Locally Linear Embedding Research Articles

Trade-offs in the latent representation of microstructure evolution

Characterizing and quantifying microstructure evolution is critical to forming quantitative relationships between material processing conditions, resulting microstructure, and observed properties. Machine-learning methods are increasingly accelerating the development of these relationships by treating microstructure evolution as a pattern recognition problem, discovering relationships explicitly or implicitly. These methods often rely on identifying low-dimensional microstructural fingerprints as latent variables. However, using inappropriate latent variables can lead to challenges in learning meaningful relationships. In this work, we survey and discuss the ability of various linear and nonlinear dimensionality reduction methods including principal component analysis, autoencoders, and diffusion maps to quantify and characterize the learned latent space microstructural representations and their time evolution. We characterize latent spaces by their ability to represent high-dimensional microstructural data in terms of compression achieved as a function of the number of latent dimensions required to represent the data accurately, their accuracy based on their reconstruction performance, and the smoothness of the microstructural trajectories in latent dimension. We quantify these metrics for common microstructure evolution problems in material science including spinodal decomposition of a binary metallic alloy, thin film deposition of a binary metallic alloy, dendritic growth, and grain growth in a polycrystal. This study provides considerations and guidelines for choosing dimensionality reduction methods when considering materials problems that involve high dimensional data and a variety of features over a range of lengths and time scales.

Abstract 11993: Integrative Analysis of Single-Cell Transcriptomics and Polygenic Risk Scores Uncovers Vascular Smooth Muscle Cell Heterogeneity in Human Aortic Aneurisms

Background: Atherosclerosis is accompanied by distinct vascular phenotypes that underly its initiation and progression, though their contribution to its pathogenesis is currently unknown. By integrating polygenetic risk profiles from genome-wide association studies (GWAS) of vascular disease with single-cell transcriptional analyses, it is possible to implicate causal cellular subpopulations and functional states. Hypothesis: We sought to build a more precise understanding of the cellular mechanisms underlying vascular disease in humans by combining single-nuclear RNA-sequencing (snRNA-seq) data from vascular tissue with known polygenic risk loci associated with vascular disease. Methods: We performed snRNA-seq on five flash-frozen human aortas, implementing a novel dissociation method to isolate and sequence 14,228 quality-controlled nuclei from three thoracic aortic aneurysms and two samples without known aortopathy, obtained from patients aged 37-70 years. Cell types were defined using canonical gene markers, and non-linear dimensional reduction via tSNE was employed to identify transcriptional sub-phenotypes. The identified pathological programs were validated using polygenic risk and by integrating GWAS data from other vascular single-nuclear transcriptomic datasets. Results: Our analysis revealed ten distinct clusters representing all major vascular cell populations, with vascular smooth muscle cells (VSMCs) and myofibroblasts emerging as the most relevant cell types in relation to vascular disease based on polygenic risk. Within the VSMC population, two distinct subpopulations exhibited differential expression of genes related to the extracellular matrix, contractility, and proliferation. RNA-trajectory analysis further uncovered a continuum of gene expression linking VSMC1, VSMC2, and myofibroblast transcriptional clusters. Conclusions: This study validates novel methods for identifying pathologic VSMC states associated with vascular disease and implicates phenotypic switching as a pathogenic mechanism. We highlight genes and pathways associated with endothelial cell and VSMC state transitions that are enriched in GWAS of coronary artery disease (CAD).

A software defect prediction method based on learnable three-line hybrid feature fusion

Software defect prediction (SDP) plays a crucial role in ensuring the security and quality of software systems. However, it faces challenges posed by high-dimensional features present in software defect datasets and the limited effectiveness of traditional nonlinear dimensionality reduction methods in extracting essential feature information. To address these issues, we propose a novel approach called learnable three-line hybrid feature fusion (LTHFFA), which incorporates the principle of three-line hybrid breeding into feature fusion for the first time. In this method, three distinct dimensionality reduction techniques are initially employed to obtain three separate sets of features. Subsequently, a learnable weight factor feature fusion method is proposed to facilitate automatically learn and dynamically update of feature weights. By integrating the three feature sets based on the principle of three-line hybrid breeding, we derive learnable three-line hybrid fusion features. These features are then utilized in the context of software defect prediction. Experimental results demonstrate the superior performance of LTHFFA compared to nine other dimensionality reduction methods across seventeen publicly available software defect datasets. LTHFFA exhibits the ability to effectively integrate multiple feature sets, reduce feature redundancy, and enhance predictive accuracy. Moreover, statistical analysis using Friedman ranking and Holm's post-hoc test confirms the significant advantage of LTHFFA over alternative dimensionality reduction methods.

