Energy Minimization Framework Research Articles

Modeling of localized phase transformation in pseudoelastic shape memory alloys accounting for martensite reorientation

A reliable prediction of the pseudoelastic behavior necessitates the involvement of martensite reorientation in the model. This is important not only under non-proportional loading but in general when the phase transformation proceeds in a localized manner, which results in complex local deformation paths. In this work, an advanced model of pseudoelasticity is developed within the incremental energy minimization framework. A novel enhancement of the model over its original version lies in the formulation of a suitable rate-independent dissipation potential that incorporates the dissipation due to martensitic phase transformation and also due to martensite reorientation, thus yielding an accurate description of the inelastic transformation strain. The finite-element implementation of the model relies on the augmented Lagrangian treatment of the non-smooth incremental energy problem. Thanks to the micromorphic regularization, the related complexities are efficiently handled at the local level, leading to a robust finite-element model. Numerical studies highlight the predictive capabilities of the model. The characteristic mechanical behavior of NiTi tube under non-proportional tension–torsion and the intricate transformation evolution under pure bending are effectively captured by the model. Additionally, a detailed analysis is carried out to elucidate the important role of martensite reorientation in promoting the striations of the phase transformation front.

A Real-Time Energy Consumption Minimization Framework for Electric Vehicles Routing Optimization Based on SARSA Reinforcement Learning

A real-time, metadata-driven electric vehicle routing optimization to reduce on-road energy requirements is proposed in this work. The proposed strategy employs the state–action–reward–state–action (SARSA) algorithm to learn the EV’s maximum travel policy as an agent. As a function of the received reward signal, the policy model evaluates the optimal behavior of the agent. Markov chain models (MCMs) are used to estimate the agent’s energy requirements on the road, in which a single Markov step represents the average energy consumption based on practical driving conditions, including driving patterns, road conditions, and restrictions that may apply. A real-time simulation in Python with TensorFlow, NumPy, and Pandas library requirements was run, considering real-life driving data for two EVs trips retrieved from Google’s API. The two trips started at 4.30 p.m. on 11 October 2021, in Los Angeles, California, and Miami, Florida, to reach EV charging stations six miles away from the starting locations. According to simulation results, the proposed AI-based energy minimization framework reduces the energy requirement by 11.04% and 5.72%, respectively. The results yield lower energy consumption compared with Google’s suggested routes and previous work reported in the literature using the DDQN algorithm.

OFDM-Based Massive Grant-Free Transmission Over Frequency-Selective Fading Channels

In massive grant-free transmission, joint user activity detection (UAD) and channel estimation (CE) is essential for data recovery at the receiver, which has been extensively researched in frequency-flat fading scenarios. However, in practical orthogonal frequency division multiplexing (OFDM)-based systems, frequency-selective fading (FSF) leads to a significant increase in the number of channel coefficients to be estimated, imposing new challenges for the design of joint UAD and CE algorithms. Therefore, this paper investigates joint UAD and CE for OFDM-based massive grant-free transmission over FSF channels. Firstly, by employing the discrete cosine transform (DCT), the joint estimation problem is formulated as the compressed sensing (CS) problem with the reduced dimension of the DCT-domain channel response vector. Then, based on the low-dimension sparse channel model, we develop a hybrid message passing (HMP) algorithm under the constrained Bethe free energy (BFE) minimization framework to achieve efficient joint UAD and CE. To deal with the lack of the DCT-domain prior information in practical scenarios, we parameterize it as the Cauchy distribution or the Laplacian distribution and learn their parameters by the proposed HMP algorithm. Numerical results confirm the superior joint UAD and CE performance of the proposed algorithm over FSF channels.

Efficient Integral-Direct Methods for Self-Consistent Reduced Density Matrix Functional Theory Calculations on Central and Graphics Processing Units

Reduced density matrix functional theory (RDMFT), a promising direction in the problem of describing strongly correlated systems, is currently limited by its explicit dependence on natural orbitals and, by extension, the costly need to construct two-electron integrals in the molecular orbital basis. While a resolution-of-the-identity approach can reduce the asymptotic scaling behavior from O(N5) to O(N4), this is still prohibitively expensive for large systems, especially considering the usually slow convergence and the resulting high number of orbital optimization steps. In this work, efficient integral-direct methods are derived and benchmarked for various approximate functionals. Furthermore, we show how these integral-direct methods can be integrated into existing self-consistent energy minimization frameworks in an efficient manner, including improved methods for calculating diagonal elements of the two-electron integral tensor as required in self-interaction-corrected functionals and second derivatives of the energy with respect to the occupation numbers. In combination, these methods provide speedups of up to several orders of magnitude while greatly diminishing memory requirements, enabling the application of RDMFT to large molecular systems of general chemical interest, such as the challenging triplet-quintet gap of the iron(II) porphyrin complex.

