High-dimensional Space Research Articles

Finite-dimensional perturbation of the Dirichlet boundary value problem for the biharmonic equation

Abstract The biharmonic equation is one of the important equations of mathematical physics, describing the behaviour of harmonic functions in higher-dimensional spaces. The main purpose of this study was to construct a finite-dimensional perturbation for the Dirichlet boundary value problem associated with the biharmonic equation. The methodological basis for this study was an integrated approach that includes mathematical analysis, algebraic methods, operator theory, and the theorem on the existence and uniqueness of a solution for a boundary value. The main tool is a finite-dimensional perturbation, which allows for examining the properties and behaviour of boundary value problems in as much detail as possible. In the study, descriptions of correctly solvable internal boundary value problems for a biharmonic equation in non-simply connected domains were considered in detail. The study is also devoted to the search for solutions and the analytical representation of resolvents of boundary value problems for a biharmonic equation in multi-connected domains. Within the framework of the study, theorems and their consequences were proved, and a finite-dimensional perturbation was constructed for the Dirichlet boundary value problem. Analytical representations of resolvents of boundary value problems for a biharmonic equation in multi-connected domains were also obtained. The examination of a finite-dimensional perturbation of the Dirichlet boundary value problem for a biharmonic equation has expanded the understanding of the properties of this equation in various contexts.

Attack on optical cryptosystems by skip connection networks

Optical encryption methods, due to their efficient operation speed and parallel processing capabilities, hold significant importance in securing multidimensional and large-volume data. Enhancing the security of optical cryptosystems from the perspective of cryptanalysis holds significant importance currently. Presently, attack methods against optical encryption are complex, and the effectiveness of these attacks is insufficient. Security analysis solutions face limitations in both breadth and depth. Therefore, this paper proposes an attack on optical cryptosystems based on a skip connection network, demonstrating the susceptibility of optical cryptosystems to attacks based on neural network algorithms. The network model is trained on plaintext-ciphertext pairs, fitting equivalent keys without various additional conditions. It approximates plaintext information in high-dimensional space, directly obtaining corresponding plaintext through ciphertext information, expanding the applicability and enhancing the effectiveness of the attack scheme. Finally, the feasibility and effectiveness of the attack scheme were verified through computer simulations. The experiments indicate that the method proposed in this paper has low computational complexity, wide applicability, produces high-quality decrypted images, and high decipherment accuracy. This provides a universal approach for analyzing the security of various optical cryptosystems from the perspective of chosen plaintext attacks.

Evolution-guided Bayesian optimization for constrained multi-objective optimization in self-driving labs

The development of automated high-throughput experimental platforms has enabled fast sampling of high-dimensional decision spaces. To reach target properties efficiently, these platforms are increasingly paired with intelligent experimental design. However, current optimizers show limitations in maintaining sufficient exploration/exploitation balance for problems dealing with multiple conflicting objectives and complex constraints. Here, we devise an Evolution-Guided Bayesian Optimization (EGBO) algorithm that integrates selection pressure in parallel with a q-Noisy Expected Hypervolume Improvement (qNEHVI) optimizer; this not only solves for the Pareto Front (PF) efficiently but also achieves better coverage of the PF while limiting sampling in the infeasible space. The algorithm is developed together with a custom self-driving lab for seed-mediated silver nanoparticle synthesis, targeting 3 objectives (1) optical properties, (2) fast reaction, and (3) minimal seed usage alongside complex constraints. We demonstrate that, with appropriate constraint handling, EGBO performance improves upon state-of-the-art qNEHVI. Furthermore, across various synthetic multi-objective problems, EGBO shows significative hypervolume improvement, revealing the synergy between selection pressure and the qNEHVI optimizer. We also demonstrate EGBO’s good coverage of the PF as well as comparatively better ability to propose feasible solutions. We thus propose EGBO as a general framework for efficiently solving constrained multi-objective problems in high-throughput experimentation platforms.

