Presence Of Multiple Local Minima Research Articles

CFDepthNet: Monocular Depth Estimation Introducing Coordinate Attention and Texture Features

Handling the depth estimation of low-texture regions using photometric error loss is a challenge due to the difficulty of achieving convergence due to the presence of multiple local minima for pixels in low-texture regions (or even no-texture regions). In this paper, based on the photometric loss, we also introduce texture feature metric loss as a constraint and combine the coordinate attention mechanism to improve the depth map's texture quality and edge detail. This paper uses a simple yet compact network structure, a unique loss function, and a relatively flexible embedded attention module, which is more effective and easier to arrange in robotic platforms with weak arithmetic power. The tests show that our network structure not only shows high quality and state-of-the-art results on the KITTI dataset, but the same training results also perform well on the cityscapes and Make3D datasets.

Variational data assimilation to improve subsurface drainage model parameters

• Identification of the most influential model parameters using the global adjoint SA. • Variational data assimilation significantly reduces the water volume discrepancy. • The gradient-based stochastic procedure performs without the need for the prior. • A new hybrid BV method offers an automatic tool to select a robust parameter set. Variational data assimilation (VDA) has been implemented to enhance the estimation of the unknown input parameters of a new agricultural subsurface drainage model (SIDRA-RU) through assimilating drainage discharge observations. The adjoint model of SIDRA-RU has been successfully generated through the generic automatic differentiation tool (TAPENADE). First, the adjoint model is used to explore the local and global adjoint sensitivities of the valuable function defined over the drainage discharge simulations with respect to model input parameters. Next, the most influential parameters are estimated by applying the Variational DA approach. The performed sensitivity analysis shows that the most influential parameters on drainage discharge are those controlling the dynamics of the water table; the second most influential parameters manage the drainflow start of each drainage season. Compared to an alternative gradient-free calibration performance, the estimation of these governing parameters by the variational method improves the overall quality of the drainage discharge prediction, in particular in terms of the cumulative water volume. Improved parameters generate less than 5 mm (1%) of the discrepancy between simulated and observed water volumes, based on the five years of daily discharge observations on the Chantemerle agricultural parcels (36 ha). Preliminary numerical tests have shown the potential presence of multiple local minima, thus pointing out the equifinality issues. The latter can be highlighted by the self-compensation of both the physical soil parameters and the main conceptual parameters. For improving the robustness of the parameter estimates, a novel hybrid “Bayesian Variational” method is suggested. This method is based on the Bayesian averaging of an ensemble of optimal estimates.

Characterization of particle size distribution in slurries using ultrasonic attenuation spectroscopy: Addressing challenges of unknown physical properties

Ultrasonic attenuation spectroscopy (UAS) has many advantages in online in-process characterization of particle size distribution (PSD) in slurries. It can be applied to systems with relatively high solid concentration and wide particle size range from nanometres to millimetres sized particles. The model used by a UAS instrument to estimate the PSD from an attenuation spectrum requires some physical properties of both the liquid and solid phases to be known. For instance, the most popular UAS model, the Epstein–Carhart and Allegra–Hawley (ECAH) model, requires fourteen physical properties. Therefore, applications where all or some of the required physical properties are unknown or difficult to measure, such as crystallization, pose a major challenge to its use. In this work, a procedure for estimating the unknown physical properties is proposed. This is done by iteratively learning the unknown physical properties to minimise the difference between the measured attenuation spectra and that predicted by the ECAH model. One of the main challenges of this procedure is the presence of multiple local minima but these can be eliminated by a combination of a global optimisation algorithm, the use of multiple particle size distributions and solid concentrations. The procedure was validated using Silica and Titania standard reference materials, and applied to the estimation of the relevant physical properties of saturated aqueous solution of SrCl2.6H2O and Sr(OH)2.8H2O. The properties thus obtained was used for acoustic monitoring of the real-time evolution of PSD during the batch cooling crystallization of SrCl2.6H2O in water.

Conformational Transitions of Amyloid-β: A Langevin and Generalized Langevin Dynamics Simulation Study.

