Multidimensional Solution Space Research Articles

An improved near-field weighted subspace fitting algorithm based on niche particle swarm optimization for ultrasonic guided wave multi-damage localization

The ultrasonic guided wave-based method for multi-damage localization has been widely proposed. However, the precision of this method is directly correlated with both the quantity of sensors employed and the intricacy of the implementation process. This relationship poses a challenge in striking a balance between the accuracy and efficiency. To improve the computational efficiency under the premise of ensuring the accuracy of multi-damage localization, this paper proposes a near-field weighted subspace fitting algorithm based on niche-particle swarm optimization. Firstly, the fitting relationship between the signal subspace of the diffraction wave and the array steering vector is established under the uniform linear array. Secondly, a multi-dimensional solution space search algorithm based on niche-particle swarm optimization is proposed to improve the search efficiency of damage. Finally, the algorithm is verified by performance comparison, finite element simulation and experiment. The results show that compared with the same type of method, the algorithm improves the computational efficiency by nearly threefold under the identifiable multi-damage conditions. Additionally, the angle error is 1 ∼ 6°, and the distance error is 1 ∼ 20 mm.

Machine learning for laser-induced electron diffraction imaging of molecular structures

Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult with increasing structural complexity, given that a global extremum must be found in a multi-dimensional solution space. Worse, pre-calculating many thousands of molecular configurations for all orientations becomes simply intractable. As a remedy, here, we propose a machine learning algorithm with a convolutional neural network which can be trained with a limited set of molecular configurations. We demonstrate structural retrieval of a complex and large molecule, Fenchone (C10H16O), from laser-induced electron diffraction (LIED) data without fitting algorithms or ab initio calculations. Retrieval of such a large molecular structure is not possible with other variants of LIED or ultrafast electron diffraction. Combining electron diffraction with machine learning presents new opportunities to image complex and larger molecules in static and time-resolved studies.

Non-convex layup optimization of the composite laminates with fast and robust FEA model and modified SPEA-II

The biggest design challenge regarding composite laminates is the selection of a stacking sequence such that the cost and/or weigth of the laminate to be minimized subject to constraints like failure criteria. The layup optimization of the composite laminates involves a very complex multidimensional solution space which is usually non-exhaustively explored using heuristic computational methods like genetic/evolutionary algorithms. To ensure the convergence of the prefered method it is necessary to evaluate a lot of layup configurations during the optimization process which involves that the evaluation of a single configuration should be fast enough to keep the overall optimization time to an acceptable level. On the other hand the mechanical behaviour of the composite laminates is very complex and it is analyzed with expensive computational tools such as finite element analysis. In this paper we propose a computational efficient framework which combines a very fast and robust Matlab-based FEA model with a non-convex evolutionary algorithm (strength pareto evolutionary algorithm II). We speed up the convergence by modifying the standard algorithm to generate new potentially pareto-optimal individuals. Also, a detalied numerical example is presented in order to highligth the steep computational time improvement between our method and a convex genetic algorithm.

Abstract 2102: Interpretable machine learning for perturbation biology

Abstract Systematic perturbation of cells followed by comprehensive measurements of molecular and phenotypic responses provides an informative data resource for constructing computational models of cell biology. Models that generalize well beyond training data can be used to identify combinatorial perturbations of potential therapeutic interest. Major challenges for machine learning on large biological datasets are to find global optima in an enormously complex multi-dimensional solution space and to mechanistically interpret the solutions. To address these challenges, we introduce a hybrid approach that combines explicit mathematical models of dynamic cell biological processes with a machine learning framework, implemented in Tensorflow. We tested the modeling framework on a perturbation-response dataset for a melanoma cell line after drug treatments. The models can be efficiently trained to accurately describe cellular behavior, as tested by cross-validation. Even though completely data-driven and independent of prior knowledge, the resulting de novo network models recapitulate known interactions. The main predictive application of our work is the identification of combinatorial candidates for cancer therapy. This approach is readily applicable to a wide range of kinetic models of cell biology. Citation Format: Judy Shen, Bo Yuan, Augustin Luna, Anil Korkut, Debora Marks, John Ingraham, Chris Sander. Interpretable machine learning for perturbation biology [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 2102.

