Large Dimensional Space Research Articles

Enhancement of Reflood Test Prediction by Integrating Machine Learning and Data Assimilation Technique

Data assimilation (DA) was revealed as a highly efficient approach to enhance the prediction’s accuracy, demonstrating the reliability of the simulation through uncertainty quantification analysis. However, in the numerical simulations, most of the tasks are highly nonlinear relationships between the parameters that directly affect the efficiency of the DA such as the large search space dimension, resulting in significant computational costs. This limitation can be overcome by implementing machine learning (ML) predictions that can efficiently expand the DA search space. Therefore, this study is aimed at enhancing the performance of DA by integrating ML and DA (IMD), proposing a new method to overcome the stand-alone DA limitations. The approach involved implementing a stand-alone DA using the multidimensional analysis of reactor safety (MARS) code to enhance the prediction of reflood tests. The output datasets obtained from the stand-alone DA were then used to train the deep neural networks (DNNs), and the accuracy of the DNN’s prediction was thoroughly evaluated with varying dataset sizes. This DNN subsequently can predict the enormous unobserved samples, enabling the identification and investigation of the prospective candidates for the subsequent DA process. The results demonstrated that the stand-alone DA achieved an accuracy enhancement of up to 41.3% in reflood test predictions, while the IMD yielded even more significant improvements, with a performance enhancement of 47.0%. These findings reveal that the IMD approach outperformed the stand-alone DA approach, particularly in the case of high flooding rate tests. In this context, the proposed integrating system can effectively overcome the high computational cost and enhance the performance of stand-alone DA.

Gauge-Optimal Approximate Learning for Small Data Classification.

Small data learning problems are characterized by a significant discrepancy between the limited number of response variable observations and the large feature space dimension. In this setting, the common learning tools struggle to identify the features important for the classification task from those that bear no relevant information and cannot derive an appropriate learning rule that allows discriminating among different classes. As a potential solution to this problem, here we exploit the idea of reducing and rotating the feature space in a lower-dimensional gauge and propose the gauge-optimal approximate learning (GOAL) algorithm, which provides an analytically tractable joint solution to the dimension reduction, feature segmentation, and classification problems for small data learning problems. We prove that the optimal solution of the GOAL algorithm consists in piecewise-linear functions in the Euclidean space and that it can be approximated through a monotonically convergent algorithm that presents-under the assumption of a discrete segmentation of the feature space-a closed-form solution for each optimization substep and an overall linear iteration cost scaling. The GOAL algorithm has been compared to other state-of-the-art machine learning tools on both synthetic data and challenging real-world applications from climate science and bioinformatics (i.e., prediction of the El Niño Southern Oscillation and inference of epigenetically induced gene-activity networks from limited experimental data). The experimental results show that the proposed algorithm outperforms the reported best competitors for these problems in both learning performance and computational cost.

On the Use of Ellipsoidal Estimation Techniques in the RRT* Suboptimal Pathfinding Algorithm

The article is devoted to the development of an algorithm for the approximate solution of the time-optimal control problem for a system of ordinary differential equations, under the condition of avoiding collisions with stationary obstacles and subject to the specified pointwise constraints on the possible values of the control parameters. The main idea is to use a modification of the algorithm for finding suboptimal paths using rapidly growing random trees (RRT*). The most difficult part of this algorithm is to find the optimal trajectories for the problems of transferring the system from one fixed position to another, close to it, without taking into account state constraints. This subproblem is proposed to be solved using the methods of ellipsoidal calculus. This approach makes it possible to efficiently search suboptimal trajectories both for linear systems with large state space dimension and for systems with nonlinear dynamics. Algorithms for the linear and non-linear cases are sequentially analyzed in the paper, and the corresponding examples of calculations are presented.