The dynamics of conformational transitions of the disordered protein, amyloid-β, is studied via Langevin and generalized Langevin dynamics simulations. The transmission coefficient for the unfold–misfold transition of amyloid-β is calculated from multiple independent trajectories that originate at the transition state with different initial velocities and are directly correlated to Kramers and Grote–Hynes theories. For lower values of the frictional coefficient, a well-defined rate constant is obtained, whereas, for higher values, the transmission coefficient decays with time, indicating a breakdown of the Kramers and Grote–Hynes theories and the emergence of a dynamic disorder, which demonstrates the presence of multiple local minima in the misfolding potential energy surface. The calculated free energy profile describes a two-state transition of amyloid-β in the energy landscape. The transition path time distribution computed from these simulations is compared with the related experimental and theoretical results for the unfold–misfold transition of amyloid-β. The high free energy barrier for this transition confirms the misfolding of amyloid-β. These findings offer an insight into the dynamics of the unfold–misfold transition of this protein.

ModPSO-CNN: an evolutionary convolution neural network with application to visual recognition

Training optimization plays a vital role in the development of convolution neural network (CNN). CNNs are hard to train because of the presence of multiple local minima. The optimization problem for a CNN is non-convex, hence, has multiple local minima. If any of the chosen hyper-parameters are not appropriate, it will end up at bad local minima, which leads to poor performance. Hence, proper optimization of the training algorithm for CNN is the key to converge to a good local minimum. Therefore, in this paper, we introduce an evolutionary convolution neural network (ModPSO-CNN) algorithm. The proposed algorithm results in the fusion of modified particle swarm optimization (ModPSO) along with backpropagation (BP) and convolution neural network (CNN). The training of CNN involves ModPSO along with backpropagation (BP) algorithm to encourage performance improvement by avoiding premature convergence and local minima. The ModPSO have adaptive, dynamic and improved parameters, to handle the issues in training CNN. The adaptive and dynamic parameters bring a proper balance between the global and local search ability, while an improved parameter keeps the diversity of the swarm. The proposed ModPSO algorithm is validated on three standard mathematical test functions and compared with three variants of the benchmark PSO algorithm. Furthermore, the performance of the proposed ModPSO-CNN is also compared with other training algorithms focusing on the analysis of computational cost, convergence and accuracy based on a standard problem specific to classification applications, such as CIFAR-10 dataset and face and skin detection dataset.

Detuning primordial black hole dark matter with early matter domination and axion monodromy

We present a scenario that ameliorates the tuning problems present in models of primordial black hole (PBH) dark matter from inflation. Our setup employs the advantages of gravitational collapse in a long epoch of early matter domination with reheating temperature ≲ 106 GeV. Furthermore, we make use of a string-inspired class of models where the inflaton is identified with a non-compact axion field. In this framework, the presence of multiple local minima in the inflaton potential can be traced back to an approximate discrete shift symmetry. This scenario allows the formation of PBHs in the observationally viable range of masses (MPBH∼ 10−16M⊙–10−13M⊙) accounting for all dark matter, and in excellent agreement with the CMB . We find a significant reduction in the required tuning of the parameters of the inflationary potential, in contrast to the standard case of PBH formation during radiation domination. However, abundant formation of light PBHs during an early phase of matter domination can be more easily in conflict with evaporation bounds. We discuss how these can be avoided under mild assumptions on the collapsing energy density fraction.

Method for the Maximization of the Likelihood Function of Speech Autoregressive Parameters Based on Line Spectrum Pairs

The paper considers the estimation of the parameters of auto­regressive model at additive white noise background. The principle of maximum likelihood is used for this purpose. The main goal is to find the maximum of likelihood function depending on parameters of autoregressive model. Representation of likelihood function through line spectrum pairs and other alternative parameters is presented. This provided possibility of likelihood function maximization by KNITRO algorithm. The presence of multiple local minima of the considered likelihood function is shown. Experimental results including the comparison with widely used expectation-maximization (EM) method are presented for the real speech signals.

