Nonlinear Dimensionality Reduction Technique Research Articles

Emission line predictions for mock galaxy catalogues: a new differentiable and empirical mapping from DESI

Abstract We present a simple, differentiable method for predicting emission line strengths from rest-frame optical continua using an empirically-determined mapping. Extensive work has been done to develop mock galaxy catalogues that include robust predictions for galaxy photometry, but reliably predicting the strengths of emission lines has remained challenging. Our new mapping is a simple neural network implemented using the JAX Python automatic differentiation library. It is trained on Dark Energy Spectroscopic Instrument Early Release data to predict the equivalent widths (EWs) of the eight brightest optical emission lines (including Hα, Hβ, [O II], and [O III]) from a galaxy’s rest-frame optical continuum. The predicted EW distributions are consistent with the observed ones when noise is accounted for, and we find Spearman’s rank correlation coefficient ρs > 0.87 between predictions and observations for most lines. Using a non-linear dimensionality reduction technique (UMAP), we show that this is true for galaxies across the full range of observed spectral energy distributions. In addition, we find that adding measurement uncertainties to the predicted line strengths is essential for reproducing the distribution of observed line-ratios in the BPT diagram. Our trained network can easily be incorporated into a differentiable stellar population synthesis pipeline without hindering differentiability or scalability with GPUs. A synthetic catalogue generated with such a pipeline can be used to characterise and account for biases in the spectroscopic training sets used for training and calibration of photo-z’s, improving the modelling of systematic incompleteness for the Rubin Observatory LSST and other surveys.

Fusion of linear and non-linear dimensionality reduction techniques for feature reduction in LSTM-based Intrusion Detection System

Securing networks is becoming increasingly crucial due to the widespread use of information technology. Intrusion Detection System (IDS) plays a crucial role in network security by detecting potential security threats in real-time. In order to create effective IDS, Deep Learning (DL) techniques like Auto Encoder (AE) and Long Short-Term Memory (LSTM) have been widely used. However, the high dimensionality and complexity of network traffic data make it challenging to extract meaningful information. The paper proposes a fusion-based approach that combines AE and Principal Component Analysis (PCA) techniques for dimensionality reduction in IDS. The proposed approach aims to capture both linear and non-linear relationships between features while reducing the dimensionality of the input data. NSL-KDD, UNSW-NB15, CIC-IDS-2017, and MSCAD datasets are used to evaluate this proposed method. The proposed approach has improved accuracy compared to the existing AE+LSTM-based approach by 3% for NSL-KDD and around 1% for UNSW-NB15 and CIC-IDS-2017, while the proposed approach gives comparable results for the MSCAD dataset. The Wilcoxon signed-rank test has been applied to confirm the statistical significance of the result.

Bioclimatic similarity between species locations and their environment revealed by dimensionality reduction analysis

Species distribution modeling is an active research topic with applications in conservation management, pest risk assessment, and population ecology. Several machine-learning methods have been applied to estimate species distribution. Non-linear dimensionality reduction techniques aim to preserve the similarity among objects at a reduced dimension for visualization, clustering, and feature selection. We propose a framework that uses Uniform Manifold Approximation and Projection (UMAP) to analyze bioclimatic variables associated with environmental (background) and species samples. Our objective was to identify geographic areas similar to those inhabited by the species. We hypothesize that the similarity between species locations and their environment in the reduced dimension will reflect similarity in the multivariate bioclimatic space. We estimated the probability of background points near a species point utilizing the latent nearest neighbor distance distribution. We tested this procedure with ten insect pest species of global importance and found that UMAP was able to generate a gradient of similarity between geographic areas and species occurrence. We also found that background-species latent distance tends to have a convergent non-linear relationship with the mean value of bioclimatic variables, thus supporting our key assumption. The performance of UMAP as a binary classifier and comparison with MaxEnt supports its use in modeling of species distribution. Potential applications are discussed for multi-species and multi-scenario analysis, as well as projection to new regions.

Non-linear dimension reduction in factor-augmented vector autoregressions

This paper introduces non-linear dimension reduction in factor-augmented vector autoregressions to analyze the effects of different economic shocks. I argue that controlling for non-linearities between a large-dimensional dataset and the latent factors is particularly useful during turbulent times of the business cycle. In simulations, I show that non-linear dimension reduction techniques yield good forecasting performance, especially when data is highly volatile. In an empirical application, I identify a monetary policy as well as an uncertainty shock excluding and including observations of the COVID-19 pandemic. Those two applications suggest that the non-linear FAVAR approaches are capable of dealing with the large outliers caused by the COVID-19 pandemic and yield reliable results in both scenarios.