Deformation twinning as a displacive transformation: Finite-strain phase-field model of coupled twinning and crystal plasticity

A finite-strain phase-field model of coupled deformation twinning and crystal plasticity is developed in the paper. Twinning is treated as a displacive transformation characterized by a volume-preserving stretch rather than a simple shear, the latter considered in the conventional approach. It is shown that the two approaches are equivalent in the sharp-interface description, but not in the diffuse-interface description. In the proposed stretch-based kinematics, each pair of conjugate twinning systems is represented by a single twin deformation variant, and thus a single order parameter suffices to consistently describe the two conjugate twinning systems, thereby treating them equally. The model is formulated in the framework of incremental energy minimization, which, upon time discretization, leads to a quasi-optimization problem due to the specific form of the incremental potential within the diffuse interfaces. To facilitate finite-element implementation, a micromorphic formulation of the model is employed. As an application, tensile twinning in HCP magnesium alloys is examined, and a set of comprehensive 2D plane-strain problems is studied to illustrate the features of the proposed approach.

Making reification concrete: A response to Bruineberg et al.

The principal target of this article is the reification Bruineberg et al. perceive of formalism within the literature on the variational free energy minimization (VFEM) framework. The authors do not provide a definition of reification, as none yet exists. Here I offer one. On this definition, the objects of the authors' critiques fall short of full-blown reification - as do the authors themselves.

Micromorphic approach to phase-field modeling of multivariant martensitic transformation with rate-independent dissipation effects

A micromorphic formulation of the phase-field model of martensitic transformation is developed within the incremental energy minimization framework. In contrast to the conventional phase-field formulation, the order parameters are viewed as local variables and the corresponding evolution equations are solved at the material-point level, i.e. at the Gauss points in the finite-element setting. From a computational standpoint, such a treatment is advantageous for complex evolution laws that may lead to computational difficulties if treated globally, as in the conventional phase-field formulation. In the micromorphic formulation, each order parameter is coupled to its micromorphic counterpart governed by a global Helmholtz-type PDE. This coupling ensures that the interfacial energy and related size effects are correctly captured by the model. In this work, the micromorphic approach is applied to a finite-strain multivariant phase-field model that incorporates rate-independent dissipation. The augmented Lagrangian technique is then used to transform the resulting non-smooth incremental minimization problem to a smooth and unconstrained saddle-point problem. Microstructure evolution under nano-indentation is studied to illustrate the approach.

Unifying Message Passing Algorithms Under the Framework of Constrained Bethe Free Energy Minimization

Variational message passing (VMP), belief propagation (BP) and expectation propagation (EP) have found their wide applications in complex statistical signal processing problems. In addition to viewing them as a class of algorithms operating on graphical models, this article unifies them under an optimization framework, namely, Bethe free energy minimization with differently and appropriately imposed constraints. This new perspective in terms of constraint manipulation can offer additional insights on the connection between different message passing algorithms and is valid for a generic statistical model. It also founds a theoretical framework to systematically derive message passing variants. Taking the sparse signal recovery (SSR) problem as an example, a low-complexity EP variant can be obtained by simple constraint reformulation, delivering better estimation performance with lower complexity than the standard EP algorithm. Furthermore, we can resort to the framework for the systematic derivation of hybrid message passing for complex inference tasks. Notably, a hybrid message passing algorithm is exemplarily derived for joint SSR and statistical model learning with near-optimal inference performance and scalable complexity.

