High-dimensional Space Research Articles

Variable resolution machine learning optimization of antennas using global sensitivity analysis

AbstractThe significance of rigorous optimization techniques in antenna engineering has grown significantly in recent years. For many design tasks, parameter tuning must be conducted globally, presenting a challenge due to associated computational costs. The popular bio-inspired routines often necessitate thousands of merit function calls to converge, generating prohibitive expenses whenever the design process relies on electromagnetic (EM) simulation models. Surrogate-assisted methods offer acceleration, yet constructing reliable metamodels is hindered in higher-dimensional spaces and systems with highly nonlinear characteristics. This work suggests an innovative technique for global antenna optimization embedded within a machine-learning framework. It involves iteratively refined kriging surrogates and particle swarm optimization for generating infill points. The search process operates within a reduced-dimensionality region established through fast global sensitivity analysis. Domain confinement enables the creation of accurate behavioral models using limited training data, resulting in low CPU costs for optimization. Additional savings are realized by employing variable-resolution EM simulations, where low-fidelity models are utilized during the global search stage (including sensitivity analysis), and high-fidelity ones are reserved for final (gradient-based) tuning of antenna parameters. Comprehensive verification demonstrates the consistent performance of the proposed procedure, its superiority over benchmark techniques, and the relevance of the mechanisms embedded into the algorithm for enhancing search process reliability, design quality, and computational efficiency.

Near-optimal quantum kernel principal component analysis

Abstract Kernel principal component analysis (kernel PCA) is a nonlinear dimensionality reduction technique that employs kernel functions to map data into a high-dimensional feature space, thereby extending the applicability of linear PCA to nonlinear data and facilitating the extraction of informative principal components. However, kernel PCA necessitates the manipulation of large-scale matrices, leading to high computational complexity and posing challenges for efficient implementation in big data environments. Quantum computing has recently been integrated with kernel methods in machine learning, enabling effective analysis of input data within intractable feature spaces. Although existing quantum kernel PCA proposals promise exponential speedups, they impose stringent requirements on quantum hardware that are challenging to fulfill. In this work, we propose a quantum algorithm for kernel PCA by establishing a connection between quantum kernel methods and block encoding, thereby diagonalizing the centralized kernel matrix on a quantum computer. The query complexity is logarithmic with respect to the size of the data vector, $D$, and linear with respect to the size of the dataset. An exponential speedup could be achieved when the dataset consists of a few high-dimensional vectors, wherein the dataset size is polynomial in $\log(D)$, with $D$ being significantly large. In contrast to existing work, our algorithm enhances the efficiency of quantum kernel PCA and reduces the requirements for quantum hardware. Furthermore, we have also demonstrated that the algorithm based on block encoding matches the lower bound of query complexity, indicating that our algorithm is nearly optimal. Our research has laid down new pathways for developing quantum machine learning algorithms aimed at addressing tangible real-world problems and demonstrating quantum advantages within machine learning.

Kernel machine tests of association using extrinsic and intrinsic cluster evaluation metrics

Modeling the network topology of the human brain within the mesoscale has become an increasing focus within the neuroscientific community due to its variation across diverse cognitive processes, in the presence of neuropsychiatric disease or injury, and over the lifespan. Much research has been done on the creation of algorithms to detect these mesoscopic structures, called communities or modules, but less has been done to conduct inference on these structures. The literature on analysis of these community detection algorithms has focused on comparing them within the same subject. These approaches, however, either do not accomodate a more general association between community structure and an outcome or cannot accommodate additional covariates that may confound the association of interest. We propose a semiparametric kernel machine regression model for either a continuous or binary outcome, where covariate effects are modeled parametrically and brain connectivity measures are measured nonparametrically. By incorporating notions of similarity between network community structures into a kernel distance function, the high-dimensional feature space of brain networks, defined on input pairs, can be generalized to non-linear spaces, allowing for a wider class of distance-based algorithms. We evaluate our proposed methodology on both simulated and real datasets.