Information maximization-based clustering of histopathology images using deep learning

Pancreatic cancer is one of the most adverse diseases and it is very difficult to treat because the cancer cells formed in the pancreas intertwine themselves with nearby blood vessels and connective tissue. Hence, the surgical procedure of treatment becomes complicated and it does not always lead to a cure. Histopathological diagnosis is the usual approach for cancer diagnosis. However, the pancreas remains so deep inside the body that experts sometimes struggle to detect cancer in it. Computer-aided diagnosis can come to the aid of pathologists in this scenario. It assists experts by supporting their diagnostic decisions. In this research, we carried out a deep learning-based approach to analyze histopathology images. We collected whole-slide images of KPC mice to implement this work. The pancreatic abnormalities observed in KPC mice develop similar histological features to human beings. We created random patches from whole-slide images. Then, a convolutional autoencoder framework was used to embed these patches into an integrated latent space. We applied ‘information maximization’, a deep learning clustering technique to cluster the identical patches in an unsupervised manner since our dataset does not have annotation. Moreover, Uniform manifold approximation and projection, a nonlinear dimension reduction technique was utilized to visualize the embedded patches in a 2-dimensional space. Finally, we calculated a few internal cluster validation metrics to determine the optimal cluster set. Our work concentrated on patch-based anomaly detection in the whole slide histopathology images of KPC mice.

Predicting Bordeaux red wine origins and vintages from raw gas chromatograms

Connecting chemical properties to various wine characteristics is of great interest to the science of olfaction as well as the wine industry. We explored whether Bordeaux wine chemical identities and vintages (harvest year) can be inferred from a common and affordable chemical analysis, namely, a combination of gas chromatography (GC) and electron ionization mass spectrometry. Using 12 vintages (within the 1990–2007 range) from 7 estates of the Bordeaux region, we report that, remarkably, nonlinear dimensionality reduction techniques applied to raw gas chromatograms recover the geography of the Bordeaux region. Using machine learning, we found that we can not only recover the estate perfectly from gas chromatograms, but also the vintage with up to 50% accuracy. Interestingly, we observed that the entire chromatogram is informative with respect to geographic location and age, thus suggesting that the chemical identity of a wine is not defined by just a few molecules but is distributed over a large chemical spectrum. This study demonstrates the remarkable potential of GC analysis to explore fundamental questions about the origin and age of wine.

Comparison of dimensionality reduction techniques for multi-variable spatiotemporal flow fields

In the field of fluid mechanics, it is a potential consensus that nonlinear dimensionality reduction (DR) techniques outperform linear methods. However, this conclusion has been obtained based on simple fluid phenomena and an incomplete evaluation system of dimensionality reduction algorithms. In this study, we use an improved evaluation system of DR methods to compare and evaluate the performance of four DR methods, including two linear techniques: Principal Component Analysis (PCA) and Independent Component Analysis (ICA), and two non-linear techniques: Isometric Mapping (ISOMAP) and Locally Linear Embedding (LLE). The four methods are applied to analyze a complex hydrodynamic flow field with cavitation by considering the joint features of multiple variables. Results show that LLE can capture redundant features that do not contribute to understanding the characteristics of flow fields, while ISOMAP is more suitable for handling datasets with multiple scales than LLE. PCA and ISOMAP can successfully capture the characteristics and evolution of flow fields. In addition, 3D supplementary information can assist ICA in improving the problem of identifying unstable flow field states.

The dimensionality reductions of environmental variables have a significant effect on the performance of species distribution models.