On polling directions for randomized direct-search approaches: application to beam angle optimization in intensity-modulated proton therapy

AbstractDeterministic direct-search methods have been successfully used to address real-world challenging optimization problems, including the beam angle optimization (BAO) problem in radiation therapy treatment planning. BAO is a highly non-convex optimization problem typically treated as the optimization of an expensive multi-modal black-box function which results in a computationally time consuming procedure. For the recently available modalities of radiation therapy with protons (instead of photons) further efficiency in terms of computational time is required despite the success of the different strategies developed to accelerate BAO approaches. Introducing randomization into otherwise deterministic direct-search approaches has been shown to lead to excellent computational performance, particularly when considering a reduced number (as low as two) of random poll directions at each iteration. In this study several randomized direct-search strategies are tested considering different sets of polling directions. Results obtained using a prostate and a head-and-neck cancer cases confirmed the high-quality results obtained by deterministic direct-search methods. Randomized strategies using a reduced number of polling directions showed difficulties for the higher dimensional search space (head-and-neck) and, despite the excellent mean results for the prostate cancer case, outliers were observed, a result that is often ignored in the literature. While, for general global optimization problems, mean results (or obtaining the global optimum once) might be enough for assessing the performance of the randomized method, in real-world problems one should not disregard the worst-case scenario and beware of the possibility of poor results since, many times, it is only possible to run the optimization problem once. This is even more important in healthcare applications where the mean patient does not exist and the best treatment possible must be assured for every patient.

Machine learning decoding of single neurons in the thalamus for speech brain-machine interfaces

Objective. Our goal is to decode firing patterns of single neurons in the left ventralis intermediate nucleus (Vim) of the thalamus, related to speech production, perception, and imagery. For realistic speech brain-machine interfaces (BMIs), we aim to characterize the amount of thalamic neurons necessary for high accuracy decoding. Approach. We intraoperatively recorded single neuron activity in the left Vim of eight neurosurgical patients undergoing implantation of deep brain stimulator or RF lesioning during production, perception and imagery of the five monophthongal vowel sounds. We utilized the Spade decoder, a machine learning algorithm that dynamically learns specific features of firing patterns and is based on sparse decomposition of the high dimensional feature space. Main results. Spade outperformed all algorithms compared with, for all three aspects of speech: production, perception and imagery, and obtained accuracies of 100%, 96%, and 92%, respectively (chance level: 20%) based on pooling together neurons across all patients. The accuracy was logarithmic in the amount of neurons for all three aspects of speech. Regardless of the amount of units employed, production gained highest accuracies, whereas perception and imagery equated with each other. Significance. Our research renders single neuron activity in the left Vim a promising source of inputs to BMIs for restoration of speech faculties for locked-in patients or patients with anarthria or dysarthria to allow them to communicate again. Our characterization of how many neurons are necessary to achieve a certain decoding accuracy is of utmost importance for planning BMI implantation.

Unveiling Code Pre-Trained Models: Investigating Syntax and Semantics Capacities

Code models have made significant advancements in code intelligence by encoding knowledge about programming languages. While previous studies have explored the capabilities of these models in learning code syntax, there has been limited investigation on their ability to understand code semantics. Additionally, existing analyses assume the number of edges between nodes at the abstract syntax tree (AST) is related to syntax distance, and also often require transforming the high-dimensional space of deep learning models to a low-dimensional one, which may introduce inaccuracies. To study how code models represent code syntax and semantics, we conduct a comprehensive analysis of 7 code models, including four representative code pre-trained models (CodeBERT, GraphCodeBERT, CodeT5, and UnixCoder) and three large language models (StarCoder, CodeLlama and CodeT5+). We design four probing tasks to assess the models’ capacities in learning both code syntax and semantics. These probing tasks reconstruct code syntax and semantics structures (AST, CDG, DDG and CFG) in the representation space. These structures are core concepts for code understanding. We also investigate the syntax token role in each token representation and the long dependency between the code tokens. Additionally, we analyze the distribution of attention weights related to code semantic structures. Through extensive analysis, our findings highlight the strengths and limitations of different code models in learning code syntax and semantics. The results demonstrate that these models excel in learning code syntax, successfully capturing the syntax relationships between tokens and the syntax roles of individual tokens. However, their performance in encoding code semantics varies. CodeT5 and CodeBERT demonstrate proficiency in capturing control and data dependencies, while UnixCoder shows weaker performance in this aspect. We do not observe LLMs generally performing much better than pre-trained models. The shallow layers of LLMs perform better than their deep layers. The investigation of attention weights reveals that different attention heads play distinct roles in encoding code semantics. Our research findings emphasize the need for further enhancements in code models to better learn code semantics. This study contributes to the understanding of code models’ abilities in syntax and semantics analysis. Our findings provide guidance for future improvements in code models, facilitating their effective application in various code-related tasks.

