiency, reliability, and robustness of the developed modified stretch energy minimization function.

Non-local gradients in bounded domains motivated by continuum mechanics: Fundamental theorem of calculus and embeddings

Abstract In this article, we develop a new set of results based on a non-local gradient jointly inspired by the Riesz s s -fractional gradient and peridynamics, in the sense that its integration domain depends on a ball of radius δ > 0 \delta \gt 0 (horizon of interaction among particles, in the terminology of peridynamics), while keeping at the same time the singularity of the Riesz potential in its integration kernel. Accordingly, we define a functional space suitable for non-local models in calculus of variations and partial differential equations. Our motivation is to develop the proper functional analysis framework to tackle non-local models in continuum mechanics, which requires working with bounded domains, while retaining the good mathematical properties of Riesz s s -fractional gradients. This functional space is defined consistently with Sobolev and Bessel fractional ones: we consider the closure of smooth functions under the natural norm obtained as the sum of the L p {L}^{p} norms of the function and its non-local gradient. Among the results showed in this investigation, we highlight a non-local version of the fundamental theorem of calculus (namely, a representation formula where a function can be recovered from its non-local gradient), which allows us to prove inequalities in the spirit of Poincaré, Morrey, Trudinger, and Hardy as well as the corresponding compact embeddings. These results are enough to show the existence of minimizers of general energy functionals under the assumption of convexity. Equilibrium conditions in this non-local situation are also established, and those can be viewed as a new class of non-local partial differential equations in bounded domains.

Deep convolutional Ritz method: parametric PDE surrogates without labeled data

The parametric surrogate models for partial differential equations (PDEs) are a necessary component for many applications in computational sciences, and the convolutional neural networks (CNNs) have proven to be an excellent tool to generate these surrogates when parametric fields are present. CNNs are commonly trained on labeled data based on one-to-one sets of parameter-input and PDE-output fields. Recently, residual-based deep convolutional physics-informed neural network (DCPINN) solvers for parametric PDEs have been proposed to build surrogates without the need for labeled data. These allow for the generation of surrogates without an expensive offline-phase. In this work, we present an alternative formulation termed deep convolutional Ritz method (DCRM) as a parametric PDE solver. The approach is based on the minimization of energy functionals, which lowers the order of the differential operators compared to residual-based methods. Based on studies involving the Poisson equation with a spatially parameterized source term and boundary conditions, we find that CNNs trained on labeled data outperform DCPINNs in convergence speed and generalization abilities. The surrogates generated from the DCRM, however, converge significantly faster than their DCPINN counterparts, and prove to generalize faster and better than the surrogates obtained from both CNNs trained on labeled data and DCPINNs. This hints that the DCRM could make PDE solution surrogates trained without labeled data possibly.

Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity

Abstract We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable to nonlocal solid mechanics, especially nonlinear elasticity. This nonlocal gradient was introduced in an earlier work, inspired by Riesz’ fractional gradient, but suitable for bounded domains. The main assumption on the integrand of the energy is polyconvexity. Thus, we adapt the corresponding results of the classical case to this nonlocal context, notably, Piola’s identity, the integration by parts of the determinant and the weak continuity of the determinant. The proof exploits the fact that every nonlocal gradient is a classical gradient.

In-situ 3D contour measurement for laser powder bed fusion based on phase guidance

In-situ layerwise imaging measurement of laser powder bed fusion (LPBF) provides a wealth of forming and defect data which enables monitoring of components quality and powder bed homogeneity. Using high-resolution camera layerwise imaging and image processing algorithms to monitor fusion area and powder bed geometric defects has been studied by many researchers, which successfully monitored the contours of components and evaluated their accuracy. However, research for the methods of in-situ 3D contour measurement or component edge warping identification is rare. In this study, a 3D contour measurement method combining gray intensity and phase difference is proposed, and its accuracy is verified by designed experiments. The results show that the high-precision of the 3D contours can be achieved by the constructed energy minimization function. This method can detect the deviations of common geometric features as well as warpage at LPBF component edges, and provides fundamental data for in-situ quality monitoring tools.

$ L^{p} $ compactness criteria with an application to variational convergence of some nonlocal energy functionals

<abstract><p>Motivated by some variational problems from a nonlocal model of mechanics, this work presents a set of sufficient conditions that guarantee a compact inclusion in the function space of $ L^{p} $ vector fields defined on a domain $ \Omega $ that is either a bounded domain in $ \mathbb{R}^{d} $ or $ \mathbb{R}^{d} $ itself. The criteria are nonlocal and are given with respect to nonlocal interaction kernels that may not be necessarily radially symmetric. Moreover, these criteria for vector fields are also different from those given for scalar fields in that the conditions are based on nonlocal interactions involving only parts of the components of the vector fields. The $ L^{p} $ compactness criteria are utilized in demonstrating the convergence of minimizers of parameterized nonlocal energy functionals.</p></abstract>