Nonlinear time series analysis of state-wise COVID-19 in Malaysia using wavelet and persistent homology

AbstractThe nonlinear progression of COVID-19 positive cases, their fluctuations, the correlations in amplitudes and phases across different regions, along with seasonality or periodicity, pose challenges to thoroughly examining the data for revealing similarities or detecting anomalous trajectories. To address this, we conducted a nonlinear time series analysis combining wavelet and persistent homology to detect the qualitative properties underlying COVID-19 daily infection numbers at the state level from the pandemic’s onset to June 2024 in Malaysia. The first phase involved investigating the evolution of daily confirmed cases by state in the time-frequency domain using wavelets. Subsequently, a topological feature-based time series clustering is performed by reconstructing a higher-dimensional phase space through a delay embedding method. Our findings reveal a prominent 7-day periodicity in case numbers from mid-2021 to the end of 2022. The state-wise daily cases are moderately correlated in both amplitudes and phases during the Delta and Omicron waves. Biweekly averaged data significantly enhances the detection of topological loops associated with these waves. Selangor demonstrates unique case trajectories, while Pahang shows the highest similarity with other states. This methodological framework provides a more detailed understanding of epidemiological time series data, offering valuable insights for preparing for future public health crises.

Fast and Efficient Lunar Finite Element Gravity Model

In this paper, the finite element method (FEM) is integrated with orthogonal polynomial approximation in high-dimensional spaces to innovatively model the Moon’s surface gravity anomaly. The aim is to approximate solutions to Laplace’s classical differential equations of gravity, employing classical Chebyshev polynomials as basis functions. Using classical Chebyshev polynomials as basis functions, the least-squares approximation was used to approximate discrete samples of the approximation function. These test functions provide an understanding of errors in approximation and corresponding errors due to differentiation and integration. These test functions provide an understanding of errors in approximation and corresponding errors due to differentiation and integration. The first application of this project is to substitute the globally valid classical spherical harmonic series of approximations with locally valid series of orthogonal polynomial approximations (i.e., using the FEM approach). With an error tolerance set at 10−9ms−2, this method is used to adapt the gravity model radially upwards from the lunar surface. The results showcase a need for a higher degree of approximation on and near the lunar surface, with the necessity decreasing as the radius increases. Notably, this method achieves a computational speedup of five orders of magnitude when applying the method to radial adaptation. More intrinsically, the second application involves using the methodology as an effective tool in solving boundary value problems. Specifically, this approach is implemented to solve classical differential equations involved with high-precision, long-term orbit propagation. This application provides a four-order-of-magnitude speedup in computational time while maintaining an error within the 10−10ms−2 error range for various orbit propagation tests. Alongside the advancements in orthogonal approximation theory, the FEM enables revolutionary speedups in orbit propagation without compromising accuracy.

High-dimensional spin-orbital single-photon sources.

Hybrid integration of solid-state quantum emitters (QEs) into nanophotonic structures opens enticing perspectives for exploiting multiple degrees of freedom of single-photon sources for on-chip quantum photonic applications. However, the state-of-the-art single-photon sources are mostly limited to two-level states or scalar vortex beams. Direct generation of high-dimensional structured single photons remains challenging, being still in its infancy. Here, we propose a general strategy to design highly entangled high-dimensional spin-orbital single-photon sources by taking full advantage of the spatial freedom to design QE-coupled composite (i.e., Moiré/multipart) metasurfaces. We demonstrate the generation of arbitrary vectorial spin-orbital photon emission in high-dimensional Hilbert spaces, mapping the generated states on hybrid-order Bloch spheres. We further realize single-photon sources of high-dimensional spin-orbital quantum emission and experimentally verify the entanglement of high-dimensional superposition states with high fidelity. We believe that the results obtained facilitate further progress in integrated solutions for the deployment of next-generation high-capacity quantum information technologies.