Quantum squirrel search algorithm based support vector machine algorithm for brain tumor classification

AbstractA Brain tumor is growth or mass of irregular cells inside your brain, several various kinds of brain tumors survive. A few brain tumors are cancerous (malignant), also various brain tumors are noncancerous (benign). The existing approach faces problem related to local optima issues, complexity in computational time, less convergence speed and less exploration ability. The stimulated quality Selection of Quantum Squirrel Search Algorithm (QSSA) is based on equally appearance with methylation information of prostate cancer. Issues with multiple models, multiple dimensions, and unimodal optimization are all addressed by this QSSA concept. The input image of the CE‐MRI dataset consists of 3064 segments with comprise (708 slices) meningiomas, (1426 slices) gliomas and (930 slices) pituitary tumors. In order to extract appropriate data from an image, a convolutional neural network (CNN) executes a number of mathematical processes, including convolutions and pooling. The CNN model's benefits include a large number of important features that can be extracted and good accuracy. Then, Support Vector Machine (SVM), a machine learning technique used for supervised learning, is typically associated within the double classification. The SVM model benefits from a large effective dimensional space and adequate memory. The proposed QSSA has obtained high Accuracy 98.3%, Sensitivity 95.4% and Specificity 97.9% than existing Correlation Learning Mechanism (CLM) which has 90.4% accuracy, 86% sensitivity and 91.5% specificity respectively.

Effects of Kaluza-Klein neutrinos on RD and [formula omitted

Recent measurements of RD and RD⁎ by the LHCb collaboration show deviations from their respective Standard Model values. These semileptonic B meson decays, associated with b→cτν¯ transition, are pointing toward new physics beyond the Standard Model via leptonic flavor universality violation. In this paper, we show that such anomaly can be resolved by the cummulative Kaluza-Klein (KK) modes of singlet right-handed neutrino which propagates in the large extra dimensional space. We found that the number of extra dimension should be 2 to explain RD and RD⁎. We show that both RD and RD⁎ constraint the energy scale MF of this extra dimension which are compatible with the limits from lepton flavor violating tau decays. In contrast, our findings are in tension with the limits coming from the neutrino experiments which set the most stringent lower bound on MF. The future measurements of RD(⁎)exp with reduced uncertainties will exclude this extra dimensional model with right-handed neutrino propagating in the bulk, if the central values stay.

A dynamic annealing learning for PLSOM neural networks: Applications in medicine and applied sciences

In recent years, the field of unsupervised learning in neural networks has witnessed significant advancements. This innovative learning technique holds great promise for applications in diverse domains, with particular significance in the realms of medicine and applied sciences such as medical image analysis, drug discovery, predictive analytics, and pattern recognition. The neighborhood function plays a crucial role in the Improved Parameter-Less Self-Organizing Map (PLSOM2) algorithm by governing the rate of change in the vicinity of the winning neuron. During learning iterations, the neighborhood size is dynamically adjusted to encompass the activated neighboring neurons relative to the winning neuron. The training process begins with a larger neighborhood radius, promoting rough ordering, and gradually refines the process by reducing the radius for fine-tuning. This dynamic neighborhood size significantly influences the final training outcome of the PLSOM2 algorithm. However, one of the major bottlenecks of the PLSOM2 algorithm has been the slow ordering time and the challenge of determining an optimal neighborhood size. These issues often lead to topological defects during training, such as kinks or warps in the output maps. Merely increasing processing time has proven insufficient to overcome these challenges. In this paper, we propose a novel dynamic neighborhood function designed to accelerate the convergence process of the PLSOM2 algorithm, achieving the best shape and adaptation of the neighborhood width. The study demonstrates that by improving the neighborhood function of the PLSOM2 algorithm, map distortion can be effectively suppressed. Importantly, this enhancement enables the algorithm to handle network size, neighborhood size, and the large dimensional output space adeptly. It adaptively decreases the neighborhood size over time, ensuring convergence while appropriately managing network growth and avoiding twisting and misconfiguration. To assess the effectiveness of the proposed method, we conducted an extensive set of experiments across eight real-world benchmark datasets. Notably, the outcomes of these experiments are presented showcases the results of paired t-tests, highlighting the consistency and robustness of the proposed algorithm's performance. Despite non-significant p-values in many cases, the algorithm consistently excels across various datasets, underlining its practical significance. On the other hand, presents the results of One-way Analysis of Variance (ANOVA) tests. These results further reinforce the consistency of the performance of algorithm, as indicated by p-values exceeding the common significance threshold of 0.05. The combined findings from both tables provide strong statistical evidence of the proposed algorithm's robustness and effectiveness across diverse datasets. The proposed research introduces a dynamic neighborhood function that not only improves the PLSOM2 algorithm's convergence but also enhances its adaptability and topological preservation. These enhancements, supported by the statistical tests results, underscore the algorithm's practical significance and its suitability for real-world applications, where statistical significance may not always capture the full extent of its capabilities.