Deep Clustering and Visualization for End-to-End High-Dimensional Data Analysis.

High-dimensional data analysis for exploration and discovery includes two fundamental tasks: deep clustering and data visualization. When these two associated tasks are done separately, as is often the case thus far, disagreements can occur among the tasks in terms of geometry preservation. Namely, the clustering process is often accompanied by the corruption of the geometric structure, whereas visualization aims to preserve the data geometry for better interpretation. Therefore, how to achieve deep clustering and data visualization in an end-to-end unified framework is an important but challenging problem. In this article, we propose a novel neural network-based method, called deep clustering and visualization (DCV), to accomplish the two associated tasks end-to-end to resolve their disagreements. The DCV framework consists of two nonlinear dimensionality reduction (NLDR) transformations: 1) one from the input data space to latent feature space for clustering and 2) the other from the latent feature space to the final 2-D space for visualization. Importantly, the first NLDR transformation is mainly optimized by one Clustering Loss, allowing arbitrary corruption of the geometric structure for better clustering, while the second NLDR transformation is optimized by one Geometry-Preserving Loss to recover the corrupted geometry for better visualization. Extensive comparative results show that the DCV framework outperforms other leading clustering-visualization algorithms in terms of both quantitative evaluation metrics and qualitative visualization.

Research on intelligent clearing of weeds in wheat fields using spectral imaging and machine learning

The intelligent management of weed clearing can improve wheat yield and reduce the use of pesticides. In this paper, our contribution is to propose a method for wheat and weed recognition based on multispectral imaging and Membrane Search Algorithm Support Vector Machine (MSA-SVM), which is the basis for intelligent weed clearing. A spectral data acquisition system is set up in the laboratory. Then, a total of 700 groups of wheat and weed spectral data are collected. The classical SVM based on spectral data is applied to identify weeds to study the classification performance of wheat and weeds in different bands. The Membrane Search Algorithm (MSA) algorithm proposed by us was used for SVM parameters optimization, and the dimension reduction algorithm was adopted to reduce the interference of redundant information. After local linear embedding (LLE) dimensionality reduction of spectral data, MSA-SVM has the highest average recognition accuracy for weeds and wheat, which is 91.00%. The experimental results show that our research can distinguish wheat from weeds, which is of great significance for the development of smart agriculture.

Research on Intelligent Recognition Model of English Translation Based on Nonlinear Dimensionality Reduction IC Features

Abstract This paper first aligns English translations with other language texts to build an English translation corpus, then trains the model for the pending translations to obtain the final target model, then enumerates all possible combinations of source language phrases and target language phrases, and filters out unsatisfied phrase translation pairs to achieve phrase extraction. And the translation model is non-linearly dimensionalized to reduce the complexity of the operation process. Finally, the dimensionality reduction effect of the data and the effect of the model translation are analyzed. The results show that the cumulative contribution rate of the t-SNE algorithm is over 95%, which can guarantee no loss of translation information. The translation accuracy of this paper’s algorithm on each language block is basically 85%-90%, the recall rate is above 85%, and the F-value is above 82%. It indicates that the method in this paper can be well adapted to the requirements of intelligent recognition of English translation.

Nonlinear dimensionality reduction methods for potentiometric multisensor systems data analysis

AbstractElectrochemical multisensor systems were proven to be a very perspective research direction in modern analytical chemistry. The multisensor approach assumes an employment of cross‐sensitive chemical sensors in combination with multivariate data processing methods. Dimensionality reduction of the data obtained from multisensor systems is a very important step and it is mostly based on the traditional tools of chemometrics, such as Principal Component Analysis (PCA). In case of chemically complex samples, the response of multisensor systems may have a complex nonlinear nature and the use of linear modelling methods does not seem optimal. However, the potential of nonlinear dimensionality reduction methods in the processing of multisensor data has not yet been systematically studied. In this report we aim to fill this gap and assess the performance of various nonlinear dimensionality reduction tools: Isomap, Self‐Organizing Kohonen Maps, and Autoencoder. These methods were explored using three datasets from potentiometric multisensor systems obtained in various real applications. It was shown that nonlinear dimensionality reduction methods give the possibility to obtain additional and more detailed information about the analyzed objects/processes compared to PCA. However, calculation time for nonlinear dimensionality reduction methods essentially exceeds that for PCA, and it can be a limiting factor for application of such algorithms.