Biquaternion linear canonical stockwell transform and associated uncertainty principles

The intersection of geometric methods and signal processing has led to significant advancements in various fields, including physics, engineering, and mathematics. In recent years, the biquaternion domain, a generalization of complex numbers with a geometric interpretation, has emerged as a promising tool for signal analysis. This paper introduces the Biquaternion Linear Canonical Stockwell Transform (BiQLCST), a novel fusion of advanced mathematical frameworks that offers enhanced signal analysis capabilities and unveils new uncertainty principles, bridging the gap between complex transformations and uncertainty analysis in high-dimensional spaces. First, we established the various fundamental properties, including linearity, shift, modulation, parity, orthogonality relation, reconstruction formula and Plancherel’s theorem. Heisenberg uncertainty principle associated with Biquaternion Linear Canonical Stockwell Transform (BiQLCST) is also established. Toward the end, some potential applications of the BiQLCST are presented.

Cascaded compressed-sensing single-pixel camera for high-dimensional optical imaging

Single-pixel detectors are popular devices in optical sciences because of their fast temporal response, high sensitivity, and low cost. However, when being used for imaging, they face a fundamental challenge in acquiring high-dimensional information of an optical field because they are essentially zero-dimensional sensors and measure only the light intensity. To address this problem, we developed a cascaded compressed-sensing single-pixel camera, which decomposes the measurement into multiple stages, sequentially reducing the dimensionality of the data from a high-dimensional space to zero dimension. This measurement scheme allows us to exploit the compressibility of a natural scene in multiple domains, leading to highly efficient data acquisition. We demonstrated our method in several demanding applications, including enabling tunable single-pixel full-waveform hyperspectral light detection and ranging (LIDAR) for the first time.

Performance of uncertainty-based active learning for efficient approximation of black-box functions in materials science.

Obtaining a fine approximation of a black-box function is important for understanding and evaluating innovative materials. Active learning aims to improve the approximation of black-box functions with fewer training data. In this study, we investigate whether active learning based on uncertainty sampling enables the efficient approximation of black-box functions in regression tasks using various material databases. In cases where the inputs are provided uniformly and defined in a relatively low-dimensional space, the liquidus surfaces of the ternary systems are the focus. The results show that uncertainty-based active learning can produce a better black-box function with higher prediction accuracy than that by random sampling. Furthermore, in cases in which the inputs are distributed discretely and unbalanced in a high-dimensional feature space, datasets extracted from materials databases for inorganic materials, small molecules, and polymers are addressed, and uncertainty-based active learning is occasionally inefficient. Based on the dependency on the material descriptors, active learning tends to produce a better black-box functions than random sampling when the dimensions of the descriptor are small. The results indicate that active learning is occasionally inefficient in obtaining a better black-box function in materials science.

SYSAI for System Health Management - a Statistical Framework for the Analysis of Diagnosis Systems

On-board failure diagnosis and health management systems (HMS) are crucial for the operation of complex autonomous aerospace systems. False alarms (false positives, FPs) or false negatives (FNs) can lead to lower system performance or even loss of mission or the autonomous vehicle. Therefore, a careful verification and validation (V&V) is important. Due to the high dimensionality of the system’s state space, however, exhaustive testing of the HMS is usually not possible. In this paper, we present how our SYSAI (System Analysis for Systems with AI components) framework can support intelligent analysis and testing of HMS on the system level. SYSAI’s capabilities to efficiently explore high-dimensional state and parameter spaces and to identify diagnosability regions and their boundaries, makes a comprehensive analysis of the diagnosis system possible and can provide feedback to the designer. We will illustrate our approach using the ADAPT (Advanced Diagnostics and Prognostics Testbed) redundant power storage and distribution system.

Systematizing cellular complexity: A Hilbertian approach to biological problems

Examining individual components of cellular systems has been successful in uncovering molecular reactions and interactions. However, the challenge lies in integrating these components into a comprehensive system-scale map. This difficulty arises due to factors such as missing links (unknown variables), overlooked nonlinearities in high-dimensional parameter space, downplayed natural noisiness and stochasticity, and a lack of focus on causal influence and temporal dynamics. Composite static and phenomenological descriptions, while appearing complicated, lack the essence of what makes the biological systems truly “complex.” The formalization of system-level problems is therefore important in constructing a meta-theory of biology. Addressing fundamental aspects of cellular regulation, adaptability, and noise management is vital for understanding the robustness and functionality of biological systems. These aspects encapsulate the challenges that cells face in maintaining stability, responding to environmental changes, and harnessing noise for functionality. This work examines these key problems that cells must solve, serving as a template for such formalization and as a step towards the axiomatization of biological investigations. Through a detailed exploration of cellular mechanisms, particularly homeostatic configuration, ion channels and harnessing noise, this paper aims to illustrate complex concepts and theories in a tangible context, providing a bridge between abstract theoretical frameworks and concrete biological phenomena.