The role of acquisition and quantification methods in myocardial blood flow estimability for myocardial perfusion imaging CT

In this work, we clarified the role of acquisition parameters and quantification methods in myocardial blood flow (MBF) estimability for myocardial perfusion imaging using CT (MPI-CT). We used a physiologic model with a CT simulator to generate time-attenuation curves across a range of imaging conditions, i.e. tube current-time product, imaging duration, and temporal sampling, and physiologic conditions, i.e. MBF and arterial input function width. We assessed MBF estimability by precision (interquartile range of MBF estimates) and bias (difference between median MBF estimate and reference MBF) for multiple quantification methods. Methods included: six existing model-based deconvolution models, such as the plug-flow tissue uptake model (PTU), Fermi function model, and single-compartment model (SCM); two proposed robust physiologic models (RPM1, RPM2); model-independent singular value decomposition with Tikhonov regularization determined by the L-curve criterion (LSVD); and maximum upslope (MUP). Simulations show that MBF estimability is most affected by changes in imaging duration for model-based methods and by changes in tube current-time product and sampling interval for model-independent methods. Models with three parameters, i.e. RPM1, RPM2, and SCM, gave least biased and most precise MBF estimates. The average relative bias (precision) for RPM1, RPM2, and SCM was ⩽11% (⩽10%) and the models produced high-quality MBF maps in CT simulated phantom data as well as in a porcine model of coronary artery stenosis. In terms of precision, the methods ranked best-to-worst are: RPM1 > RPM2 > Fermi > SCM > LSVD > MUP other methods. In terms of bias, the models ranked best-to-worst are: SCM > RPM2 > RPM1 > PTU > LSVD other methods. Models with four or more parameters, particularly five-parameter models, had very poor precision (as much as 310% uncertainty) and/or significant bias (as much as 493%) and were sensitive to parameter initialization, thus suggesting the presence of multiple local minima. For improved estimates of MBF from MPI-CT, it is recommended to use reduced models that incorporate prior knowledge of physiology and contrast agent uptake, such as the proposed RPM1 and RPM2 models.

GOSH: derivative-free global optimization using multi-dimensional space-filling curves

Global optimization is a field of mathematical programming dealing with finding global (absolute) minima of multi-dimensional multiextremal functions. Problems of this kind where the objective function is non-differentiable, satisfies the Lipschitz condition with an unknown Lipschitz constant, and is given as a “black-box” are very often encountered in engineering optimization applications. Due to the presence of multiple local minima and the absence of differentiability, traditional optimization techniques using gradients and working with problems having only one minimum cannot be applied in this case. These real-life applied problems are attacked here by employing one of the mostly abstract mathematical objects—space-filling curves. A practical derivative-free deterministic method reducing the dimensionality of the problem by using space-filling curves and working simultaneously with all possible estimates of Lipschitz and Holder constants is proposed. A smart adaptive balancing of local and global information collected during the search is performed at each iteration. Conditions ensuring convergence of the new method to the global minima are established. Results of numerical experiments on 1000 randomly generated test functions show a clear superiority of the new method w.r.t. the popular method DIRECT and other competitors.

Method and advantages of genetic algorithms in parameterization of interatomic potentials: Metal oxides

The method and the advantages of an evolutionary computing based approach using a steady state genetic algorithm (GA) for the parameterization of interatomic potentials for metal oxides within the shell model framework are developed and described. We show that the GA based methodology for the parameterization of interatomic force field functions is capable of (a) simultaneous optimization of the multiple phases or properties of a material in a single run, (b) facilitates the incremental re-optimization of the whole system as more data is made available for either additional phases or material properties not included in previous runs, and (c) successful global optimization in the presence of multiple local minima in the parameter space. As an example, we apply the method towards simultaneous optimization of four distinct crystalline phases of Barium Titanate (BaTiO3 or BTO) using an ab initio density functional theory (DFT) based reference dataset. We find that the optimized force field function is capable of the prediction of the two phases not used in the optimization procedure, and that many derived physical properties such as the equilibrium lattice constants, unit cell volume, elastic properties, coefficient of thermal expansion, and average electronic polarization are in good agreement with the experimental results available from the literature.

Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions

Abstract. The calibration of stochastic point process rainfall models, such as of the Bartlett-Lewis type, suffers from the presence of multiple local minima which local search algorithms usually fail to avoid. To meet this shortcoming, four relatively new global optimization methods are presented and tested for their ability to calibrate the Modified Bartlett-Lewis Model. The list of tested methods consists of: the Downhill Simplex Method, Simplex-Simulated Annealing, Particle Swarm Optimization and Shuffled Complex Evolution. The parameters of these algorithms are first optimized to ensure optimal performance, after which they are used for calibration of the Modified Bartlett-Lewis model. Furthermore, this paper addresses the choice of weights in the objective function. Three alternative weighing methods are compared to determine whether or not simulation results (obtained after calibration with the best optimization method) are influenced by the choice of weights.