Predicting cognitive decline in a low-dimensional representation of brain morphology

Identifying early signs of neurodegeneration due to Alzheimer’s disease (AD) is a necessary first step towards preventing cognitive decline. Individual cortical thickness measures, available after processing anatomical magnetic resonance imaging (MRI), are sensitive markers of neurodegeneration. However, normal aging cortical decline and high inter-individual variability complicate the comparison and statistical determination of the impact of AD-related neurodegeneration on trajectories. In this paper, we computed trajectories in a 2D representation of a 62-dimensional manifold of individual cortical thickness measures. To compute this representation, we used a novel, nonlinear dimension reduction algorithm called Uniform Manifold Approximation and Projection (UMAP). We trained two embeddings, one on cortical thickness measurements of 6237 cognitively healthy participants aged 18–100 years old and the other on 233 mild cognitively impaired (MCI) and AD participants from the longitudinal database, the Alzheimer’s Disease Neuroimaging Initiative database (ADNI). Each participant had multiple visits (n ge 2), one year apart. The first embedding’s principal axis was shown to be positively associated (r = 0.65) with participants’ age. Data from ADNI is projected into these 2D spaces. After clustering the data, average trajectories between clusters were shown to be significantly different between MCI and AD subjects. Moreover, some clusters and trajectories between clusters were more prone to host AD subjects. This study was able to differentiate AD and MCI subjects based on their trajectory in a 2D space with an AUC of 0.80 with 10-fold cross-validation.

A novel untrained SSVEP-EEG feature enhancement method using canonical correlation analysis and underdamped second-order stochastic resonance.

Compared with the light-flashing paradigm, the ring-shaped motion checkerboard patterns avoid uncomfortable flicker or brightness modulation, improving the practical interactivity of brain-computer interface (BCI) applications. However, due to fewer harmonic responses and more concentrated frequency energy elicited by the ring-shaped checkerboard patterns, the mainstream untrained algorithms such as canonical correlation analysis (CCA) and filter bank canonical correlation analysis (FBCCA) methods have poor recognition performance and low information transmission rate (ITR). To address this issue, a novel untrained SSVEP-EEG feature enhancement method using CCA and underdamped second-order stochastic resonance (USSR) is proposed to extract electroencephalogram (EEG) features. In contrast to typical unsupervised dimensionality reduction methods such as common average reference (CAR), principal component analysis (PCA), multidimensional scaling (MDS), and locally linear embedding (LLE), CCA exhibits higher adaptability for SSVEP rhythm components. This study recruits 42 subjects to evaluate the proposed method and experimental results show that the untrained method can achieve higher detection accuracy and robustness. This untrained method provides the possibility of applying a nonlinear model from one-dimensional signals to multi-dimensional signals.

A 3D Chromosome Structure Reconstruction method with High Resolution Hi-C Data using Nonlinear Dimensionality Reduction and Divide-and-conquer strategy.

Chromosomes are fundamental components of genetic material, and their structural characteristics play an essential role in the regulation of gene expression. The advent of high-resolution Hi-C data has enabled scientists to explore the three-dimensional structure of chromosomes. However, most of the currently available methods for reconstructing chromosome structures are unable to achieve high resolutions, such as 5 Kilobase (KB). In this study, we present NeRV-3D, an innovative method that utilizes a nonlinear dimensionality reduction visualization algorithm to reconstruct 3D chromosome structures at low resolutions. Additionally, we introduce NeRV-3D-DC, which employs a divide-and-conquer technique to reconstruct and visualize 3D chromosome structures at high resolutions. Our results demonstrate that both NeRV-3D and NeRV-3D-DC outperform existing methods in terms of 3D visualization effects and evaluation metrics on simulated and actual Hi-C datasets. The implementation of NeRV-3D-DC can be found at https://github.com/ghaiyan/NeRV-3D-DC.