Hypergraph-Based Numerical Spiking Neural Membrane Systems with Novel Repartition Protocols.

The classic spiking neural P (SN P) systems abstract the real biological neural network into a simple structure based on graphs, where neurons can only communicate on the plane. This study proposes the hypergraph-based numerical spiking neural membrane (HNSNM) systems with novel repartition protocols. Through the introduction of hypergraphs, the HNSNM systems can characterize the high-order relationships among neurons and extend the traditional neuron structure to high-dimensional nonlinear spaces. The HNSNM systems also abstract two biological mechanisms of synapse creation and pruning, and use plasticity rules with repartition protocols to achieve planar, hierarchical and spatial communications among neurons in hypergraph neuron structures. Through imitating register machines, the Turing universality of the HNSNM systems is proved by using them as number generating and accepting devices. A universal HNSNM system consisting of 41 neurons is constructed to compute arbitrary functions. By solving NP-complete problems using the subset sum problem as an example, the computational efficiency and effectiveness of HNSNM systems are verified.

Age-Invariant Face Recognition Using FaceNet and Multi-task Cascaded Convolutional Networks (MTCNN)

In an era where face recognition technology serves as a cornerstone for security, surveillance, and human-computer interaction, the persistence of age-related variations in facial appearance presents a significant challenge. This research introduces an innovative solution that amalgamates the capabilities of the FaceNet deep learning model with Multi-task Cascaded Convolutional Networks (MTCNN) to achieve precise and robust face recognition across diverse age groups. Leveraging FaceNet's prowess in extracting distinctive features from facial images and mapping them to a high-dimensional feature space for efficient face matching, our system incorporates MTCNN as a pre-processing step to accurately detect and align faces, effectively mitigating age-related changes in facial geometry. Crucially, this novel approach obviates the need for age-specific databases and age group categorization, rendering it a versatile and practical solution for age-invariant face recognition. Rigorous experimentation on benchmark datasets underscores the system's resilience and accuracy across a broad spectrum of age groups, culminating in state-of-the-art results in age-invariant face recognition. The implications of this proposed approach are profound, promising to fortify security measures and enhance user experiences in applications such as access control, personal identification, and customer service, while ensuring dependable and accurate face recognition, irrespective of an individual's age. Key Words: Face recognition, face aging, generative adversarial networks

Real-time prediction of fuel consumption and emissions based on deep autoencoding support vector regression for cylinder pressure-based feedback control of marine diesel engines

Predictive models serving as virtual sensors for online optimization and feedback control of diesel engines is gaining increasing attention. However, existing prediction models fall short in simultaneously achieving high prediction accuracy and fast computational speed. In this paper, a novel machine learning algorithm called deep autoencoding support vector regression (DASVR) was proposed, which combines the powerful non-linear feature extraction capability of artificial neural network (ANN) with the good adaptability of support vector regression (SVR) to low-dimensional input spaces. ANN-based autoencoder is firstly employed to extract features from the original high-dimensional input space, forming a low-dimensional latent variable space. SVR is then employed to perform non-linear mapping between latent variables and target output variables. Experiments were conducted on a 16-cylinder marine diesel engine under different load, rail pressure, and injection timing conditions. Prediction models for fuel consumption, NOx, PM, HC, and PM emissions were established based on experimental data and DASVR algorithm. The maximum error of DASVR-based models for the five desired output variables is less than 3.8 % under different operating conditions. DAVSR-based predictive models outperform conventional ANN-based and SVR-based models in terms of both prediction accuracy and real-time capability, and can theoretically meet the real-time requirement below 3000 r/min.