Global optimization of nonlinear least-squares problems by branch-and-bound and optimality constraints

We study a simple, yet unconventional approach to the global optimization of unconstrained nonlinear least-squares problems. Non-convexity of the sum of least-squares objective in parameter estimation problems may often lead to the presence of multiple local minima. Here, we focus on the spatial branch-and-bound algorithm for global optimization and experiment with one of its implementations, BARON (Sahinidis in J. Glob. Optim. 8(2):201–205, 1996), to solve parameter estimation problems. Through the explicit use of first-order optimality conditions, we are able to significantly expedite convergence to global optimality by strengthening the relaxation of the lower-bounding problem that forms a crucial part of the spatial branch-and-bound technique. We analyze the results obtained from 69 test cases taken from the statistics literature and discuss the successes and limitations of the proposed idea. In addition, we discuss software implementation for the automation of our strategy.

Comparative Study on Optimal Stiffener Placement for Curvilinearly Stiffened Panels

Recent studies have shown that curved stiffeners offer potential for structural tailoring of metallic panels. However, the optimal placement of the stiffener curves has remained a challenge, due to both the presence ofmultiple localminima in the design space as well as the associated CPU cost to solve the problem. This paper presents two new approaches to design the stiffener curves by decomposition of the design space into size and shape variables. The approaches are built on a heuristic concept of effectiveness of a stiffener configuration, which argues that the most effective configuration will also provide the lowest optimized panel mass. The first approach estimates the best stiffener configuration, based purely on the first buckling mode of the unstiffened panel. The approach defines a heuristic metric for the effectiveness of a stiffener in increasing the buckling load capacity of a panel. The second approach uses optimization methods on both the sizing and shape variable subspaces. Mass is minimized over the sizing variable subspace, with constraint on buckling, while the buckling eigenvalue is maximized over the shape design variable subspace by varying the stiffener curves. The results are compared with optimization over a unified design space using a global optimization procedure, and it is shown that the proposedmethods lead to better designs at lower CPU cost.

Aerostructural Optimization of Nonplanar Lifting Surfaces

to findoptimalnonplanarliftingsurfacesandtoexplainthevariousfactorsandtradeoffsatplay.Apanelmethodand anequivalentbeam finite-elementmodelareusedtoexplorenonplanarliftingsurfaces,whiletakingintoaccountthe coupling and design tradeoffs between aerodynamics and structures. Both single-discipline aerodynamic optimization and multidisciplinary aerostructural optimization problems are investigated. The design variables are chosen to give the lifting-surface arrangement as much freedom as possible. This is accomplished by allowing a number of wing segments to vary their area, taper, twist, sweep, span, and dihedral, with the constraint that they must not intersect each other. Because of the complexity of the resulting design space and the presence of multiple localminima, anaugmentedLagrangianparticle swarmoptimizer isusedto solvethe optimizationproblems.When only aerodynamics are considered, closed lifting-surface configurations, such as the box wing and joined wing, are found to be optimal. When aerostructural optimization is performed, a winglet configuration is found to be optimal when the overall span is constrained, and a wing with a raked wingtip is optimal when there is no such constraint.

Fitting VAD winds to aliased Doppler radial‐velocity observations: A global minimization problem in the presence of multiple local minima

AbstractWhen the horizontal vector wind is estimated by the traditional velocity azimuth display (VAD) analysis from radar radial‐velocity observations on a selected range circle, the observations should be thoroughly de‐aliased first. When the effect of aliasing is formulated into the cost function, the VAD analysis can be applied to raw aliased radial‐velocity observations, but the minimization problem for the VAD fitting is complicated by the multiple local minima caused by the zigzag‐discontinuities of the aliasing operator. An efficient two‐step VAD algorithm is thus developed in this paper to find the global minimum in properly transformed subspaces of the VAD wind parameters. The algorithm is then extended into a three‐step volume velocity processing (VVP) method to estimate the vertical profile of horizontal winds from each volume of radar radial‐velocity scans. Examples are presented to illustrate the capability and robustness of the method. Copyright © 2010 Royal Meteorological Society