Policy Gradient-Based Core Placement Optimization for Multichip Many-Core Systems.

As many deep neural network models become deeper and more complex, processing devices with stronger computing performance and communication capability are required. Following this trend, the dependence on multichip many-core systems that have high parallelism and reasonable transmission costs is on the rise. In this work, in order to improve routing performance of the system, such as routing runtime and power consumption, we propose a reinforcement learning (RL)- based core placement optimization approach, considering application constraints, such as deadlock caused by multicast paths. We leverage the capability of deep RL from indirect supervision as a direct nonlinear optimizer, and the parameters of the policy network are updated by proximal policy optimization. We treat the routing topology as a network graph, so we utilize a graph convolutional network to embed the features into the policy network. One step size environment is designed, so all cores are placed simultaneously. To handle large dimensional action space, we use continuous values matching with the number of cores as the output of the policy network and discretize them again for obtaining the new placement. For multichip system mapping, we developed a community detection algorithm. We use several datasets of multilayer perceptron and convolutional neural networks to evaluate our agent. We compare the optimal results obtained by our agent with other baselines under different multicast conditions. Our approach achieves a significant reduction of routing runtime, communication cost, and average traffic load, along with deadlock-free performance for inner chip data transmission. The traffic of interchip routing is also significantly reduced after integrating the community detection algorithm to our agent.

Variance-based sensitivity analysis of oil spill predictions in the Red Sea region

To support accidental spill rapid response efforts, oil spill simulations may generally need to account for uncertainties concerning the nature and properties of the spill, which compound those inherent in model parameterizations. A full detailed account of these sources of uncertainty would however require prohibitive resources needed to sample a large dimensional space. In this work, a variance-based sensitivity analysis is conducted to explore the possibility of restricting a priori the set of uncertain parameters, at least in the context of realistic simulations of oil spills in the Red Sea region spanning a two-week period following the oil release. The evolution of the spill is described using the simulation capabilities of Modelo Hidrodinâmico, driven by high-resolution metocean fields of the Red Sea (RS) was adopted to simulate accidental oil spills in the RS. Eight spill scenarios are considered in the analysis, which are carefully selected to account for the diversity of metocean conditions in the region. Polynomial chaos expansions are employed to propagate parametric uncertainties and efficiently estimate variance-based sensitivities. Attention is focused on integral quantities characterizing the transport, deformation, evaporation and dispersion of the spill. The analysis indicates that variability in these quantities may be suitably captured by restricting the set of uncertain inputs parameters, namely the wind coefficient, interfacial tension, API gravity, and viscosity. Thus, forecast variability and confidence intervals may be reasonably estimated in the corresponding four-dimensional input space.

Stochastic representation of many-body quantum states

The quantum many-body problem is ultimately a curse of dimensionality: the state of a system with many particles is determined by a function with many dimensions, which rapidly becomes difficult to efficiently store, evaluate and manipulate numerically. On the other hand, modern machine learning models like deep neural networks can express highly correlated functions in extremely large-dimensional spaces, including those describing quantum mechanical problems. We show that if one represents wavefunctions as a stochastically generated set of sample points, the problem of finding ground states can be reduced to one where the most technically challenging step is that of performing regression—a standard supervised learning task. In the stochastic representation the (anti)symmetric property of fermionic/bosonic wavefunction can be used for data augmentation and learned rather than explicitly enforced. We further demonstrate that propagation of an ansatz towards the ground state can then be performed in a more robust and computationally scalable fashion than traditional variational approaches allow.

