Continuous Formulation Research Articles

Neural Disparity Refinement.

We propose a framework that combines traditional, hand-crafted algorithms and recent advances in deep learning to obtain high-quality, high-resolution disparity maps from stereo images. By casting the refinement process as a continuous feature sampling strategy, our neural disparity refinement network can estimate an enhanced disparity map at any output resolution. Our solution can process any disparity map produced by classical stereo algorithms, as well as those predicted by modern stereo networks or even different depth-from-images approaches, such as the COLMAP structure-from-motion pipeline. Nonetheless, when deployed in the former configuration, our framework performs at its best in terms of zero-shot generalization from synthetic to real images. Moreover, its continuous formulation allows for easily handling the unbalanced stereo setup very diffused in mobile phones.

Market informed portfolio optimization methods with hybrid quantum computing

AbstractThis document presents a portfolio optimization framework that employs a hybrid quantum computing algorithm and a futures market sentiment indicator—The Market Sentiment Meter (MSM) variable, developed jointly by CME Group and 1QBit. The methodology used was the Variational Quantum Eigensolver (VQE). The work presented here is divided into four portfolio optimization problem formulations, of binary and continuous variable formulations, determining which assets to pick their weights. This work demonstrates that adding the MSM variable can improve the performance of hybrid quantum solutions, by informing the asset selection problem with market environment information through the four MSM states.

Multi-objective route planning of an unmanned air vehicle in continuous terrain: An exact and an approximation algorithm

Unmanned Aerial Vehicles (UAVs) are widely used for military and civilian purposes. Effective route planning is an important component of their successful missions. In this study, we address the route planning problem of a UAV tasked with collecting information from various target locations in a protected terrain. We consider multiple targets, three objectives, and time-dependent information availability. Modeling the movement of UAVs in a continuous terrain in the presence of multiple objectives is complex. Conflicting objectives typically lead to a continuum of efficient trajectory options between two targets. We formulate the routing problem as a mixed-integer programming (MIP) model that captures the movement in the continuous terrain. We demonstrate the superiority of the continuous terrain formulation over the simplified discretized terrain formulation. We also develop an approximation algorithm that reduces the computational requirements of the MIP model substantially while ensuring a desired level of precision.

Continuous twin-screw melt granulation of drug-loaded electrospun fibers

Electrospinning (ES) is a promising continuous formulation strategy to produce amorphous solid dispersions (ASDs) and thereby improve the dissolution of poorly water-soluble drugs. However, processing the electrospun material into solid dosage forms (e.g. tablets) is challenging due to the poor flow properties. In this research, continuous twin-screw melt granulation was applied to improve the flowability of the fibers and therefore ease the further processing steps. During this work, two ASD compositions were investigated: one containing 60 % poly-vinylpyrrolidone-vinyl acetate 6:4 copolymer and 40 % itraconazole (ITR), and another one containing hydroxypropyl methylcellulose (HPMC) and ITR in the same ratio. Both fiber compositions were granulated with polyethene glycol as the binder material, while the effects of the process parameters were examined. The application of higher granulation temperature and screw configurations with increased shear forces compromised the fibrous structure, induced crystallization of the ASD, and decreased the dissolution. However, the stability of the ITR-HPMC fibers proved to be higher as their granulation at 60 °C led to granules with adequate flow properties and dissolution. Moreover, tablets with fewer excipients were pressed from them, resulting in a 34 % reduction in weight. Consequently, this process can complement ES technology and facilitate its industrial implementation.

Nonlinear twofold saddle point-based mixed finite element methods for a regularized μ(I)-rheology model of granular materials

We propose and analyze new mixed finite element methods for a regularized μ(I)-rheology model of granular flows with an equivalent viscosity depending nonlinearly on the pressure and the Euclidean norm of the symmetric part of the velocity gradient. To this end, and besides the velocity, the pressure and the aforementioned strain rate, we introduce a modified stress tensor that includes the convective term, and the skew-symmetric vorticity, as auxiliary tensor unknowns, thus yielding a mixed variational formulation within a Banach spaces framework. Then, the pressure is obtained through an iterative postprocess suggested by the incompressibility condition of the fluid, which allows us to express this unknown in terms of the aforementioned stress and the velocity. A fixed-point strategy combined with a solvability result for a class of nonlinear twofold saddle point operator equations in Banach spaces, is employed to show, along with the classical Banach fixed-point theorem, the well-posedness of the continuous and discrete formulations. In particular, PEERS and AFW elements of order ℓ⩾0 for the stress, the velocity, and the skew-symmetric vorticity, and piecewise polynomials of degree ⩽ℓ+n (resp. ⩽ℓ+1) for the strain rate with PEERS (resp. with AFW), yield stable Galerkin schemes. Optimal a priori error estimates are derived and associated rates of convergence are established. Finally, numerical results confirming the latter and illustrating the good performance of the methods, are reported.