Non-Learning Stereo-Aided Depth Completion Under Mis-Projection via Selective Stereo Matching

We propose a non-learning depth completion method for a sparse depth map captured using a light detection and ranging (LiDAR) sensor guided by a pair of stereo images. Generally, conventional stereo-aided depth completion methods have two limiations. (i) They assume the given sparse depth map is accurately aligned to the input image, whereas the alignment is difficult to achieve in practice. (ii) They have limited accuracy in the long range because the depth is estimated by pixel disparity. To solve the abovementioned limitations, we propose selective stereo matching (SSM) that searches the most appropriate depth value for each image pixel from its neighborly projected LiDAR points based on an energy minimization framework. This depth selection approach can handle any type of mis-projection. Moreover, SSM has an advantage in terms of long-range depth accuracy because it directly uses the LiDAR measurement rather than the depth acquired from the stereo. SSM is a discrete process; thus, we apply variational smoothing with binary anisotropic diffusion tensor (B-ADT) to generate a continuous depth map while preserving depth discontinuity across object boundaries. Experimentally, compared with the previous state-of-the-art stereo-aided depth completion, the proposed method reduced the mean absolute error (MAE) of the depth estimation to 0.65 times and demonstrated approximately twice more accurate estimation in the long range. Moreover, under various LiDAR-camera calibration errors, the proposed method reduced the depth estimation MAE to 0.34-0.93 times from previous depth completion methods.

Comparative Perceptual Assessment of Visual Signals Using Free Energy Features

In this paper, we put forward the concept of comparative perceptual quality assessment (C-PQA), which refers to the judgment of relative qualities of two visual signals of the same content, but subject to different types and levels of distortions. While it is straightforward for human observers to fulfill the CPQA task in daily lives, it remains a difficult challenge for the current research of perceptual quality assessment (PQA). Among the existing PQA algorithms, the full-reference (FR) and reducedreference (RR) methods both need prior knowledge of the original images while the no-reference (NR) algorithms usually work with a single input image. C-PQA is inherently different from those existing methods in that it takes an image pair as input and predicts their relative quality without using any knowledge about the original image. In this paper, we propose a brain theory inspired approach to C-PQA that emulates the process of comparing the relative quality of two visual stimuli as performed by the human visual system (HVS) within the framework of free energy minimization. The brain's internal generative models initialized on the inputs are then used to explain both images. During the internal generative modeling, a group of features are extracted and then integrated to determine the relative quality of two images. We designed a dedicated image database to test the proposed C-PQA algorithm. Experimental results show that the proposed method achieves up to 98% prediction accuracy in line with the subjective ratings, outperforming many state of the art PQA algorithms.

Robust Focus Volume Regularization in Shape From Focus.

Shape from focus (SFF) reconstructs 3D shape of the scene from a sequence of multi-focus images, and the quality of reconstructed shape mainly depends on the accuracy of image focus volume (FV). Traditional SFF techniques exhibit poor performance in preserving structural edges and fine details while removing noisy artifacts, and mostly they do not incorporate any additional shape prior. Therefore, in this paper, we propose to refine FV by formulating an energy minimization framework that employs a nonconvex regularizer and incorporates two types of shape priors. The proposed regularizer is robust against noisy focus values. The first proposed shape prior is input image sequence and it is a single and static shape prior. While, the second shape prior corresponds to a series of shape priors. These shape priors are FVs which are iteratively obtained on-the-fly. Both of these shape priors constrain the solution space for output FV. We optimize nonconvex energy function through majorize-minimization algorithm which iteratively guarantees a local minimum and converges quickly. Experiments have been conducted to evaluate accuracy and convergence properties of the proposed method. Experimental results of synthetic and real image sequences demonstrate that our method achieves superior results in terms of ability to reconstruct accurate 3D shapes as compared to existing approaches.

A Blind Spectral Unmixing in Wavelet Domain

In this article, a wavelet-based energy minimization framework is developed for joint estimation of endmembers and abundances without assuming pure pixels while considering noisy scenario. Spectrally dense and overlapped hyperspectral data are represented using biorthogonal wavelet bases that yield a compact linear mixing model in the wavelet domain. It acts as the data term and helps to reduce solution space of the unmixed components. Three prior terms are incorporated to better handle the ill-posedness, i.e., the logarithm of determinant volume regularizer enforces minimum endmember simplex, smoothness (spatial) prior to individual abundance maps, and spectral constraint through learning dictionary of abundances. Alternating nonnegative least-squares is employed to optimize the regularized and constrained nonnegative matrix factorization functional in the wavelet domain. We conduct theoretical analysis, discuss convergence and algorithmic details. Experiments are conducted on synthetic and three real benchmark hyperspectral data AVIRIS Cuprite, HYDICE Urban, and AVIRIS Jasper Ridge. The efficacy of the proposed algorithm is evaluated by comparing results with state of the art.