Failure Estimation of the Composite Laminates in Layup Optimization Using Finite Element Analysis and Deep Learning

Layup optimization of the composite laminates is a very complex problem due to the convoluted multidimensional solution space which is usually explored by addressing different heuristic methods from which the most reliable are the genetic algorithms (GA). The optimization process converges by evaluating a lot of layup configurations which imply that the evaluation should be not only robust but also very fast. The most accurate numerical tool used to simulate the mechanical behavior of the composite laminates is the finite element analysis (FEA) which unfortunately is a computational intensive method. Some studies proposed very fast FEA models specially designed for the layup optimization with the lower bound of the execution time determined by the global linear system solving. Other studies pushed this bound even lower using classical machine learning techniques trained with prior observations (layup configurations) evaluated with FEA. It has been shown that the trained models can successfully replace the computational intensive FEA. The results are very important because the optimization time is dramatically reduced, while the estimation errors induced by the statistical models are acceptable. In this paper, we propose different deep neural network architectures such as multilayer perceptron (MLP) and convolutional and recurrent neural networks (CNN and RNN) that significantly reduce the estimation errors. For example, the classification error reduces from 2% to zero compared to previous studies, for the same numerical example. Also, we use different sets of predictors which allow the failure estimation for each layer in the composite laminate opposite to the previous studies which model the failure response only for the whole structure.

Modeling and nonlinear analysis of stepped beam energy harvesting from galloping vibrations

This paper presents a nonlinear distributed-parameter model for harvesting energy from galloping oscillation. The stepped beam structure is beneficial to increase the stress and strain of the piezoelectric elements, thereby enhancing the power generation. The finite element analysis is used to verify the feasibility and effectiveness of the developed harvester. A nonlinear distributed-parameter model for the piezoelectric energy harvester with a stepped beam is developed. The instantaneous fluid force in the transverse direction is analyzed. Based on Euler-Bernoulli beam theory, a distributed-parameter model for undamped free vibration is derived, which can be used for the modal analysis. The electromechanical coupling model is established by using the piezoelectric effect theory. The forced vibration subjected to the galloping excitation load is analyzed by using the mode superposition method. The state vector and the fourth order Runge-Kutta algorithm are used to seek the numerical solution. The effects of the electrical load resistance, length, width and thickness of the piezoelectric beam, exposure area and mass of the bluff body on the output power are investigated. In order to find the optimal design of the energy harvester, optimization design is performed based on the established theoretical model. The particle swarm optimization algorithm is employed to search the optimal solution in multidimensional space. Finally, experimental work was carried out, the electrical output characteristics of the energy harvester prototypes were measured. The simulation results are validated with the experimental data. It is demonstrated that the optimal configuration of the energy harvester can improve the output power from galloping phenomenon effectively.

Discovering of gapped motifs using particle swarm optimisation

In bioinformatics, motif discovery is one of the fundamental and important computational problems. Identifying these recurring patterns in biological sequences helps us to better understand the mechanisms that regulate gene expression. Recently several evolutionary algorithms have been developed to solve motif discovery problem, because of their efficiency in searching multidimensional solution space. HPSO, IPSO-GA, PMbPSO and PSO+ are based on particle swarm optimisation (PSO) algorithms. Among these, PSO+ is the first one to be proposed for finding gapped motifs. PSO+ is less efficient in finding gapped motifs that are located at the centre of a motif. Here, our contribution is, to find gapped motifs that are present at the centre of two conserved regions efficiently by adopting features of PSO to solve the problem. We performed experiments on simulated and real biological datasets. It is observed that our approach is able to detect known gapped TFBS more accurately and efficiently.

Fabrication of atomic junctions with experimental parameters optimized using ground-state searches of Ising spin computing

Feedback-controlled electromigration (FCE) is employed to control metal nanowires with quantized conductance and create nanogaps and atomic junctions. In the FCE method, the experimental parameters are commonly selected based on experience. However, optimization of the parameters by way of tuning is intractable because of the impossibility of attempting all different combinations systematically. Therefore, we propose the use of the Ising spin model to optimize the FCE parameters, because this approach can search for a global optimum in a multidimensional solution space within a short calculation time. The FCE parameters were determined by using the energy convergence properties of the Ising spin model. We tested these parameters in actual FCE experiments, and we demonstrated that the Ising spin model could improve the controllability of the quantized conductance in atomic junctions. This result implies that the proposed method is an effective tool for the optimization of the FCE process in which an intelligent machine can conduct the research instead of humans.

Using old results to produce new solutions in age–period–cohort multiple classification models

The best fitting solutions to the age–period–cohort multiple classification (APCMC) model lie on a line of solutions in multidimensional solution space. This means that there are an infinite number of best fitting solutions to an APCMC model. This paper uses that fact to show how researchers can find new solutions based on previously published solutions that are more consistent with theory and/or substantive research in a specific area of research. These results can refine and/or challenge the published research. Finally, the paper demonstrates how results from a previous study can be used to derive some important estimable functions that are true for any just identifying constrained solution to an APCMC model.