Computation-Driven Rational Design of Self-Assembled Short Peptides for Catalytic Hydrogen Production.

Self-assembling peptides represent a captivating area of study in nanotechnology and biomaterials. This interest is largely driven by their unique properties and the vast application potential across various fields such as catalytic functions. However, design complexities, including high-dimensional sequence space and structural diversity, pose significant challenges in the study of such systems. In this work, we explored the possibility of self-assembled peptides to catalyze the hydrolysis of hydrosilane for hydrogen production using ab initio calculations and carried out wet-lab experiments to confirm the feasibility of these catalytic reactions under ambient conditions. Further, we delved into the nuanced interplay between sequence, structural conformation, and catalytic activity by combining modeling with experimental techniques such as transmission electron microscopy and nuclear magnetic resonance and proposed a dual mode of the microstructure of the catalytic center. Our results reveal that although research in this area is still at an early stage, the development of self-assembled peptide catalysts for hydrogen production has the potential to provide a more sustainable and efficient alternative to conventional hydrogen production methods. In addition, this work also demonstrates that a computation-driven rational design supplemented by experimental validation is an effective protocol for conducting research on functional self-assembled peptides.

CompleteDT: Point cloud completion with information-perception transformers

In this work, we propose a novel point cloud completion network, called CompleteDT. To fully capture the 3D geometric structure of point clouds, we introduce an Information-Perception Transformer (IPT) that can simultaneously capture local features and global geometric relations. CompleteDT comprises a Feature Encoder, Query Generator, and Query Decoder. Feature Encoder extracts local features from multi-resolution point clouds to capture intricate geometrical structures. Query Generator uses the proposed IPT, utilizing the Point Local Attention (PLA) and Point Global Attention (PGA) modules, to learn local features and global correlations, and generate query features that represent predicted point clouds. The PLA captures local information within local points by adaptively measuring weights of neighboring points, while PGA adapts multi-head self-attention by transforming it into a layer-by-layer form where each head learns global features in a high-dimensional space of different dimensions. By dense connections, the module allows for direct information exchange between each head and facilitates the capture of long global correlations. By combining the strengths of both PLA and PGA, the IPT can fully leverage local and global features to facilitate CompleteDT to complete point clouds. Lastly, the query features undergo refining to generate a complete point cloud through the Query Decoder. Our experimental results demonstrate that CompleteDT outperforms current state-of-the-art methods, effectively learning from incomplete inputs and predicting complete outputs.

Adaptive multi-spectral mimicking with 2D-material nanoresonator networks

Abstract Active nanophotonic materials that can emulate and adapt between many different spectral profiles—with high fidelity and over a broad bandwidth—could have a far-reaching impact, but are challenging to design due to a high-dimensional and complex design space. Here, we show that a metamaterial network of coupled 2D-material nanoresonators in graphene can adaptively match multiple complex absorption spectra via a set of input voltages. To design such networks, we develop a semi-analytical auto-differentiable dipole-coupled model that allows scalable optimization of high-dimensional networks with many elements and voltage signals. As a demonstration of multi-spectral capability, we design a single network capable of mimicking four spectral targets resembling select gases (nitric oxide, nitrogen dioxide, methane, nitrous oxide) with very high fidelity (> 90%). Our results could impact the design of highly reconfigurable optical materials and platforms for applications in sensing, communication and display technology, and signature and thermal management.