Estimating process‐based model parameters from species distribution data using the evolutionary algorithm CMA‐ES

Abstract Two main types of species distribution models are used to project species range shifts in future climatic conditions: correlative and process‐based models. Although there is some continuity between these two types of models, they are fundamentally different in their hypotheses (statistical relationships vs. mechanistic relationships) and their calibration methods (SDMs tend to be occurrence data driven while PBMs tend to be prior driven). One of the limitations to the use of process‐based models is the difficulty to parameterize them for a large number of species compared to correlative SDMs. We investigated the feasibility of using an evolutionary algorithm (called covariance matrix adaptation evolution strategy, CMA‐ES) to calibrate process‐based models using species distribution data. This method is well established in some fields (robotics, aerodynamics, etc.), but has never been used, to our knowledge, in ecology, despite its ability to deal with very large space dimensions. Using tree species occurrence data across Europe, we adapted the CMA‐ES algorithm to find appropriate values of model parameters. We estimated simultaneously 27–77 parameters of two process‐based models simulating forest tree's ecophysiology for three species with varying range sizes and geographical distributions. CMA‐ES provided parameter estimates leading to better prediction of species distribution than parameter estimates based on expert knowledge. Our results also revealed that some model parameters and processes were strongly dependent, and different parameter combinations could therefore lead to high model accuracy. We conclude that CMA‐ES is an efficient state‐of‐the‐art method to calibrate process‐based models with a large number of parameters using species occurrence data. Inverse modelling using CMA‐ES is a powerful method to calibrate process‐based parameters which can hardly be measured. However, the method does not warranty that parameter estimates are correct because of several sources of bias, similarly to correlative models, and expert knowledge is required to validate results.

A Comprehensive Review and Application of Metaheuristics in Solving the Optimal Parameter Identification Problems

For many electrical systems, such as renewable energy sources, their internal parameters are exposed to degradation due to the operating conditions. Since the model’s accuracy is required for establishing proper control and management plans, identifying their parameters is a critical and prominent task. Various techniques have been developed to identify these parameters. However, metaheuristic algorithms have received much attention for their use in tackling a wide range of optimization issues relating to parameter extraction. This work provides an exhaustive literature review on solving parameter extraction utilizing recently developed metaheuristic algorithms. This paper includes newly published articles in each studied context and its discussion. It aims to approve the applicability of these algorithms and make understanding their deployment easier. However, there are not any exact optimization algorithms that can offer a satisfactory performance to all optimization issues, especially for problems that have large search space dimensions. As a result, metaheuristic algorithms capable of searching very large spaces of possible solutions have been thoroughly investigated in the literature review. Furthermore, depending on their behavior, metaheuristic algorithms have been divided into four types. These types and their details are included in this paper. Then, the basics of the identification process are presented and discussed. Fuel cells, electrochemical batteries, and photovoltaic panel parameters identification are investigated and analyzed.

Deep echo state networks in data marketplaces

Data Marketplaces are the digital platform for data buyers and data sellers to trade information as valuable products or items. The expectation taken for granted from the users of a data marketplace is the truth of the exchanged information. However, the trade of factual data also means the marketable product is no longer unique but a series of replicas. If every user within the data marketplace owns the same information, this data eventually becomes valueless. There are specific instances where the traded products are sought to be always unique, for instance predictions or digital art. This article applies Deep Echo State Networks (ESNs) in data marketplaces that map tradeable data into a larger dimensional space via the dynamics of reservoirs with fixed and non-linear properties. These reservoirs generate unique tradeable data products that cannot be replicated, therefore ensuring its exclusivity and commercial value. The validation results show that ESNs can also be applied to generate random tradeable products in different dimensional spaces. Specifically, the reservoir with its associated neural perturbation emulates a digital creator that generates unique and exclusive content based on 1D functions and 2D images.

Blockchain Mining With Multiple Selfish Miners

This paper studies a fundamental problem regarding the security of blockchain PoW consensus on how the existence of multiple misbehaving miners influences the profitability of selfish mining. Each selfish miner maintains a private chain and makes it public opportunistically for acquiring more rewards incommensurate to his Hash power. We first establish a general Markov chain model to characterize the state transition of public and private chains for Basic Selfish Mining ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BSM</i> ), and derive the stationary <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">profitable threshold</i> of Hash power in closed form. It reduces from 25% for a single attacker to below 21.48% for two symmetric attackers theoretically, and further reduces to around 10% with eight symmetric attackers experimentally. We next explore the profitable threshold when one of the attackers performs strategic mining based on Partially Observable Markov Decision Process (POMDP) that only half of the attributes pertinent to a mining state are observable to him. An online algorithm is presented to compute the nearly optimal policy efficiently despite the large state space and high dimensional belief space. The profitable threshold is much lower for the strategic attacker. Last, we formulate a simple model of absolute mining revenue that yields an interesting observation: selfish mining is never profitable at the first difficulty adjustment period, but relies on the reimbursement of stationary selfish mining gains in future periods. The delay till being profitable of an attacker increases with the decrease of his Hash power, making blockchain miners more cautious about performing selfish mining.