Beam SNR Prediction Using Channel Charting

We consider a machine learning approach for beam handover in mmWave 5G New Radio systems, in which User Equipments (UEs) perform autonomous beam selection, conditioned on a used Base Station (BS) beam. We develop a network-centric approach for predicting beam Signal-to-Noise Ratio (SNR) from Channel State Information (CSI) features measured at the BS, which consists of two phases; offline and online. In the offline training phase, we construct CSI features and dimensionality-reduced Channel Charts (CC). We annotate the CCs with per-beam SNRs for different combinations of a BS beam and the corresponding best UE beam, and train models to predict SNR from CSI features for different BS/UE beam combinations. In the online phase, we predict SNRs of beam combinations not being used at the moment. We develop a low complexity out-of-sample algorithm for dimensionality reduction in the online phase. We consider <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -nearest neighbors, Gaussian process regression, and neural network-based predictions. To evaluate the efficacy of the proposed framework, we perform simulations for a street segment with synthetically generated CSI. We investigate the complexity-accuracy trade-off for different dimensionality reduction techniques and different predictors. Our results reveal that nonlinear dimensionality reduction of CSI features with neural network prediction shows the best performance, and the performance of the best CSI-based prediction method is comparable to prediction based on using known physical location.

Epitranscriptomic subtyping, visualization, and denoising by global motif visualization

Advances in sequencing technologies have empowered epitranscriptomic profiling at the single-base resolution. Putative RNA modification sites identified from a single high-throughput experiment may contain one type of modification deposited by different writers or different types of modifications, along with false positive results because of the challenge of distinguishing signals from noise. However, current tools are insufficient for subtyping, visualization, and denoising these signals. Here, we present iMVP, which is an interactive framework for epitranscriptomic analysis with a nonlinear dimension reduction technique and density-based partition. As exemplified by the analysis of mRNA m5C and ModTect variant data, we show that iMVP allows the identification of previously unknown RNA modification motifs and writers and the discovery of false positives that are undetectable by traditional methods. Using putative m6A/m6Am sites called from 8 profiling approaches, we illustrate that iMVP enables comprehensive comparison of different approaches and advances our understanding of the difference and pattern of true positives and artifacts in these methods. Finally, we demonstrate the ability of iMVP to analyze an extremely large human A-to-I editing dataset that was previously unmanageable. Our work provides a general framework for the visualization and interpretation of epitranscriptomic data.

Self-supervised deep clustering of single-cell RNA-seq data to hierarchically detect rare cell populations.

Single-cell RNA sequencing (scRNA-seq) is a widely used technique for characterizing individual cells and studying gene expression at the single-cell level. Clustering plays a vital role in grouping similar cells together for various downstream analyses. However, the high sparsity and dimensionality of large scRNA-seq data pose challenges to clustering performance. Although several deep learning-based clustering algorithms have been proposed, most existing clustering methods have limitations in capturing the precise distribution types of the data or fully utilizing the relationships between cells, leaving a considerable scope for improving the clustering performance, particularly in detecting rare cell populations from large scRNA-seq data. We introduce DeepScena, a novel single-cell hierarchical clustering tool that fully incorporates nonlinear dimension reduction, negative binomial-based convolutional autoencoder for data fitting, and a self-supervision model for cell similarity enhancement. In comprehensive evaluation using multiple large-scale scRNA-seq datasets, DeepScena consistently outperformed seven popular clustering tools in terms of accuracy. Notably, DeepScena exhibits high proficiency in identifying rare cell populations within large datasets that contain large numbers of clusters. When applied to scRNA-seq data of multiple myeloma cells, DeepScena successfully identified not only previously labeled large cell types but also subpopulations in CD14 monocytes, T cells and natural killer cells, respectively.

Transcriptomics and biochemical evidence of trigonelline ameliorating learning and memory decline in the senescence-accelerated mouse prone 8 (SAMP8) model by suppressing proinflammatory cytokines and elevating neurotransmitter release

In recent years, exploring natural compounds with functional properties to ameliorate aging-associated cognitive decline has become a research priority to ensure healthy aging. In the present study, we investigated the effects of Trigonelline (TG), a plant alkaloid, on memory and spatial learning in 16-week-old senescence-accelerated mouse model SAMP8 using an integrated approach for cognitive and molecular biology aspects. After 30 days of oral administration of TG at the dose of 5 mg/kg/day, the mice were trained in Morris Water Maze task. TG-treated SAMP8 mice exhibited significant improvement in the parameters of escape latency, distance moved, and annulus crossing index. Next, we performed a whole-genome transcriptome profiling of the mouse hippocampus using microarrays. Gene ontology analyses showed that a wide range of biological processes, including nervous system development, mitochondrial function, ATP synthesis, and several signaling pathways related to inflammation, autophagy, and neurotransmitter release, were significantly enriched in TG-treated SAMP8 compared to nontreated. Further, a nonlinear dimensionality reduction technique, Uniform Manifold Approximation and Projection (UMAP), was applied to identify clusters of functions that revealed TG primarily regulated pathways related to inflammation, followed by those involved in neurotransmitter release. In addition, a protein–protein interaction network analysis indicated that TG may exert its biological effects through negatively modulating Traf6-mediated NF-κB activation. Finally, ELISA test showed that TG treatment significantly decreased proinflammatory cytokines- TNFα and IL6 and increased neurotransmitters- dopamine, noradrenaline, and serotonin in mouse hippocampus. Altogether, our integrated bio-cognitive approach highlights the potential of TG in alleviating age-related memory and spatial impairment.