Learnable faster kernel-PCA for nonlinear fault detection: Deep autoencoder-based realization

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First, the form and the parameters of the kernel function are usually selected blindly, depending seriously on trial-and-error. As a result, there may be serious performance degradation in case of inappropriate selections. Second, at the online monitoring stage, KPCA has much computational burden and poor real-time performance, because the kernel method requires to leverage all the offline training data. In this work, to deal with the two drawbacks, a learnable faster realization of the conventional KPCA is proposed. The core idea is to parameterize all feasible kernel functions using the novel nonlinear DAE-FE (deep autoencoder based feature extraction) framework and propose DAE-PCA (deep autoencoder based principal component analysis) approach in detail. The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs, which helps to improve the accuracy of fault detection. Furthermore, the online computational efficiency improves by many times compared with the conventional KPCA. Finally, the Tennessee Eastman (TE) process benchmark and wastewater treatment plant (WWTP) benchmark are employed to illustrate the effectiveness of the proposed method, where the average fault detection rates of DAE-PCA are at least 0.27% and 4.69% higher than those of other methods, and its online computational efficiency is faster 90.48% and 24.57% times than that of KPCA respectively.

A Dichotomy for the Dimension of Solenoidal Attractors on High Dimensional Space

A Dichotomy for the Dimension of Solenoidal Attractors on High Dimensional Space

3D Clustering of Gene Expression Data from Systemic Autoinflammatory Diseases Using Self-Organizing Maps (Clust3D)

Background and objectiveSystemic autoinflammatory diseases (SAIDs) are characterized by widespread inflammation, but for most of them there is a lack of specific biomarkers for accurate diagnosis. Although a number of machine learning algorithms have been used to analyze SAID datasets, aiding in the discovery of novel biomarkers, there is a growing recognition of the importance of SAID timeseries clustering, as it can capture the temporal dynamics of gene expression patterns. MethodologyThis paper proposes a novel clustering methodology to efficiently associate three-dimensional data. The algorithm utilizes competitive learning to create a self-organizing neural network and adjust neuron positions in time-dependent and high dimensional feature space in order to assign them as clustering centers. The quantitative evaluation of the clustering was based on well-known clustering indices. Furthermore, a differential expression analysis and classification pipeline was employed to assess the capability of the proposed methodology to extract more accurate pathway-specific genes from its clusters. For that, a comparative analysis was also conducted against a heuristic timeseries clustering method. ResultsThe proposed methodology achieved better overall clustering indices scores and classification metrics using genes derived from its clusters. Notable cases include a threefold increase in the Calinski-Harabasz clustering index, a twofold improvement in the Davies–Bouldin clustering index and a ~60% increase in the classification specificity score. ConclusionA novel clustering methodology was developed and applied on several gene expression timeseries datasets from systemic autoinflammatory diseases, and its ability to efficiently produce well separated clusters compared to existing heuristic methods was demonstrated.

Merging experiment data and simulation data for parameter identification of shaft seal

A parameter identification method which merges experimentally monitored signals and physics-based simulation data is proposed, targeting the identification tasks in shaft seals which are challenging due to the high-dimensional parameter space. Features were extracted from the monitored acoustic emission signals following a proposed cross-timescale analysis routine, and the simulation data were augmented using Kriging surrogate model to obtain a dataset with stratified fidelity. Then, a transferable architecture of convolutional neural network modified for periodical data was proposed, with which part of the parameters trained by simulation data were reserved when training model using acoustic emission data acquired in experiments. Cross validation shows that transfer learning can effectively improve the performance, provided data augmentation and proper transfer mode. In conclusion, the study provides an effective parameter identification method which merges the simulation data which carry the physical knowledge and the experiment data which carry directly monitored results.

Anomaly detection using large-scale multimode industrial data: An integration method of nonstationary kernel and autoencoder

Kernel methods and neural networks (NNs) are two mainstream nonlinear data modeling methods and have been widely applied to industrial process monitoring. However, they both present imperfect properties, so the relevant applications are limited. On the one hand, kernels are not so reconstructable, scalable, and robust to hyperparameters that they suffer performance degradation for large-scale data modeling and monitoring. On the other hand, the high-dimensional parameter space of NNs that is sorted to parameter initialization presents severe anomaly detection performance inconsistency, which makes the industry cautious about using NNs. Motivated by these facts, we propose to integrate kernels and NNs, forming a new model structure that is scalable, reconstructable, and performance-consistent. Specifically, a novel autoencoder-based nonstationary pattern selection kernel (AE-NPSK) is proposed by (1) selecting from the training set the critical edges and interior data as the centers of the radial basis functions in the hidden layers and (2) adaptively adjusting the kernel width in the training procedure. Also, the new NN has strong performance consistency, which facilitates the search for optimal parameters. Finally, we test the performance of the proposed method on the challenging multimode processes. The results validate the efficacy of the proposed method.