Free energy landscape analysis of two-dimensional dipolar solvent model at temperatures below and above the rotational freezing point

Ionic solvation in a polar solvent is modeled by a central charge surrounded by dipolar molecules posted on two-dimensional distorted lattice sites with simple rotational dynamics. Density of states is calculated by applying the Wang-Landau algorithm to both the energy and polarization states. The free energy landscapes of solvent molecules as a function of polarization are depicted to explore the competition between the thermal fluctuation and solvation energy. Without a central charge, for temperatures higher than the energy scale of the dipole-dipole interactions, the energy landscape for the small polarization region exhibits a parabolic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] for electron transfer reaction, while there is an additional quartic contribution to the landscape for the large polarization region. When the temperature drops, the simulated free energy landscapes are no longer smooth due to the presence of multiple local minima arising from the frustrated interaction among the dipoles. The parabolic contribution becomes negligible and the energy landscape becomes quartic in shape. For a strong central charge, the energy landscape exhibits an asymmetric profile due to the contributions of linear and cubic terms that arise from the charge-dipole interactions.

Evaluation of achievable registration accuracy of the femur during minimally invasive total hip replacement

The aim of the paper was to investigate whether accurate, point-based registration of the intra-operative femur will be achieved within the context of minimally invasive surgery for total hip replacement. Computer tomography images, collected for pre-operative planning purposes, were used to simulate the intra-operative registration procedure using algorithms for various levels of measurement noise, different small areas of the femur available to the surgeon, and a limited number of collected data points (20-60). This helped with the choice of design variables to perform in vitro registration on a plastic bone model to validate the procedure, which included a multistart algorithm developed for intra-operative registration. The algorithm minimised the distance between the measured and image-derived surfaces and was able to cope with the presence of multiple local minima given sufficient computational effort, even with realistically large measurement noise. It was found that, if a small patch of the femur was used, accessible by a needle that could at times penetrate thin layers of soft tissue, errors in the order of 1.0 mm in translation and 0.5 degrees in rotation were achievable.

A Multiscale Approach to Production-Data Integration Using Streamline Models

Summary We propose a multiscale approach to data integration that accounts for the varying resolving power of different data types from the very outset. Starting with a coarse description, we match the production response at the wells by recursively refining the reservoir grid. A multiphase streamline simulator is used for modeling fluid flow in the reservoir. The well data are then integrated using conventional geostatistics, for example sequential simulation methods. There are several advantages to our proposed approach. First, we explicitly account for the resolution of the production response by refining the grid only up to a level sufficient to match the data, avoiding over-parameterization and incorporation of artificial regularization constraints. Second, production data are integrated at a coarse scale with fewer parameters, which makes the method significantly faster compared to direct fine-scale inversion of the production data. Third, decomposition of the inverse problem by scale greatly facilitates the convergence of iterative descent techniques to the global solution, particularly in the presence of multiple local minima. Finally, the streamline approach allows for parameter sensitivities to be computed analytically using a single simulation run, thus further enhancing the computational speed. The proposed approach has been applied to synthetic as well as field examples. The synthetic examples illustrate the validity of the approach and also address several key issues, such as convergence of the algorithm, computational efficiency, and advantages of the multiscale approach compared to conventional methods. The field example is from the Goldsmith San Andres Unit (GSAU) in west Texas and includes multiple patterns consisting of 11 injectors and 31 producers. Using well-log data and water-cut history from producing wells, we characterize the permeability distribution, thus demonstrating the feasibility of the proposed approach for large-scale field applications.

Crystallization process optimization using artificial neural networks

AbstractThis paper presents a new procedure for optimization of continuous mixed suspensionmixed product removal (MSMPR) crystallizing systems. Owing to the difficulties of theoretical modelling, simulation of the MSMPR crystallization process is based on the use of artificial neural networks (ANN). The optimization criterion is a compound objective function corresponding to an intended mean crystal size dimension and a minimal dispersion. The presence of multiple local minima has called for investigation by several optimization techniques. Ultimately, Luus' and Jaakola's random adaptive method proved to be most effective. The results obtained lend support to the general procedure proposed.