Quantiprot - a Python package for quantitative analysis of protein sequences

BackgroundThe field of protein sequence analysis is dominated by tools rooted in substitution matrices and alignments. A complementary approach is provided by methods of quantitative characterization. A major advantage of the approach is that quantitative properties defines a multidimensional solution space, where sequences can be related to each other and differences can be meaningfully interpreted.ResultsQuantiprot is a software package in Python, which provides a simple and consistent interface to multiple methods for quantitative characterization of protein sequences. The package can be used to calculate dozens of characteristics directly from sequences or using physico-chemical properties of amino acids. Besides basic measures, Quantiprot performs quantitative analysis of recurrence and determinism in the sequence, calculates distribution of n-grams and computes the Zipf’s law coefficient.ConclusionsWe propose three main fields of application of the Quantiprot package. First, quantitative characteristics can be used in alignment-free similarity searches, and in clustering of large and/or divergent sequence sets. Second, a feature space defined by quantitative properties can be used in comparative studies of protein families and organisms. Third, the feature space can be used for evaluating generative models, where large number of sequences generated by the model can be compared to actually observed sequences.

Failure estimation of the composite laminates using machine learning techniques

The problem of layup optimization of the composite laminates involves a very complex multidimensional solution space which is usually non-exhaustively explored using different heuristic computational methods such as genetic algorithms (GA). To ensure the convergence to the global optimum of the applied heuristic during the optimization process it is necessary to evaluate a lot of layup configurations. As a consequence the analysis of an individual layup configuration should be fast enough to maintain the convergence time range to an acceptable level. On the other hand the mechanical behavior analysis of composite laminates for any geometry and boundary condition is very convoluted and is performed by computational expensive numerical tools such as finite element analysis (FEA). In this respect some studies propose very fast FEA models used in layup optimization. However, the lower bound of the execution time of FEA models is determined by the global linear system solving which in some complex applications can be unacceptable. Moreover, in some situation it may be highly preferred to decrease the optimization time with the cost of a small reduction in the analysis accuracy. In this paper we explore some machine learning techniques in order to estimate the failure of a layup configuration. The estimated response can be qualitative (the configuration fails or not) or quantitative (the value of the failure factor). The procedure consists of generating a population of random observations (configurations) spread across solution space and evaluating using a FEA model. The machine learning method is then trained using this population and the trained model is then used to estimate failure in the optimization process. The results obtained are very promising as illustrated with an example where the misclassification rate of the qualitative response is smaller than 2%.

Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum

We study the Cauchy problem for multi-dimensional compressible radiation hydrodynamics equations with vacuum. First, we present some sufficient conditions on the blow-up of smooth solutions in multi-dimensional space. Then, we obtain the invariance of the support of density for the smooth solutions with compactly supported initial mass density by the property of the system under the vacuum state. Based on the above-mentioned results, we prove that we cannot get a global classical solution, no matter how small the initial data are, as long as the initial mass density is of compact support. Finally, we will see that some of the results that we obtained are still valid for the isentropic flows with degenerate viscosity coefficients as well as for one-dimensional case.

Encapsulating the Role of Solution Response Space Roughness on Global Optimal Solution: Application in Identification of Unknown Groundwater Pollution Sources

A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local optima. Optimal Identification of unknown groundwater pollution sources poses similar challenges. Optimization based methodology is often applied to identify the unknown source characteristics such as location and flux release history over time, in a polluted aquifer. Optimization based models for identification of these characteristics of unknown ground-water pollution sources rely on comparing the simulated effects of candidate solutions to the observed effects in terms of pollutant concentration at specified sparse spatiotemporal locations. The optimization model minimizes the difference between the observed pollutant concentration measurements and simulated pollutant concentration measurements. This essentially constitutes the objective function of the optimization model. However, the mathematical formulation of the objective function can significantly affect the accuracy of the results by altering the response contour of the solution space. In this study, two separate mathematical formulations of the objective function are compared for accuracy, by incorporating different scenarios of unknown groundwater pollution source identification problem. Simulated Annealing (SA) is used as the solution algorithm for the optimization model. Different mathematical formulations of the objective function for minimizing the difference between the observed and simulated pollutant concentration measurements show different levels of accuracy in source identification results. These evaluation results demonstrate the impact of objective function formulation on the optimal identification, and provide a basis for choosing an appropriate mathematical formulation for unknown pollution source identification in contaminated aquifers.