Piecewise Time Polynomials-Based Control Methods for Obstacle Avoidance and Precision Positioning of Tower Crane Systems with Varying Cable Lengths

During the hoisting and lowering operations of a tower crane, dynamic variations in cable lengths significantly influence the oscillation frequency and amplitude of the load. These variations complicate the oscillation characteristics, heightening the challenge of balancing obstacle avoidance with precise positioning. To tackle this issue, we propose a trajectory planning and tracking control method that integrates hoisting control to reduce the impact of varying cable lengths on load swinging and achieve accurate positioning during obstacle navigation. A novel definition of swing angle is introduced to model the crane’s rigid and swinging components separately, enhancing model accuracy while simplifying complexity. A piecewise polynomial constructs the load trajectory in a low-dimensional flat space, which is then mapped to a high-dimensional generalized state space through a homeomorphic transformation, ensuring trajectory smoothness and traceability. A fractional-order sliding mode controller is employed to facilitate rapid and precise tracking of the actuated degrees of freedom, suppressing load oscillation while maintaining positioning accuracy. Experimental validation on a tower crane platform shows that the proposed strategy enables smooth obstacle avoidance and precise target point reaching, even with varying cable lengths.

Hydrodynamic Shape Optimization of a Naval Destroyer by Machine Learning Methods

This paper explores the integration of advanced machine learning (ML) techniques within simulation-based design optimization (SBDO) processes for naval applications, focusing on the hydrodynamic shape optimization of the DTMB 5415 destroyer model. The use of unsupervised learning for design-space dimensionality reduction, combined with supervised learning through active learning-based multi-fidelity surrogate modeling, allows for significant improvements in computational efficiency while addressing complex, high-dimensional design spaces. By applying these ML techniques to both single- and multi-objective optimizations, aimed at minimizing resistance and enhancing seakeeping performance, the proposed framework demonstrates its practical value in hydrodynamic design. This approach provides a scalable and efficient solution, reducing the reliance on high-fidelity simulations while accelerating the optimization process, without substantial modifications to existing toolchains. A design-space dimensionality reduction of approximately 70% is achieved, reducing the design variables from 22 to 7 while retaining 95% of the original geometric variance. Additionally, computational cost reductions of 65% to 98% are observed, compared to using the full design space and high-fidelity simulations only.

Transfer learning for high-dimensional linear regression via the elastic net

In this paper, the high-dimensional linear regression problem is explored via the Elastic Net under the transfer learning framework. Within this framework, potentially related source datasets are leveraged to enhance estimation or prediction beyond what can be achieved solely with the target data. When transferable sources are known, an oracle transfer learning algorithm is proposed based on the Elastic Net. Additionally, the ℓ1/ℓ2 estimation error bounds for the corresponding estimator are established. When the transferable sources are unknown, a novel procedure for detecting transferable sources via the Elastic Net is also proposed, with its selection consistency demonstrated under regular conditions. This method transforms the source detection problem into a variable selection problem in high-dimensional space and always gets results that are consistent with the true outcomes. The performance of these methods is further demonstrated through a variety of numerical examples. Finally, our approach is applied to analyze several real datasets for illustrative purposes.