Effect of circular and elliptical cutouts on the free vibration analysis of sandwich FGM plate under the elastic foundations

The present article investigates the effect of circular and elliptical cutouts on vibrational characteristics of porous sandwich functionally graded material (SFGM) plates with FGM core resting on Pasternak elastic foundation. The structural kinematics of the plate are formulated based on nonpolynomial-based higher-order shear deformation theory (HSDT). Geometric discontinuities have been incorporated in terms of circular and elliptical cutouts in the SFGM plates. The sandwich structure is considered to be comprised of two homogeneous face sheets and a porous FGM core with various cutout shapes and sizes. The variation of material properties from the homogeneous face sheet to the FGM core has been carefully modeled using modified power law distribution. Further, a C0 continuous finite element formulation with a four-noded, isoparametric quadrilateral element with seven degrees of freedom (DOFs) per node has been employed to accomplish the results. The accuracy of the present results has been demonstrated through convergence and validation studies. A comprehensive study has been carried out to investigate the influence of volume fraction index, even and uneven porosity distribution, circular and elliptical cutouts, as well as H-elliptical and V-elliptical type cutout shapes on the frequency parameter of SFGM plates with the elastic foundation. The numerical results demonstrate the aforementioned parameters significantly impact the vibrational frequency of the SFGM plates.

Mixed variational formulation and finite-element implementation of second-order poro-elasticity

We present a variational formulation of second-order poro-elasticity that can be readily implemented into finite-element codes by using standard Lagrangian interpolation functions. Point of departure is a two-field minimization principle in terms of the displacement and the fluid flux as independent variables. That principle is taken as a basis for the derivation of continuous and incremental saddle-point formulations in terms of an extended set of independent variables. By static condensation this formulation is then reduced to a minimization principle in terms of the displacement and fluid flux as well as associated higher-order fields. Once implemented into a finite-element code, the resulting formulation can be applied to the numerical simulation of porous media in consideration of second-order effects. Here, we analyze the model response by means of several example problems including two standard tests in poro-elasticity, namely the consolidation problems of Terzaghi and Mandel, and compare the results with those of a corresponding first-order model. As becomes clear, the second-order formulation can unleash its full potential when applied to the study of porous media having spatial dimensions comparable to the size of their microstructure. In particular, it is capable to regularize steep field gradients at external as well as internal surfaces and to describe material dilatation effects known from experiments.

A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines

Abstract In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in a space-time domain. Based on the Babuška–Nečas theory we prove unique solvability both for the continuous variational formulation and for a standard Galerkin finite element discretization in the space-time domain. This approach allows for an adaptive resolution of the solution both in space and time, but it requires the solution of the overall system of algebraic equations. While the use of parallel solution algorithms seems to be mandatory, this also allows for a parallelization simultaneously in space and time. This approach is used for the eddy current approximation of the Maxwell equations which results in an elliptic-parabolic interface problem. Numerical results for linear and nonlinear constitutive material relations confirm the applicability and accuracy of the proposed approach.

Comparison of finite element and discrete exterior calculus in computation of time-harmonic wave propagation with controllability

This paper discusses computation of time-harmonic wave problems using a mixed formulation and the controllability method introduced by Roland Glowinski. As an example, a scattering problem (in an exterior domain) is considered, and the continuous problem is first formulated in terms of differential forms. Based on the continuous formulation, we write the discrete problem and the controllability algorithm for methods based on both the finite element exterior calculus (FEEC) and the discrete exterior calculus (DEC). As the discrete exterior calculus method provides us with a diagonal “mass matrix”, time-stepping in the DEC approach is remarkably more efficient than in the FEEC approach. For the computations in this paper, we choose the lowest order Whitney elements (a.k.a. Raviart–Thomas elements) for the FEEC approach, and in the DEC discretization we use different diagonal approximations for the Hodge star. Especially, in the DEC approach, a “harmonic Hodge” approximation is used, the derivation of which is based on the time-harmonicity of the problem. Different type of grids are used to study the sensitivity of the solution to the quality of the grid. Putting an effort on meshes regular enough, the computed DEC-solution is as accurate as the FEEC-solution, but reached in the fraction of the time. Both methods seem to be able to keep the solution accuracy rather well in computations with a high wave number (corresponding to a high frequency and a small wave length).