Synergizing fitness learning with proximity-based food source selection in artificial bee colony algorithm for numerical optimization

Evolutionary computation (EC) paradigm has undergone extensions in the recent years diverging from the natural process of genetic evolution to the simulation of natural life processes exhibited by the living organisms. Bee colonies exemplify a high level of intrinsic interdependence and co-ordination among its members, and algorithms inspired from the bee colonies have gained recent prominence in the field of swarm based metaheuristics. The artificial bee colony (ABC) algorithm was recently developed, by simulating the minimalistic foraging model of honeybees in search of food sources, for solving real-parameter, non-convex, and non-smooth optimization problems. The single parameter perturbation in classical ABC resulted in fairly commendable performance for simple problems without epistasis of variables (separable). However, it suffered from narrow search zone and slow convergence which eventually led to poor exploitation tendency. Even with the increase in dimensionality, a significant deterioration was observed in the ability of ABC to locate the optimum in a huge search volume. Some of the probable shortcomings in the basic ABC approach, as observed, are the single parameter perturbation instead of a multiple one, ignoring the fitness to reward ratio while selecting food sites, and most importantly the absence of environmental factors in the algorithm design. Research has shown that spatial environmental factors play a crucial role in insect locomotion and foragers seem to learn the direction to be undertaken based on the relative analysis of its proximal surroundings. Most importantly, the mapping of the forager locomotion from three dimensional search spaces to a multidimensional solution space calls forth the implementation of multiple modification schemes. Based on the fundamental observation pertaining to the dynamics of ABC, this article proposes an improved variant of ABC aimed at improving the optimizing ability of the algorithm over an extended set of problems. The hybridization of the proposed fitness learning mechanism with a weighted selection scheme and proximity based stimuli helps to achieve a fine blending of explorative and exploitative behaviour by enhancing both local and global searching ability of the algorithm. This enhances the ability of the swarm agents to detect optimal regions in the unexplored fitness basins. With respect to its immediate surroundings, a proximity based component is added to the normal positional modification of the onlookers and is enacted through an improved probability selection scheme that takes the T/E (total reward to distance) ratio metric into account. The biologically-motivated, hybridized variant of ABC achieves a statistically superior performance on majority of the tested benchmark instances, as compared to some of the most prominent state-of-the-art algorithms, as is demonstrated through a detailed experimental evaluation and verified statistically.

Estimable functions in age-period-cohort models: a unified approach

Age-period-cohort (APC) models have an intriguing appeal because each of these factors may be independently associated with age-period-specific rates (or other values). Unfortunately, one can not uniquely estimate the effects that generated the outcome data because these effects are linearly dependent. It is possible, however, to estimate certain linear combinations of these effects that are themselves unique estimates of the data generating parameters. The author demonstrates that all of the least square solutions for the APC model lie on a line in multidimensional solution space. This characteristic of the solutions to the APC model allows for a unified approach to the derivation of estimable functions, which is then used to derive the most prominent estimable functions in the APC literature and can be used to discover new ones.

An Adaptive Monte Carlo Approach to Phase-Based Multimodal Image Registration

In this paper, a novel multiresolution algorithm for registering multimodal images, using an adaptive Monte Carlo scheme is presented. At each iteration, random solution candidates are generated from a multidimensional solution space of possible geometric transformations, using an adaptive sampling approach. The generated solution candidates are evaluated based on the Pearson type-VII error between the phase moments of the images to determine the solution candidate with the lowest error residual. The multidimensional sampling distribution is refined with each iteration to produce increasingly more plausible solution candidates for the optimal alignment between the images. The proposed algorithm is efficient, robust to local optima, and does not require manual initialization or prior information about the images. Experimental results based on various real-world medical images show that the proposed method is capable of achieving higher registration accuracy than existing multimodal registration algorithms for situations, where little to no overlapping regions exist.