How to effectively obtain species-related low-dimensional data from massive environmental variables has become an urgent problem for species distribution models (SDMs). In this study, we will explore whether dimensionality reduction on environmental variables can improve the predictive performance of SDMs. We first used two linear (i.e., principal component analysis (PCA) and independent components analysis) and two nonlinear (i.e., kernel principal component analysis (KPCA) and uniform manifold approximation and projection) dimensionality reduction techniques (DRTs) to reduce the dimensionality of high-dimensional environmental data. Then, we established five SDMs based on the environmental variables of dimensionality reduction for 23 real plant species and nine virtual species, and compared the predictive performance of those with the SDMs based on the selected environmental variables through Pearson's correlation coefficient (PCC). In addition, we studied the effects of DRTs, model complexity, and sample size on the predictive performance of SDMs. The predictive performance of SDMs under DRTs other than KPCA is better than using PCC. And the predictive performance of SDMs using linear DRTs is better than using nonlinear DRTs. In addition, using DRTs to deal with environmental variables has no less impact on the predictive performance of SDMs than model complexity and sample size. When the model complexity is at the complex level, PCA can improve the predictive performance of SDMs the most by 2.55% compared with PCC. At the middle level of sample size, the PCA improved the predictive performance of SDMs by 2.68% compared with the PCC. Our study demonstrates that DRTs have a significant effect on the predictive performance of SDMs. Specifically, linear DRTs, especially PCA, are more effective at improving model predictive performance under relatively complex model complexity or large sample sizes.

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.

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.

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.

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.

WCGAN-GP based synthetic attack data generation with GA based feature selection for IDS

Cyber-attack is one of the alarming issues in today's era. Firewalls, Intrusion Detection Systems (IDSs), and other techniques are popularly applied to prevent those attacks. Intrusion Detection System (IDS) works as the watchdog to monitor the network traffic and identify an alert when an unauthorized action is detected. However, most IDSs are designed on traditional datasets, which do not address the data imbalance problem. As a result, their performance is not good enough against minority class samples. In order to overcome the aforementioned problem and detect cyber-attacks with higher precision, this paper proposes a novel IDS applying Wasserstein Conditional Generative Adversarial Network – Gradient Penalty (WCGAN-GP) and Genetic Algorithm (GA). The objective of the two components- WCGAN-GP and Genetic Algorithm are introduced in the proposed work for synthetic data generation, feature optimization, and attack detection system. The proposed model generates synthetic samples that follow the underlying data distribution of actual data. This paper uses a novel fitness function for the convergence of the Genetic algorithm and produces an optimal feature vector for the classification problem. In this work, an extensive experimental study applying NSL-KDD and UNSW-NB15 datasets in combination with generated samples and reduced feature set from the proposed model is carried out to evaluate the performance of different machine learning models. Observations show that Xgboost gives the best performances among others. To justify using a genetic algorithm for feature optimization, this paper has compared the proposed model with other traditional feature selection approaches such as PCA, Autoencoder, and T-SNE on the proposed model. It is found that the proposed GA-based feature selection outperforms others. The reason behind it is that the GA-based feature selection technique offers certain advantages over PCA and Autoencoder-based dimensionality reduction techniques, such as the ability to handle non-linearity between features in the data, enhanced flexibility in feature selection, interpretability, and human insight, handling high-dimensional data, robustness to noise and outliers. It also offers an advantage over T-SNE, a nonlinear dimensionality reduction technique in terms of computational efficiency. Furthermore, the model is also compared with other state-of-the-art which address data imbalance problems. Our proposed model with Xgboost classifier gives better results than other existing approaches in terms of accuracy (95.54%), precision (92.61%), recall (95.54%), F1-score (93.41%), and false alarm rate (4.30%) on the NSL-KDD dataset and accuracy (89.58%), precision (89.46%), recall (89.58%), F1-score (88.89%) and false alarm rate (1.18%) on the UNSW-NB15 dataset.

Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging applications. Wassmap represents images via probability measures in Wasserstein space, then uses pairwise Wasserstein distances between the associated measures to produce a low-dimensional, approximately isometric embedding. We show that the algorithm is able to exactly recover parameters of some image manifolds, including those generated by translations or dilations of a fixed generating measure. Additionally, we show that a discrete version of the algorithm retrieves parameters from manifolds generated from discrete measures by providing a theoretical bridge to transfer recovery results from functional data to discrete data. Testing of the proposed algorithms on various image data manifolds shows that Wassmap yields good embeddings compared with other global and local techniques.