A gray box framework that optimizes a white box logical model using a black box optimizer for simulating cellular responses to perturbations.

Predicting cellular responses to perturbations requires interpretable insights into molecular regulatory dynamics to perform reliable cell fate control, despite the confounding non-linearity of the underlying interactions. There is a growing interest in developing machine learning-based perturbation response prediction models to handle the non-linearity of perturbation data, but their interpretation in terms of molecular regulatory dynamics remains a challenge. Alternatively, for meaningful biological interpretation, logical network models such as Boolean networks are widely used in systems biology to represent intracellular molecular regulation. However, determining the appropriate regulatory logic of large-scale networks remains an obstacle due to the high-dimensional and discontinuous search space. To tackle these challenges, we present a scalable derivative-free optimizer trained by meta-reinforcement learning for Boolean network models. The logical network model optimized by the trained optimizer successfully predicts anti-cancer drug responses of cancer cell lines, while simultaneously providing insight into their underlying molecular regulatory mechanisms.

Model predictive manipulation of compliant objects with multi-objective optimizer and adversarial network for occlusion compensation

Background:The manipulation of compliant objects by robotic systems remains a challenging task, largely due to their variable shapes and the complex, high-dimensional nature of their interaction dynamics. Traditional robotic manipulation strategies struggle with the accurate modeling and control necessary to handle such materials, especially in the presence of visual occlusions that frequently occur in dynamic environments. Meanwhile, for most unstructured environments, robots are required to have autonomous interactions with their surroundings. Methods:To solve the shape manipulation of compliant objects in an unstructured environment, we begin by exploring the regression-based algorithm of representing the high-dimensional configuration space of deformable objects in a compressed form that enables efficient and effective manipulation. Simultaneously, we address the issue of visual occlusions by proposing the integration of an adversarial network, enabling guiding the shaping task even with partial observations of the object. Afterwards, we propose a receding-time estimator to coordinate the robot action with the computed shape features while satisfying various performance criteria. Finally, model predictive controller is utilized to compute the robot’s shaping motions subject to safety constraints. Detailed experiments are presented to evaluate the proposed manipulation framework. Significant findings:Our MPC framework utilizes the compressed representation and occlusion-compensated information to predict the object’s behavior, while the multi-objective optimizer ensures that the resulting control actions meet multiple performance criteria. Through rigorous experimental validation, our approach demonstrates superior manipulation capabilities in scenarios with visual obstructions, outperforming existing methods in terms of precision and operational reliability. The findings highlight the potential of our integrated approach to significantly enhance the manipulation of compliant objects in real-world robotic applications.

Electrothermal Coupling Methodologies and Their Influence on the Optimization of Aircraft Electric Motors

This work presents a fully coupled electrothermal motor analysis and optimization framework, where the motor’s electromagnetic performance depends on its temperature distribution, and the temperature distribution simultaneously depends on its electromagnetic performance. Notably, we analytically compute derivatives through this nonlinear, multidisciplinary analysis using coupled adjoints, which enables the exploration of high-dimensional design spaces. We demonstrate the framework on a series of optimization problems that investigate the effect of feedback coupling and serve to highlight the framework’s utility and flexibility. Furthermore, our results indicate that modeling the motor’s electrothermal coupling is critical to accurate performance prediction. We show that designs optimized using a feedforward-coupled model are found to be either infeasible or nonoptimal under the fully coupled feedback analysis; both conditions are unacceptable for aircraft applications, in which performance is critical.