Evolution Strategies under the 1/5 Success Rule

For large space dimensions, the log-linear convergence of the elitist evolution strategy with a 1/5 success rule on the sphere fitness function has been observed, experimentally, from the very beginning. Finding a mathematical proof took considerably more time. This paper presents a review and comparison of the most consistent theories developed so far, in the critical interpretation of the author, concerning both global convergence and the estimation of convergence rates. I discuss the local theory of the one-step expected progress and success probability for the (1+1) ES with a normal/uniform distribution inside the sphere mutation, thereby minimizing the SPHERE function, but also the adjacent global convergence and convergence rate theory, essentially based on the 1/5 rule. Small digressions into complementary theories (martingale, irreducible Markov chain, drift analysis) and different types of algorithms (population based, recombination, covariance matrix adaptation and self-adaptive ES) complete the review.

Random fixed points, systemic risk and resilience of heterogeneous financial network.

We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional spaces, and our aim is to study their almost-sure solutions. An underlying directed random graph defines the connections between various components of the FP equations. Existence of an edge between nodes i,j implies the i-th FP equation depends on the j-th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random 'neighbour' components. We obtain finite dimensional limit FP equations in a much smaller dimensional space, whose solutions aid to approximate the solution of FP equations for almost all realizations, as the number of nodes increases. We use Maximum theorem for non-compact sets to prove this convergence.We apply the results to study systemic risk in an example financial network with large number of heterogeneous entities. We utilized the simplified limit system to analyse trends of default probability (probability that an entity fails to clear its liabilities) and expected surplus (expected-revenue after clearing liabilities) with varying degrees of interconnections between two diverse groups. We illustrated the accuracy of the approximation using exhaustive Monte-Carlo simulations.Our approach can be utilized for a variety of financial networks (and others); the developed methodology provides approximate small-dimensional solutions to large-dimensional FP equations that represent the clearing vectors in case of financial networks.

On the origins and evolution of qualia: An experience-space perspective.

This paper elaborates on a proposal for mapping a configuration space for selector circuits (SCs), defined as the subset of neural correlates of consciousness (NCCs) responsible for evoking particular qualia, to its experiential counterpart, experience-space (E-space), as part of an investigation into the nature of conscious experience as it first emerged in evolution. The dimensionality of E-space, meaning the degrees of freedom required to specify the properties of related sets of qualia, is at least two, but the utility of E-space as a hypothetical construct is much enhanced by assuming it is a large dimensional space, with at least several times as many dimensions as there are categories of qualia to occupy them. Phenomenal consciousness can then be represented as having originated as one or more multidimensional ur-experiences that combined multiple forms of experience together. Taking this as a starting point, questions concerning evolutionary sequence can be addressed, including how the quale best suited to a given sensory modality would have been extracted by evolution from a larger set of possibilities, a process referred to here as dimensional sorting, and how phenomenal consciousness would have been experienced in its earliest manifestations. There is a further question as to whether the E-space formulation is meaningful in analytical terms or simply a descriptive device in graphical form, but in either case it provides a more systematic way of thinking about early stages in the evolution of consciousness than relying on narrative and conjecture alone.

Scalable Controllability Analysis of Structured Networks

This article deals with strong structural controllability of structured networks. A structured network is a family of heterogeneous structured systems (called node systems) that are interconnected by means of a structured interconnection law, all given by pattern matrices. Here, we consider structured networks with single-input–single-output node systems. It is shown that such a structured network is strongly structurally controllable if and only if an associated structured system is. This structured system will, in general, have a very large state space dimension and, therefore, existing tests for verifying strong structural controllability are not tractable. The main result of this article circumvents this problem. We show that controllability can be tested by replacing the original network by a new network in which all original node systems have been replaced by (auxiliary) node systems with state space dimensions either 1 or 2. Hence, controllability of the original network can be verified by testing controllability of a structured system with state space dimension at most twice the number of node systems, regardless of the state space dimensions of the original node systems.