Application of Neural Network and Global Optimization in History Matching

Abstract This article presents the application of global optimizers combined with Artificial Neural Networks (ANN) to the history matching problem. An evolutionary algorithm is executed on the proxy generated through the ANN technique. The results obtained from evolutionary algorithms are fine-tuned by using a local optimizer based on the Hooke and Jeeves optimization method. The methodology is applied in two reservoir models and promising results were obtained. Introduction The history matching process consists of adjusting or alternating the key parameters in a reservoir model. The process uses comparisons among production data obtained from reservoir well tests, to develop the model. Some important steps in history matching include the choice of the parameters, the objective function definition, sensitivity analysis and the stopping criteria. Some problems related to history matching are:history matching is generally realized manually;because of the manual element, history matching is not efficient with very large amounts of data;the number of parameters for the reservoir model that can be used to find a solution for a problem can be large, which makes it difficult to determine which parameter will resolve the problem;the algorithms used are local optimizers which do not work satisfactorily in multi-dimensional solution space with several different minimums; andconventional history matching works with only one reservoir model, and does not have the ability to work with multiple models. To solve the problems mentioned above, reservoir engineers have proposed automatic history matching. Some advantages of automatic history matching are:the reduction in the number of tasks related to manipulating the reservoir models;optimization algorithms in automatic history matching can work with objective functions, parameterization, stopping criteria and, possibly, sensitivity and uncertainty analysis together;automatic history matching has the capacity to work simultaneously with multiple reservoir models with uncertainty associated with each model, thereby, satisfying the problem regarding which parameter to use to resolve the matter investigated;automatic history matching has the capacity to work with large amount of data, allowing the use of new technologies that have been recently introduced for reservoir management, such as 4D seismic downhole gauge; andautomatic history matching offers the possibility to combine the experience of reservoir engineers with rules transformed in mathematical algorithms. One of the most important topics of research on automatic history matching is the development of optimization algorithms. These algorithms are divided into two groups in accordance with the type of objective function with which they work: global optimizers, which are able to work with noisy multi-modal objective functions; and local optimizers, which are able to work with uni-modal objective functions. The algorithms that have been used more in practical cases are based on the following methods: the Gauss-Newton Method(1), the Levenberg-Marquardt Method(2) and the Fletcher-Powell Method(3). The difficulty with the algorithms generated with these methods is that they do not work efficiently with non-linearity. Moreover, they are local optimizers. The research about global optimizers in automatic history matching is fundamental(4).

Existence of multidimensional shock waves and phase boundaries

In this paper, a kind of Riemann problem for the Euler equations in a van der Waals fluid is considered. We constructed the weak solution in multidimensional space which contains one shock front and one subsonic phase boundary. We mainly follow the arguments of Majda's [A. Majda, The stability of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 275 (1983) 1–95; A. Majda, The existence of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 281 (1983) 1–93] and Métivier's [G. Métivier, Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d'espace, Trans. Amer. Math. Soc. 296 (1986) 431–479] work. The linear stability results are based on Majda's [A. Majda, The stability of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 275 (1983) 1–95] work for the single shock front and Wang and Xin's [Y.-G. Wang, Z. Xin, Stability and existence of multidimensional subsonic phase transitions, Acta Math. Appl. Sin. 19 (2003) 529–558] work for the single phase boundary. The initial boundary value problem concerned in this paper is different from the boundary value problem for double shock fronts concerned in [G. Métivier, Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d'espace, Trans. Amer. Math. Soc. 296 (1986) 431–479], we slightly modified Métivier's frame work to establish the existence for the solution to the nonlinear problem.

Solving multidimensional bioeconomic problems with singular-perturbation reduction methods: Application to managing pest resistance to pesticidal crops

We investigate the application of ‘singular-perturbation’ reduction methods from the dynamical-systems literature to solve continuous-time multidimensional bioeconomic models resulting from integrating economics with increasingly complex biological structures. These methods reduce multidimensional solution space to the lower-dimensional subspace confining long-term dynamics. They arise naturally in problems with state variables evolving on widely disparate time scales. In particular, we demonstrate how the methods reduce the solution space of a linear-control specification—characterized by two state variables adjusting at widely disparate rates—to a single differential equation in the slow variable. All other system variables are determined by algebraic equations. We apply singular-perturbation methods to investigate the optimal management of pest resistance to pesticidal crops. The pest population evolves on a fast-time scale, while the population's genetic composition evolves on a slow-time scale. In comparison with past work, we can more fully characterize the continuous-time dynamics associated with a complex genetic specification.

Economic dynamics of reservoir sedimentation management: Optimal control with singularly perturbed equations of motion

We analyze the economic dynamics of reservoir sedimentation management using the hydrosuction-dredging sediment-removal system. System dynamics depend on two interdependent hydraulic processes evolving at different rates. The accumulation of water impounded in the reservoir evolves on a ‘fast’ time scale, while the loss of water storage capacity to trapped sediments evolves on a ‘slow’ time scale. We formulate a multidimensional optimal control problem with singularly perturbed equations of motion to accommodate the disparate time scales. We apply singular perturbation methods to approximate (via polynomial series expansion) a ‘slow’ manifold reducing multi-dimensional solution space to the single-dimensional subspace confining long-term dynamics.