A Generative Model for Generic Light Field Reconstruction.

Recently deep generative models have achieved impressive progress in modeling the distribution of training data. In this work, we present for the first time a generative model for 4D light field patches using variational autoencoders to capture the data distribution of light field patches. We develop a generative model conditioned on the central view of the light field and incorporate this as a prior in an energy minimization framework to address diverse light field reconstruction tasks. While pure learning-based approaches do achieve excellent results on each instance of such a problem, their applicability is limited to the specific observation model they have been trained on. On the contrary, our trained light field generative model can be incorporated as a prior into any model-based optimization approach and therefore extend to diverse reconstruction tasks including light field view synthesis, spatial-angular super resolution and reconstruction from coded projections. Our proposed method demonstrates good reconstruction, with performance approaching end-to-end trained networks, while outperforming traditional model-based approaches on both synthetic and real scenes. Furthermore, we show that our approach enables reliable light field recovery despite distortions in the input.

ROBUST AND ACCURATE PLANE SEGMENTATION FROM POINT CLOUDS OF STRUCTURED SCENES

Abstract. Plane segmentation from the point cloud is an important step in various types of geo-information related to human activities. In this paper, we present a new approach to accurate segment planar primitives simultaneously by transforming it into the best matching issue between the over-segmented super-voxels and the 3D plane models. The super-voxels and its adjacent topological graph are firstly derived from the input point cloud as over-segmented small patches. Such initial 3D plane models are then enriched by fitting centroids of randomly sampled super-voxels, and translating these grouped planar super-voxels by structured scene prior (e.g. orthogonality, parallelism), while the generated adjacent graph will be updated along with planar clustering. To achieve the final super-voxels to planes assignment problem, an energy minimization framework is constructed using the productions of candidate planes, initial super-voxels, and the improved adjacent graph, and optimized to segment multiple consistent planar surfaces in the scenes simultaneously. The proposed algorithms are implemented, and three types of point clouds differing in feature characteristics (e.g. point density, complexity) are mainly tested to validate the efficiency and effectiveness of our segmentation method.

Laplacian Coordinates: Theory and Methods for Seeded Image Segmentation

Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated computational tools whose performance strongly depends on how good the training data reflect a sought image pattern. Moreover, poor adherence to the image contours, lack of unique solution, and high computational cost are other common issues present in most seeded segmentation methods. In this work we introduce Laplacian Coordinates, a quadratic energy minimization framework that tackles the issues above in an effective and mathematically sound manner. The proposed formulation builds upon graph Laplacian operators, quadratic energy functions, and fast minimization schemes to produce highly accurate segmentations. Moreover, the presented energy functions are not prone to local minima, i.e., the solution is guaranteed to be globally optimal, a trait not present in most image segmentation methods. Another key property is that the minimization procedure leads to a constrained sparse linear system of equations, enabling the segmentation of high-resolution images at interactive rates. The effectiveness of Laplacian Coordinates is attested by a comprehensive set of comparisons involving nine state-of-the-art methods and several benchmarks extensively used in the image segmentation literature.

Feature-Aware Trilateral Filter With Energy Minimization for 3D Mesh Denoising

Sharp edges and corners are crucial features for high-quality and fine-detailed 3D meshes, which we tend to treat as noises in previous tasks of mesh denoising mistakenly. A challenge arises on how to handle both surfaces and features simultaneously in 3D mesh denoising. Classical works mainly focused on surfaces, whereas features also reasonably need proper processes. In this paper, we propose a feature-aware trilateral filter under the framework of energy minimization for 3D mesh denoising and address the above challenge. Concretely, we treat the challenge as an energy minimization model, where the data and smooth terms are both carefully designed. Apart from this, we introduce a feature-aware trilateral filter for high-quality mesh guidance to the model. In this filter, features are detected and distinguished from surfaces for consequent guidance. With the help of the model and filter, more priors are involved, and we can make global optimization for better denoising performance. We perform experiments on both synthetic and scanned meshes, where both subjective and objective evaluations are displayed to show the superior performance of our method to state-of-the-art methods. Furthermore, two experiments, including ablation tests and parameter sensitivities tests, are conducted to show the robustness and efficiency of our method thoroughly. All these results demonstrate that our method is suitable for robust and efficient performance in future mesh-oriented applications.