ESPA+: Scalable Entropy-Optimal Machine Learning Classification for Small Data Problems

Classification problems in the small data regime (with small data statistic T and relatively large feature space dimension D) impose challenges for the common machine learning (ML) and deep learning (DL) tools. The standard learning methods from these areas tend to show a lack of robustness when applied to data sets with significantly fewer data points than dimensions and quickly reach the overfitting bound, thus leading to poor performance beyond the training set. To tackle this issue, we propose eSPA+, a significant extension of the recently formulated entropy-optimal scalable probabilistic approximation algorithm (eSPA). Specifically, we propose to change the order of the optimization steps and replace the most computationally expensive subproblem of eSPA with its closed-form solution. We prove that with these two enhancements, eSPA+ moves from the polynomial to the linear class of complexity scaling algorithms. On several small data learning benchmarks, we show that the eSPA+ algorithm achieves a many-fold speed-up with respect to eSPA and even better performance results when compared to a wide array of ML and DL tools. In particular, we benchmark eSPA+ against the standard eSPA and the main classes of common learning algorithms in the small data regime: various forms of support vector machines, random forests, and long short-term memory algorithms. In all the considered applications, the common learning methods and eSPA are markedly outperformed by eSPA+, which achieves significantly higher prediction accuracy with an orders-of-magnitude lower computational cost.

A Generalization of Possibilistic Fuzzy C-Means Method for Statistical Clustering of Data

The Fuzzy C-means (FCM) algorithm has been widely used in the field of clustering and classification but has encountered difficulties with noisy data and outliers. Other versions of algorithms related to possibilistic theory have given good results, such as Fuzzy C- Means(FCM), possibilistic C-means (PCM), Fuzzy possibilistic C-means (FPCM) and possibilistic fuzzy C- Means algorithm (PFCM).This last algorithm works effectively in some environments but encountered more shortcomings with noisy databases. To solve this problem, we propose in this manuscript, a new algorithm named Improved Possibilistic Fuzzy C-Means (ImPFCM) by combining the PFCM algorithm with a very powerful statistical method. The properties of this new ImPFCM algorithm show that it is not only applicable on clusters of spherical shapes, but also on clusters of different sizes and densities. The results of the comparative study with very recent algorithms indicate the performance and the superiority of the proposed approach to easily group the datasets in a large-dimensional space and to use not only the Euclidean distance but more sophisticated standards norms, capable to deal with much more complicated problems. On the other hand, we have demonstrated that the ImPFCM algorithm is also capable of detecting the cluster center with high accuracy and performing satisfactorily in multiple environments with noisy data and outliers.

Интеллектуальный поиск точных решений задачи планирования открытых горных работ

A method of intelligent search for accurate solutions to the planning of open-pit mining has been developed. The method is implemented within the framework of the Constraint Programming Paradigm that allows us to process heterogeneous qualitative and quantitative constraints (in particular, economic, technological, etc.) simultaneously, as well as to maintain the model of subject domain being developed which is open to adding new constraints or deleting existing constraints. Various constraints can be added to the model, including those for which it is difficult to find a suitable analytical expression. In contrast to existing methods of local search the proposed method systematically explores the search space. The method allows us to find a global optimum in large dimensional spaces that describe practically significant problems arising in production. Currently, to solve this problem, the methods of integer linear programming are widely used. But its fundamental disadvantage is the need to represent all the constraints in the form of linear equalities and inequalities. However, in practice, some combinatorial optimization problems cannot be linearized and solved using traditional methods of mathematical programming. The developed method is illustrated by the example of a three-dimensional problem of finding the position of an intermediate pit wall by the processing periods taking into account the specified performance for mineral and overburden rocks and the objective profit function taking into account discounting. The types of constraints necessary for modeling the problem under consideration are identified. The possibility of applying the existing inference procedures on constraints is considered for these types. The method proposed makes it possible to obtain accurate solutions due to the intellectualization of the solution process by using highly efficient algorithms of reducing the search space for each type of constraints and specialized heuristics for pruning unpromising alternatives in the search tree.