A Bayesian approach to modeling finite element discretization error

In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated based on observations from a finite element discretization. To avoid the computation of intractable integrals, a second, finer, discretization is introduced that is assumed sufficiently dense to represent the true solution field. A prior distribution is assumed over the fine discretization, which is then updated based on observations from the coarse discretization. This yields a posterior distribution with a mean that serves as an estimate of the solution, and a covariance that models the uncertainty associated with this estimate. Two particular choices of prior are investigated: a prior defined implicitly by assigning a white noise distribution to the right-hand side term, and a prior whose covariance function is equal to the Green’s function of the partial differential equation. The former yields a posterior distribution with a mean close to the reference solution, but a covariance that contains little information regarding the finite element discretization error. The latter, on the other hand, yields posterior distribution with a mean equal to the coarse finite element solution, and a covariance with a close connection to the discretization error. For both choices of prior a contradiction arises, since the discretization error depends on the right-hand side term, but the posterior covariance does not. We demonstrate how, by rescaling the eigenvalues of the posterior covariance, this independence can be avoided.

Confronting transitions in fishery fleet structure and selectivity: practical recommendations for integrated age-structured stock assessments based on simulation analysis

Dynamic shifts in fleet structure and gear usage lead to complex implications for representing fishery selectivity in stock assessment models. There is generally a lack of consensus on how assessment models should be configured to confront changes in fishery fleet structure or associated selectivity forms, while balancing complexity-parsimony tradeoffs. We conducted a simulation analysis to evaluate the performance of alternative assessment models when confronted with fleet transitions among gear types, which included differences in (1) rates of transition (i.e., a fast or slow transition among gears), and (2) selectivity forms for each modeled fleet (i.e., asymptotic or dome-shaped). In general, explicitly modeling fleet structure (i.e., multi-fleet models) performed well, but demonstrated bias in biomass estimates and management reference points when selectivity forms were mis-specified. Single-fleet models were only unbiased when time-varying selectivity (e.g., using time blocks or continuous formulations) was estimated to account for changes among gear types. Our results suggest that single-fleet models with time-varying fishery selectivity are adequate for operational management advice, but research oriented multi-fleet models should be used as validation tools to explore model consistency within single-fleet models.

Mathematical models and algorithms for designing main pipeline for transporting georesources

Relevance. The practical importance of the tasks of utility networks design, namely, the problems of optimizing the structure of the main pipeline according to given criteria, such as efficiency, reliability etc., under conditions of limitations, for example, the compatibility of various types of utilities. Since the main pipeline is laid on the ground with various physical and geological factors, natural and situational conditions, it is advisable to take the reliability of its operation as a global criterion. The task of network optimization is proposed in the form of displaying the main pipeline along the selected routes in three-dimensional space, which considers various existing communications and objects, as well as elevation marks of the area. The paper presents the problems of optimizing networks, both in the continuous case and in the discrete case, and also studies various indicators of the reliability of the operation of the main pipeline. Aim. To develop a model for laying the main pipeline in three-dimensional space, considering the reliability of the pipeline transport; to conduct a comparative analysis for various reliability indicators and topologies of the main pipeline. Objects. Utility communications and networks laid in three-dimensional space. Methods. Calculus of variations, discrete optimization methods, graph theory and hypernet theory methods, network reliability analysis methods. Results. The task of optimizing the main pipeline transport is given taking into account its nesting along the route in three-dimensional space with the choice of an optimization criterion (economic efficiency, reliability, etc.). The problem is presented in the form of continuous and discrete formulations, which is important for its development both within the theory of the calculus of variations and discrete optimization. In this work, the problem was studied within the framework of the theory of graphs and hypernets, which allow, firstly, taking into account the nesting of one structure (main pipeline) into another (a discrete analogue of three-dimensional space) and, secondly, clearly illustrating the results of numerical experiments. It is shown that under the conditions of a given variants for laying a secondary network along the primary channels, various optimal structures are obtained when considering various reliability indicators as a criterion, which can be used to implement a design solution for the construction and operation of pipeline transport for various purposes.