3-D full-field reconstruction of chemically reacting flow towards high-dimension conditions through machine learning

Monitoring chemically reacting flow is crucial for optimizing and controlling the conversion processes in various chemical engineering scenarios. These processes are often influenced by multiple factors, creating a high-dimensional condition space that imposes intensive computational cost to computational fluid dynamics (CFD) methods. We present a machine learning (ML) framework to reconstruct the 3-D scalar field preserving the accuracy and resolution of CFD modeling. We demonstrate the framework’s effectiveness through a case study on biomass combustion in an industrial-scale grate furnace, which exemplifies the challenges of modeling chemically reacting flow in complex geometric domains influenced non-linearly by multiple parameters. The framework implements three core principles: (1) a Reactor-Structure-Resembled Network (RSRNet) reflecting the operational logics of the reactor, (2) an incremental learning strategy based on random Latin Hypercube Sampling, and (3) the incorporation of self-extracted high-level features from data as soft constraints in the loss function. Ground truth data were calculated through a CFD model, with all cases sampled from a 11-variable condition space. Using only 240 randomly sampled cases (around 1 % total cases in the discretized condition space), RSRNet precisely replicated 1-D and 2-D scalar distributions through incremental training. Further reconstruction of 3-D temperature field only used 40 3-D CFD cases, resulting in the training and testing errors decreased to 7.94 × 10-4 and 1.55 × 10-3, respectively, approaching the level of the 2-D reconstruction, with the average error in temperature field predictions not exceeding 50 K. The generalization ability was validated using a separate test dataset with continuously changing excess air ratio and capacity ratio in wide ranges, including some extreme values, and the model successfully captured complex phenomena under unseen conditions.

Elliptic geometry-based kernel matrix for improved biological sequence classification

Protein sequence classification plays a pivotal role in bioinformatics as it enables the comprehension of protein functions and their involvement in diverse biological processes. While numerous machine learning models have been proposed to tackle this challenge, traditional approaches face limitations in capturing the intricate relationships and hierarchical structures inherent in genomic sequences. These limitations stem from operating within high-dimensional non-Euclidean spaces. To address this issue, we introduce the application of the elliptic geometry-based approach for protein sequence classification. First, we transform the problem in elliptic geometry and integrate it with the Gaussian kernel to map the problem into the Mercer kernel. The Gaussian-Elliptic approach allows for the implicit mapping of data into a higher-dimensional feature space, enabling the capture of complex nonlinear relationships. This feature becomes particularly advantageous when dealing with hierarchical or tree-like structures commonly encountered in biological sequences. Experimental results highlight the effectiveness of the proposed model in protein sequence classification, showcasing the advantages of utilizing elliptic geometry in bioinformatics analyses. It outperforms state-of-the-art methods by achieving 76% and 84% accuracies for DNA and Protein datasets, respectively. Furthermore, we provide theoretical justifications for the proposed model. This study contributes to the burgeoning field of geometric deep learning, offering insights into the potential applications of elliptic representations in the analysis of biological data.

Transformation of valence signaling in a mouse striatopallidal circuit

The ways in which sensory stimuli acquire motivational valence through association with other stimuli is one of the simplest forms of learning. Although we have identified many brain nuclei that play various roles in reward processing, a significant gap remains in understanding how valence encoding transforms through the layers of sensory processing. To address this gap, we carried out a comparative investigation of the mouse anteromedial olfactory tubercle (OT), and the ventral pallidum (VP) - 2 connected nuclei of the basal ganglia which have both been implicated in reward processing. First, using anterograde and retrograde tracing, we show that both D1 and D2 neurons of the anteromedial OT project primarily to the VP and minimally elsewhere. Using two-photon calcium imaging, we then investigated how the identity of the odor and reward contingency of the odor are differently encoded by neurons in either structure during a classical conditioning paradigm. We find that VP neurons robustly encode reward contingency, but not identity, in low-dimensional space. In contrast, the OT neurons primarily encode odor identity in high-dimensional space. Although D1 OT neurons showed larger responses to rewarded odors than other odors, consistent with prior findings, we interpret this as identity encoding with enhanced contrast. Finally, using a novel conditioning paradigm that decouples reward contingency and licking vigor, we show that both features are encoded by non-overlapping VP neurons. These results provide a novel framework for the striatopallidal circuit in which a high-dimensional encoding of stimulus identity is collapsed onto a low-dimensional encoding of motivational valence.

Transformation of valence signaling in a mouse striatopallidal circuit.