What is of interest for tourists in an alpine destination: personalized recommendations for daily activities based on view data

Smartphones are nowadays important tools for tourists. For instance, while on the go in a destination, tourists can use smartphones to find places of interest and to identify activities that might be of interest, as well as a wealth of related information and even special offers in real-time. However, it is time consuming and not easy for tourists in an unknown destination to choose among the numerous options available. Recommendations for instance from other tourists with similar interests would help immensely. Indeed, places and activities are often reviewed and rated by other tourists, however, this information is typically not personalized. This article proposes a recommender system as part of an evolving mobile destination app. Our recommender app is capable of providing personalized recommendations to tourists thereby facilitating and enriching tourists’ experience and stay. This work is based on two qualitative studies towards exploring the information needs of tourists in an alpine destination. These studies were conducted using the mobile ethnography approach and semi-structured interviews. A hybrid recommender system is proposed that uses implicit user feedback in the form of view duration. The proposed system was tested using real data derived from tourists using the mobile app in a Swiss alpine destination. The results of these experiments demonstrate that the system is capable of providing high-quality and diverse recommendations. The core contribution of this work lies in the transformation of the viewing durations to a set of preference values and in learning the optimized weights of the parameters of a hybrid system utilizing an energy minimization framework.

Phase-field modeling of multivariant martensitic microstructures and size effects in nano-indentation

A finite-strain phase-field model is developed for the analysis of multivariant martensitic transformation during nano-indentation. Variational formulation of the complete evolution problem is developed within the incremental energy minimization framework. Computer implementation is performed based on the finite-element method which allows a natural treatment of the finite-strain formulation and of the contact interactions. A detailed computational study of nano-indentation reveals several interesting effects including the pop-in effect associated with nucleation of martensite and the energy-lowering breakdown of the symmetry of microstructure. The effect of the indenter radius is also examined revealing significant size effects governed by the interfacial energy.

Gradient-enhanced thermomechanical 3D model for simulation of transformation patterns in pseudoelastic shape memory alloys

Stress-induced martensitic transformation in polycrystalline NiTi under tension often proceeds through formation and propagation of macroscopic phase transformation fronts, i.e., diffuse interfaces that separate the transformed and untransformed domains. A gradient-enhanced 3D finite-strain model of pseudoelasticity is developed in this work with the aim to describe the related phenomena. The underlying softening response is regularized by enhancing the Helmholtz free energy of a non-gradient model with a gradient term expressed in terms of the martensite volume fraction. To facilitate finite-element implementation, a micromorphic-type regularization is then introduced following the approach developed recently in the 1D small-strain context. The complete evolution problem is formulated within the incremental energy minimization framework, and the resulting non-smooth minimization problem is solved by employing the augmented Lagrangian technique. In order to account for the thermomechanical coupling effects, a general thermomechanical framework, which is consistent with the second law of thermodynamics and considers all related couplings, is also developed. Finite-element simulations of representative 3D problems show that the model is capable of representing the loading-rate effects in a NiTi dog-bone specimen and complex transformation patterns in a NiTi tube under tension. A parametric study is also carried out to investigate the effect of various parameters on the characteristics of the macroscopic transformation front.

Real-time pose and shape reconstruction of two interacting hands with a single depth camera

We present a novel method for real-time pose and shape reconstruction of two strongly interacting hands. Our approach is the first two-hand tracking solution that combines an extensive list of favorable properties, namely it is marker-less, uses a single consumer-level depth camera, runs in real time, handles inter- and intra-hand collisions, and automatically adjusts to the user's hand shape. In order to achieve this, we embed a recent parametric hand pose and shape model and a dense correspondence predictor based on a deep neural network into a suitable energy minimization framework. For training the correspondence prediction network, we synthesize a two-hand dataset based on physical simulations that includes both hand pose and shape annotations while at the same time avoiding inter-hand penetrations. To achieve real-time rates, we phrase the model fitting in terms of a nonlinear least-squares problem so that the energy can be optimized based on a highly efficient GPU-based Gauss-Newton optimizer. We show state-of-the-art results in scenes that exceed the complexity level demonstrated by previous work, including tight two-hand grasps, significant inter-hand occlusions, and gesture interaction. 1