A new microscopic traffic-flow model based on the spatiotemporal continuous system concept considering nonlinear human response

A brand-new traffic model is introduced to precisely simulate the individual movement of vehicles, departing from the traditional macroscopic perspective (Eulerian scope or fluid dynamics concept) to adopt a microscopic approach (Lagrangian scope). This model is built on the first principle of Newton’s kinetic equation, explicitly incorporating nonlinear relations to represent human responses to a physical stimulus (observed information), such as the velocity gap between one’s own vehicle and a certain targeted one or the gap to a preceding vehicle, unlike the conventional car-following concept. The model posits that a driver’s recognition occurs intermittently rather than continuously, following specific probabilistic distributions of which the formulation is physically justified. Overall, the model can be described as a spatiotemporally continuous formulation unlike cellular automaton (CA) traffic models, crucial for capturing traffic dynamics at the micro and macro levels. The model is validated using a real traffic-flow dataset from a highway, and the results of the conventional CA traffic model are compared with those of the present one” along with a note for authorial verification. Animated simulations confirm that the present model can reproduce realistic flow dynamics characterized by smoother acceleration and deceleration compared to the conventional CA traffic model. The complete simulation source code for replicating the model is made publicly available.

A mixed finite element method for the forward problem of electrical impedance tomography with the shunt model

We propose a mixed finite element method for the forward problem of electrical impedance tomography with the shunt model. The method is based on a constrained minimization formulation in terms of the current density, where parts of the Lagrange multiplier are interpreted as the voltages on the electrodes. We justify the well-posedness of this continuous formulation, estimate the regularity of its solution, and use Raviart–Thomas elements for its discretization. The resulting mixed method is then proved to be stable, and converge especially with respect to the voltages on the electrodes. Simulation on a 2D model also gives consistent results.

Vibration analysis of sandwich functionally graded material plate with cut-outs using artificial neural network technique

In the present article, the effect of geometric discontinuities on the vibrational response of porous sandwich functionally graded material (SFGM) plates with double FGM facesheets has been investigated using the artificial neural network (ANN) technique. Generalized governing equations for the SFGM plate have been derived based on nonpolynomial based higher-order shear deformation theory (HSDT). Geometric discontinuities have been incorporated in terms of cut-outs in the SFGM plates. The FGM layers integrate a porosity model, while the core layer is considered a ceramic layer within the SFGM plate structure. Further, a C° continuous isoparametric finite element formulation with a four-noded, isoparametric quadrilateral element with seven degrees of freedom (DOFs) per node has been employed to accomplish the results. The accuracy of the present results has been demonstrated through convergence and validation studies. A comprehensive study has been carried out to investigate the influence of volume fraction index, even and uneven porosity distribution and cut-outs on the frequency parameter of SFGM plates. However, the finite element method (FEM) is computationally challenging. Therefore, the motivation behind adopting ANN technique to develop a predictive model for reasonable accuracy with less computational time. The ANN technique is proposed to predict the NDFP of the SFGM plate using cut-outs under various conditions using numerical simulation datasets. An optimised ANN model has been developed with an architecture of (6–5–10–5–1), exhibits best performance based on mean error value, which accurately predicts the Non-Dimensional Frequency Parameter (NDFP) of the SFGM plate.

Application of a simple two-point measurement strategy with emphasizing low-frequency signals to the force monitoring of cables

When dealing with vibration tests of tensioned suspenders and cables, signals containing relatively high frequency components in comparing to the fundamental frequency are normally required in order to carry out reliable diagnoses for force estimations. Meanwhile, the necessity of obtaining a precise and broadband spectrum of the vibration signals would inevitably need to acquire relatively detailed time responses. One typical difficulty, which arises when incorporating vibration analyses into monitoring tasks, is the inefficiency caused by the post- processing for the huge amounts of time data. In this work, a set of simple yet effective formulas associated with two-point measurements will be briefly addressed. The proposed formulas are derived based on the continuous formulations of the string model, and the corresponding applications to the tension estimations of slender members will be demonstrated using numerical and experimental data related to stayed cables of various restrained scenarios and linked-suspenders as well. The purposes of this work are twofold; firstly to introduce the potential usefulness of the proposed measurement strategy to form effective schemes for the tension assessments; secondly to evolve an efficient incorporation of wireless measuring techniques without the need of processing cumbersome time data which are the common consequences the analysts would encounter in the analysis tasks. Finally, this work aims to highlight practical ideas in guiding the use of the proposed techniques in the monitoring of cables/suspenders in field.