The ways in which sensory stimuli acquire motivational valence through association with other stimuli is one of the simplest forms of learning. Although we have identified many brain nuclei that play various roles in reward processing, a significant gap remains in understanding how valence encoding transforms through the layers of sensory processing. To address this gap, we carried out a comparative investigation of the mouse anteromedial olfactory tubercle (OT), and the ventral pallidum (VP) - 2 connected nuclei of the basal ganglia which have both been implicated in reward processing. First, using anterograde and retrograde tracing, we show that both D1 and D2 neurons of the anteromedial OT project primarily to the VP and minimally elsewhere. Using two-photon calcium imaging, we then investigated how the identity of the odor and reward contingency of the odor are differently encoded by neurons in either structure during a classical conditioning paradigm. We find that VP neurons robustly encode reward contingency, but not identity, in low-dimensional space. In contrast, the OT neurons primarily encode odor identity in high-dimensional space. Although D1 OT neurons showed larger responses to rewarded odors than other odors, consistent with prior findings, we interpret this as identity encoding with enhanced contrast. Finally, using a novel conditioning paradigm that decouples reward contingency and licking vigor, we show that both features are encoded by non-overlapping VP neurons. These results provide a novel framework for the striatopallidal circuit in which a high-dimensional encoding of stimulus identity is collapsed onto a low-dimensional encoding of motivational valence.

Deep reinforcement learning-based multi-objective optimization for electricity–gas–heat integrated energy systems

With the increasing global attention on energy efficiency and carbon emissions, the optimization of integrated energy systems (IES) has become the key to improve energy efficiency and reduce pollution emissions. However, most of the existing optimization methods cannot effectively deal with the complexity of high dimensional continuous action space. Therefore, this paper focuses on a novel multi-objective optimization strategy for the electricity–gas–heat integrated energy systems (EGH-IES). Firstly, considering the absorption capacity of wind power and the emission of pollutant gases, a multi-objective optimization model is constructed based on the mechanism model and operation constraints of each device in EGH-IES, in which the integrated operation cost and the environmental factors are taken as optimization objectives. Then, the multi-objective optimization problem is designed as the optimal strategy of interaction learning between agent and environment in reinforcement learning, and the output power of the devices constitutes the action of reinforcement learning. Additionally, the Ornstein–Uhlenbeck process is introduced to enhance the training efficiency and exploration performance of the agent, and the deep deterministic policy gradients (DDPG) algorithm is employed to optimize the action, thus the output power of the appliances could be obtained. Finally, the simulation results show that compared with deep Q network (DQN) method and proximal policy optimization (PPO) method, the reward function value of the proposed method increases by 2.43% and 6.09%, respectively, which represents a reduction in economic cost and pollutant emissions. These verify the effectiveness and superiority of the proposed multi-objective optimization scheme in cost reduction and benefit improvement for the EGH-IES.

Improving information theory of context-aware phrase embeddings in HR domain

The object of the study is context-aware phrase representations. The growing need to automate candidate recruitment and job recommendation processes has paved the way for the utilization of text embeddings. These embeddings involve translating the semantic essence of text into a continuous, high-dimensional vector space. By learning context-aware rich and meaningful representations of phrases within the human resource domain, the efficacy of similarity searches and matching procedures is enhanced, which contributes to a more streamlined and effective recruitment process. However, existing approaches do not take into account the context when modeling phrases. This necessitates the improvement of information technology analysis in this area. In this paper, it is proposed to mark the beginning and end of phrases in the text using special tokens. This made it possible to reduce the requirements for computing power by calculating all phrase representations present in the text simultaneously. The effectiveness of the improvement was tested on a new dataset to compare and evaluate the models in the task of modeling phrases in the field of human resources management. The proposed approach to modeling phrase representations with regard to context in the field of human resources management leads to an improvement in computational efficiency by up to 50 % and an increase in accuracy by up to 10 %. The architecture of the machine learning model for creating context-aware phrase representations is developed, which is characterized by the presence of blocks for taking into account phrase boundaries. Experiments and comparisons with existing approaches have confirmed the effectiveness of the proposed solution. In practice, the proposed information analysis technology can be used to automate the process of identifying and normalizing candidates' skills in online recruiting