Absence of enterotypes in the human gut microbiomes reanalyzed with non-linear dimensionality reduction methods.

Enterotypes of the human gut microbiome have been proposed to be a powerful prognostic tool to evaluate the correlation between lifestyle, nutrition, and disease. However, the number of enterotypes suggested in the literature ranged from two to four. The growth of available metagenome data and the use of exact, non-linear methods of data analysis challenges the very concept of clusters in the multidimensional space of bacterial microbiomes. Using several published human gut microbiome datasets of variable 16S rRNA regions, we demonstrate the presence of a lower-dimensional structure in the microbiome space, with high-dimensional data concentrated near a low-dimensional non-linear submanifold, but the absence of distinct and stable clusters that could represent enterotypes. This observation is robust with regard to diverse combinations of dimensionality reduction techniques and clustering algorithms.

Abnormal higher-order network interactions in Parkinson's disease visual hallucinations.

Visual hallucinations in Parkinson's disease can be viewed from a systems-level perspective, whereby dysfunctional communication between brain networks responsible for perception predisposes a person to hallucinate. To this end, abnormal functional interactions between higher-order and primary sensory networks have been implicated in the pathophysiology of visual hallucinations in Parkinson's disease, however the precise signatures remain to be determined. Dimensionality reduction techniques offer a novel means for simplifying the interpretation of multidimensional brain imaging data, identifying hierarchical patterns in the data that are driven by both within- and between-functional network changes. Here, we applied two complementary non-linear dimensionality reduction techniques-diffusion-map embedding and t-distributed stochastic neighbour embedding (t-SNE)-to resting state functional MRI data, in order to characterize the altered functional hierarchy associated with susceptibility to visual hallucinations. Our study involved 77 people with Parkinson's disease (31 with hallucinations; 46 without hallucinations) and 19 age-matched healthy control subjects. In patients with visual hallucinations, we found compression of the unimodal-heteromodal gradient consistent with increased functional integration between sensory and higher order networks. This was mirrored in a traditional functional connectivity analysis, which showed increased connectivity between the visual and default mode networks in the hallucinating group. Together, these results suggest a route by which higher-order regions may have excessive influence over earlier sensory processes, as proposed by theoretical models of hallucinations across disorders. By contrast, the t-SNE analysis identified distinct alterations in prefrontal regions, suggesting an additional layer of complexity in the functional brain network abnormalities implicated in hallucinations, which was not apparent in traditional functional connectivity analyses. Together, the results confirm abnormal brain organization associated with the hallucinating phenotype in Parkinson's disease and highlight the utility of applying convergent dimensionality reduction techniques to investigate complex clinical symptoms. In addition, the patterns we describe in Parkinson's disease converge with those seen in other conditions, suggesting that reduced hierarchical differentiation across sensory-perceptual systems may be a common transdiagnostic vulnerability in neuropsychiatric disorders with perceptual disturbances.

Extraction and Joint Method of PV–Load Typical Scenes Considering Temporal and Spatial Distribution Characteristics

Regarding the generation and integration of typical scenes of PV and loads in urban photovoltaic distribution networks, as well as the insufficient consideration of the spatiotemporal correlation between PV and loads, this paper proposes a typical scene extraction method based on local linear embedding, kernel density estimation, and a joint PV–load typical scene extraction method based on the FP-growth algorithm. Firstly, the daily operation matrices of PV and load are constructed by using the historical operation data of PV and load. Then, the typical scenes are extracted by the dimensionality reduction of local linear embedding and the kernel density estimation method. Finally, the strong association rules of PV–meteorological conditions and load–meteorological conditions are mined based on the FP-growth algorithm, respectively. The association of PV–load typical daily operation scenarios is completed using meteorological conditions as a link. This experiment involved one year of operation data of a distribution network containing PV in Qingyuan, Guangdong Province. The typical scene extraction joint method, Latin hypercube sampling method, and k-means clustering-based scene generation method proposed in this paper are used for comparison, respectively. The results show that compared to the other two scenario generation methods, the error between the typical scenario obtained by this method and the actual operating scenario of the distribution network is smaller. The extracted typical PV and load scenarios can better fit the actual PV and load operation scenarios, which have more reference value for the operation planning of actual distribution networks containing PV.