Validation of a statistical-dynamic framework for predicting energy consumption: A study on vehicle energy conservation equation

Predictive models for vehicle energy consumption are crucial for sustainable development in urban road traffic systems. This paper comprehensively reviews classic predictive models and develops a novel statistical-dynamical energy consumption prediction framework called Vehicle Energy Conservation Equation (VECE). VECE is constructed based on the principles of vehicle energy flow and regression analysis, employing a continuous and concise mathematical formulation. Its coefficients possess clear physical interpretations, allowing for application in various vehicle categories. To validate VECE, this study collected energy consumption data from 28 vehicles, including 9 diesel vehicles, 16 gasoline vehicles, 1 ethanol gasoline vehicle, and 2 battery electric vehicles. A rigorous data processing procedure was designed. Data analysis revealed that the VECE coefficients are correlated with vehicle type, speed, and acceleration. VECE's predictive performance is minimally impacted by the number of vehicle categories, effectively modeling energy consumption for vehicles of the same fuel type or size category. Comparative analysis with E-EcoGest, VT-Micro, PERE, and CMEM demonstrates the moderate accuracy of VECE in predicting instantaneous vehicle energy consumption while excelling in predicting cumulative energy consumption. The minimum relative percentage error for the cumulative predicted values is 4.2%. Overall, VECE demonstrates outstanding performance in computational simplicity, coefficient interpretability, adaptability, and extensibility, making it a crucial tool for achieving energy-efficient road transport systems.

Gradient-based wind farm layout optimization with inclusion and exclusion zones

Abstract. Wind farm layout optimization is usually subjected to boundary constraints of irregular shapes. The analytical expressions of these shapes are rarely available, and, consequently, it can be challenging to include them in the mathematical formulation of the problem. This paper presents a new methodology to integrate multiple disconnected and irregular domain boundaries in wind farm layout optimization problems. The method relies on the analytical gradients of the distances between wind turbine locations and boundaries, which are represented by polygons. This parameterized representation of boundary locations allows for a continuous optimization formulation. A limitation of the method, if combined with gradient-based solvers, is that wind turbines are placed within the nearest polygons when the optimization is started in order to satisfy the boundary constraints; thus the allocation of wind turbines per polygon is highly dependent on the initial guess. To overcome this and improve the quality of the solutions, two independent strategies are proposed. A case study is presented to demonstrate the applicability of the method and the proposed strategies. In this study, a wind farm layout is optimized in order to maximize the annual energy production (AEP) in a non-uniform wind resource site. The problem is constrained by the minimum distance between wind turbines and five irregular polygon boundaries, defined as inclusion zones. Initial guesses are used to instantiate the optimization problem, which is solved following three independent approaches: (1) a baseline approach that uses a gradient-based solver; (2) approach 1 combined with the relaxation of the boundaries, which allows for a better design space exploration; and (3) the application of a heuristic algorithm, “smart-start”, prior to the gradient-based optimization, improving the allocation of wind turbines within the inclusion polygons based on the potential wind resource and the available area. The results show that the relaxation of boundaries combined with a gradient-based solver achieves on average +10.2 % of AEP over the baseline, whilst the smart-start algorithm, combined with a gradient-based solver, finds on average +20.5 % of AEP with respect to the baseline and +9.4 % of AEP with respect to the relaxation strategy.

Power-series solutions of fractional-order compartmental models

Compartmental models based on coupled differential equations of fractional order have been widely employed in the literature for modeling. An abstraction of these models is given by a system with polynomial vector field. We investigate the use of power series for solving generic polynomial differential equations in any dimension, with Caputo fractional derivative. As is well known, power series convert a continuous formulation into a discrete system of difference equations, which are easily solved by recursion. The novelty of this paper is that we rigorously prove that the series converge on a neighborhood of the initial instant, which is an analogue of the Cauchy–Kovalevskaya theorem. Besides, these series are proved to be continuous with respect to the fractional index. For applications, a general-purpose symbolic implementation of truncated power series is developed, and its execution is illustrated for the fractional SIR epidemiological model.

Predicting pairwise interaction affinities with ℓ0-penalized least squares–a nonsmooth bi-objective optimization based approach*

In this paper, we introduce a novel nonsmooth optimization-based method LMBM-Kron ℓ 0 LS for solving large-scale pairwise interaction affinity prediction problems. The aim of LMBM-Kron ℓ 0 LS is to produce accurate predictions using as sparse a model as possible. We apply the least squares approach with Kronecker product kernels for a loss function and a continuous formulation of ℓ 0 pseudonorm for regularization. Thus, we end up solving a nonsmooth optimization problem. In addition, we apply a specific bi-objective criterion to strike a balance between the prediction accuracy of the learned model and the sparsity of the obtained solution. We compare LMBM-Kron ℓ 0 LS with some state-of-the-art methods using three benchmark and two simulated data sets under four distinct experimental settings, including zero-shot learning. Moreover, both binary and continuous interaction affinity labels are considered with LMBM-Kron ℓ 0 LS. The results show that LMBM-Kron ℓ 0 LS finds sparse solutions without sacrificing too much in the prediction performance.