Beam bending and Λ-fractional analysis

<abstract> <p>Since the global stability criteria for Λ-fractional mechanics have been established, the Λ-fractional beam bending problem is discussed within that context. The co-existence of the phase phenomenon is revealed, allowing for elastic curves with non-smooth curvatures. The variational bending problem in the Λ-fractional space is considered. Global minimization of the total energy function of beam bending is necessarily applied. The variational Euler-Lagrange equation yields an equilibrium equation of the elastic curve, with the simultaneous possible corners being expressed by Weierstrass-Erdmann corner conditions.</p> </abstract>

Measurement-Based Control for Minimizing Energy Functions in Quantum Systems

In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure that, under a given feedback control law, ensures convergence to the minimum energy eigenstate of a given energy function. By including quantum non-demolition (QND) measurements in the loop, convergence to a pure state can be ensured from an arbitrary mixed initial state. Based on existing results on strict control Lyapunov functions, we formulate a semidefinite optimization problem, whose solution defines a non-unique control Hamiltonian, which is sufficient to ensure almost sure convergence to the minimum energy eigenstate under the given feedback law and the action of QND measurements. A numerical example is provided to showcase the proposed methodology.

Energy Consumption Monitoring with Evaluation of Hidden Energy Losses

This article presents a computational method for monitoring the energy consumption of technological systems with the assessment of their hidden energy losses caused by erroneous actions of personnel or equipment failures. Herewith, energy losses are calculated as the difference between the actual energy consumed and the minimum energy required to conduct the process in all operating modes. The minimum required energy is determined by the machine learning method based on stationary consumption precedents. Two approaches to the implementation of energy consumption monitoring with the assessment of hidden energy losses are considered – hardware and software. The hardware approach is based on the preliminary definition of normative, or minimum specific energy consumption in each technological mode. The software approach is based on the modeling of stationary areas of energy consumption in the form of precedents and their further analysis in the space of influential technological parameters. The paper notes the advantages and disadvantages of the proposed monitoring method, it is emphasized that the method is able to work with both linear and non-linear functions of energy dependence on the parameters of the technological process. It is noted in the paper that the advantage of the proposed method is the automated construction of the minimum energy function.

A note on local minimizers of energy on complete manifolds

In this paper, we study the geometric rigidity of complete Riemannian manifolds admitting local minimizers of energy functionals. More precisely, assuming the existence of a non-trivial local minimizer and under suitable assumptions, a Riemannian manifold under consideration must be a product manifold furnished with a warped metric. Secondly, under similar hypotheses, we deduce a geometrical splitting in the same fashion as in the Cheeger-Gromoll splitting theorem and we also get information about local minimizers.

Dynamic Modeling of Intrinsic Self-Healing Polymers Using Deep Learning.

The properties of self-healing polymers are traditionally identified through destructive testing. This means that the mechanics are explored in hindsight with either theoretical derivations and/or simulations. Here, a self-healing property evolution using energy functional dynamical (SPEED) model is proposed to predict and understand the mechanics of self-healing of polymers using images of cuts dynamically healing over time. Using machine learning, an energy functional minimization (EFM) model extracted an effective underlying dynamical system from a time series of two-dimensional cut images on a self-healing polymer of constant thickness. This model can be used to capture the physics behind the self-healing dynamics in terms of potential and interface energies. When combined with a static property prediction model, the SPEED model can predict the macroscopic evolution of material properties after training only on a small set of experimental measurements. Such temporal evolutions are usually inaccessible from pure experiments or computational modeling due to the need for destructive testing. As an example, we validate this approach on toughness measurements of an intrinsic self-healing conductive polymer by capturing over 100 000 image frames of cuts to build the machine learning (ML) model. The results show that the SPEED model can be applied to predict the temporal evolution of macroscopic properties using few measurements as training data.

Skull Surface Reconstruction with Euler’s Elastica Model from Point Cloud Data

In order to reconstruct accurate smooth implicit surfaces from skull point cloud data with complex topological relations, a variational level set method based on Euler’s Elastica model is proposed. Firstly, Euler’s Elastica is introduced into the variational energy functional as a regularization constraint, and the variational energy functional minimization problem is transformed into a series of subproblems by the augmented Lagrange method. Secondly, each subproblem is solved by generalized soft threshold formula, analytical formula and fast Fourier transform respectively. Finally, the projection algorithm is used during the computation to avoid the re-initialization of the level set function effectively. The experimental results show that the proposed variational level set method based on Euler’s Elastica has better convergence and effectiveness than the existing methods, which can improve the reconstruction accuracy and avoid missing surface edges.