MANAGEMENT OF FLOOD AND SEPARATING DAMAGE FROM ENVIRONMENTAL EFFECTS USING BAYESIAN CONVOLUTIONAL NEURAL NETWORK

&lt;p&gt;Flood management is the act of determining the frequency, magnitude, and duration of flood episodes based on the elements of a river basin that may be monitored. Floods endanger human lives and inflict significant property damage. It is essential for creating suitable flood risk management plans, lowering flood dangers, and evacuating people from flood-prone locations. Hydrodynamic methods for managing floods may be replaced with deep learning. Existing methods, however, concentrate on employing CNNs or RNNs to capture either the spatial or temporal flood patterns. Despite several advancements in flood control technology, less focus has been placed on minimising the damage that these systems do to the environment in order to boost their dependability and effectiveness. When the data is skewed, CNNs might overfit. We demonstrate how automated regularisation and uncertainty quantification allows Bayesian-CNN to get beyond these drawbacks. We have created a unique method to make use of the uncertainties that the Bayesian-CNN provides, which greatly improves performance on a big portion of the test data (around a 6% increase in accuracy on 77% of test data). By projecting the data into a low-dimensional space using a nonlinear dimensionality reduction approach, we also provide an entirely novel rationale for the uncertainty. This dimensionality reduction makes it possible to visualize the test data for interpretation and displays the data's structure in a low-dimensional feature space. This paper discusses and makes use of uncertainties for flood control while demonstrating the benefits of Bayesian-CNN over state-of-the-art technology. As a consequence, the Bayesian-CNN obtains 95.7% F1-score, 99.3% F1-score, 98.5% precision, and 98.3% recall.&lt;/p&gt;&#x0D;

Laplacian-based Cluster-Contractive t-SNE for High-Dimensional Data Visualization

Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces to extract hidden and useful information or facilitate visual understanding and interpretation of the data. However, few of them take into consideration the potential cluster information contained implicitly in the high-dimensional data. In this article, we propose Lap tSNE, a new graph-layout nonlinear dimensionality reduction method based on t-SNE, one of the best techniques for visualizing high-dimensional data as 2D scatter plots. Specifically, Lap tSNE leverages the eigenvalue information of the graph Laplacian to shrink the potential clusters in the low-dimensional embedding when learning to preserve the local and global structure from high-dimensional space to low-dimensional space. It is nontrivial to solve the proposed model because the eigenvalues of normalized symmetric Laplacian are functions of the decision variable. We provide a majorization-minimization algorithm with convergence guarantee to solve the optimization problem of Lap tSNE and show how to calculate the gradient analytically, which may be of broad interest when considering optimization with Laplacian-composited objective. We evaluate our method by a formal comparison with state-of-the-art methods on seven benchmark datasets, both visually and via established quantitative measurements. The results demonstrate the superiority of our method over baselines such as t-SNE and UMAP. We also provide out-of-sample extension, large-scale extension, and mini-batch extension for our Lap tSNE to facilitate dimensionality reduction in various scenarios.

Reduced‐order modeling framework using two‐level neural networks

AbstractEstablished reduced‐order modeling (ROM) methods, for instance, Galerkin‐projection, approximate the solution by linearly projecting high‐dimensional spaces to a lower‐dimensional space spanned by the reduced basis. However, the accuracy of these methods may be insufficient for complex and multiscale simulations due to the restriction to a linear space. Alternatively, autoencoders (AEs) can be used for nonlinear dimensionality reduction. We combine nonlinear dimensionality reduction techniques with time series prediction to build data‐driven ROMs. The presented framework consists of two‐level neural networks. The high‐dimensional space is nonlinearly compressed in the first level using the encoder function of the AE. Subsequently, the temporal evolution of the latent vector is predicted in the second level. The original solution can be easily reconstructed using the decoder function of the AE. In comparison with the projection‐based ROMs, for example, proper orthogonal decomposition (POD) with Galerkin projection, this framework allows naturally to include parameters in the prediction without nonlinear interpolation of the linear basis. We demonstrate the framework on a two‐dimensional flow field simulation around circular bodies parameterized with the inlet fluid velocity.