Understanding Unsupervised Deep Learning for Text Line Segmentation

We propose an unsupervised feature learning approach for segmenting text lines of handwritten document images with no labelling effort. Humans can easily group local text line features to global coarse patterns. We leverage this coherent visual perception of text lines as a supervising signal by formulating the feature learning as a global pattern differentiation task. The machine is trained to detect whether a document patch contains a similar global text line pattern with its identity or neighbours, and a different global text line pattern with its 90-degree-rotated identity or neighbours. Clustering the central windows of document image patches using their extracted features, forms blob lines which strike through the text lines. The blob lines guide an energy minimization function for extracting text lines in a binary image and guide a seam carving function for detecting baselines in a colour image. In identifying the aspect of the input patch that supports the actual prediction and clustering, we contribute toward the understanding of input patch functionality. We evaluate the method on several variants of text line segmentation datasets to demonstrate its effectiveness, visualize what it has learned, and enable it to comprehend its clustering strategy from a human perspective.

On the existence and limit behavior of ground states for two coupled Hartree equations

We study the ground states for a system of two coupled Hartree equations with both attractive intraspecies and attractive interspecies interactions in RN (N≥3), which can also be described by L2-constraint minimizers of mass critical Hartree energy functionals with trapping potentials. The existence and nonexistence of minimizers are classified completely by establishing the refined Gagliardo-Nirenberg type inequality. Based on some delicate estimates of the Hartree energy functional, the limit behavior of minimizers is also analyzed as the interspecies interaction strength goes to a critical value, where each component of minimizers blows up and concentrates at a flattest common minimum point of trapping potentials. An optimal blow-up rate of minimizers for the Hartree energy functional is concomitantly obtained.

As-locally-uniform-as-possible reshaping of vector clip-art

Vector clip-art images consist of regions bounded by a network of vector curves. Users often wish to reshape , or rescale, existing clip-art images by changing the locations, proportions, or scales of different image elements. When reshaping images depicting synthetic content they seek to preserve global and local structures. These structures are best preserved when the gradient of the mapping between the original and the reshaped curve networks is locally as close as possible to a uniform scale; mappings that satisfy this property maximally preserve the input curve orientations and minimally change the shape of the input's geometric details, while allowing changes in the relative scales of the different features. The expectation of approximate scale uniformity is local ; while reshaping operations are typically expected to change the relative proportions of a subset of network regions, users expect the change to be minimal away from the directly impacted regions and expect such changes to be gradual and distributed as evenly as possible. Unfortunately, existing methods for editing 2D curve networks do not satisfy these criteria. We propose a targeted As-Locally-Uniform-as-Possible (ALUP) vector clip-art reshaping method that satisfies the properties above. We formulate the computation of the desired output network as the solution of a constrained variational optimization problem. We effectively compute the desired solution by casting this continuous problem as a minimization of a non-linear discrete energy function, and obtain the desired minimizer by using a custom iterative solver. We validate our method via perceptual studies comparing our results to those created via algorithmic alternatives and manually generated ones. Participants preferred our results over the closest alternative by a ratio of 6 to 1.

Constraining pseudo‐label in self‐training unsupervised domain adaptation with energy‐based model

Deep learning is usually data starved, and the unsupervised domain adaptation (UDA) is developed to introduce the knowledge in the labeled source domain to the unlabeled target domain. Recently, deep self-training presents a powerful means for UDA, involving an iterative process of predicting the target domain and then taking the confident predictions as hard pseudo-labels for retraining. However, the pseudo-labels are usually unreliable, thus easily leading to deviated solutions with propagated errors. In this paper, we resort to the energy-based model and constrain the training of the unlabeled target sample with an energy function minimization objective. It can be achieved via a simple additional regularization or an energy-based loss. This framework allows us to gain the benefits of the energy-based model, while retaining strong discriminative performance following a plug-and-play fashion. The convergence property and its connection with classification expectation minimization are investigated. We deliver extensive experiments on the most popular and large-scale UDA benchmarks of image classification as well as semantic segmentation to demonstrate its generality and effectiveness.

An Efficient Threshold Dynamics Method for Topology Optimization for Fluids

We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power in the fluid and the perimeter approximated by nonlocal energy, subject to a fluid volume constraint and the incompressibility condition. We show that the minimization problem can be solved with an iterative scheme in which the Stokes equation is approximated by a Brinkman equation. The indicator functions of the fluid-solid regions are then updated according to simple convolutions followed by a thresholding step. We demonstrate mathematically that the iterative algorithm has the total energy decaying property. The proposed algorithm is simple and easy to implement. A simple adaptive time strategy is also used to accelerate the convergence of the iteration. Extensive numerical experiments in both two and three dimensions show that the proposed iteration algorithm converges in much fewer iterations and is more efficient than many existing methods. In addition, the numerical results show that the algorithm is very robust and insensitive to the initial guess and the parameters in the model.