A multi-dimensional dataset of Ordovician to Silurian graptolite specimens for virtual examination, global correlation, and shale gas exploration

Abstract. Multi-elemental and multi-dimensional data are more and more important in the development of data-driven research, as is the case in modern paleontology, in which, in an examination by experts, or some day artificial intelligence, every fossil specimen plays a fundamental role. We here release a dataset of 1550 graptolite specimens representing 113 Ordovician to Silurian graptolite species or subspecies that are significant in global stratigraphic correlation and shale gas exploration. The dataset contains 2951 high-resolution images and a data table of each specimen's scientific information, including the taxonomic, geologic, and geographic information, comments, and references. Our dataset provides images for specialists or laypeople worldwide, is supported by the tool FSIDvis (Fossil Specimen Image Dataset Visualizer), which we developed to facilitate the interactive exploration of the rich-attribution image dataset, and includes a nonlinear-dimension reduction technique, t-SNE (t-distributed stochastic neighbor embedding), to project image data into a two-dimensional space to visualize and explore the similarities. Our dataset potentially contributes to virtual examinations of specimens, global bio-stratigraphic correlation, and improvement of the shale gas exploration efficiency. All data, images and the spreadsheet are available at https://doi.org/10.5281/zenodo.6688670 (Xu, 2022).

Asset-return momentum prediction through pattern recognition

Asset-price momentum effects are important to study in finance. A novel nonparametric pattern-recognition algorithm is proposed to identify intraday momentum based on price patterns. Specifically, a classification-regression model for predicting future price-movement patterns is designed by combining Bayesian analysis and a nonparametric density-estimation method (with different similarity measures). The model is applied to asset prices in both original and compressed forms through nonlinear dimension-reduction techniques. Regardless of the data form, this model’s predictive power is statistically and empirically significant. The model most effectively predicts asset prices with high levels of long-range dependence. Empirical analysis demonstrates that the intraday-momentum effect can occur over longer time horizons than the half-hour documented in the literature. The intraday-trading strategy based on the similarity-prediction model achieves an increased expected return and a Sharpe ratio of 11% and 0.7, respectively, compared to alternative benchmark models.

T-SNE: A study on reducing the dimensionality of hyperspectral data for the regression problem of estimating oenological parameters

In recent years there is a growing importance in using machine learning techniques to improve procedures in precision agriculture: in this work we perform a study on models capable of predicting oenological parameters from hyperspectral images of wine grape berries, a specially relevant topic to boost production tasks for winemakers. Specifically, we explore the capabilities of a novel technique mostly used for visualization, t-Distributed Stochastic Neighbor Embedding (t-SNE), for reducing the dimensionality of the highly complex hyperspectral data and compare its performance with Principal Component Analysis (PCA) method, which despite the introduction of many nonlinear dimensionality reduction techniques over the years, had achieved the best results for real-world data across several studies in literature. Additionally we explore the potential of Kernel t-SNE, an extension to the t-SNE method that allows for the usage of the technique in streaming data or online scenarios. Our results show that, in a direct comparison, t-SNE achieves better metrics than PCA for most of the data sets in this work and that the regressor (Support Vector Regression, SVR) performs better with the t-SNE reduced features as inputs, accomplishing better predictions with lower error rates. Comparing the results with current literature, our shallow learning model paired with t-SNE achieves either better or on par results than those reported, even competing with more advanced models that use deep learning techniques, which should propel the introduction of t-SNE in more studies that require dimensionality reduction.

Robust correlation estimation and UMAP assisted topological analysis of omics data for disease subtyping

Deciphering information hidden in the gene expression assays for identifying disease subtypes has significant importance in precision medicine. However, computational limitations thwart this process due to the intricacy of the biological networks and the curse of dimensionality of gene expression data. Therefore, clustering in such scenarios often becomes the first choice of exploratory data analysis to identify natural structures and intrinsic patterns in the data. However, sparse and high dimensional nature of omics data prevents conventional clustering algorithms to discover subtypes that are clinically relevant and statistically significant. Hence, non-linear dimensionality reduction techniques coupled with clustering in such scenarios often becomes imperative to improve the clustering results. In this study, we present a robust pipeline to discover disease subtypes with clinical relevance. Specifically, we focus on discovering patient sub-groups that have a residual life patterns remarkably different from other sub-groups. This is significant because by refining prognosis, subtyping can reduce uncertainty in approximating patients expected outcome. The methodology present is based on robust correlation estimation, UMAP– a non-linear dimensionality reduction method and mapper– a tool from topology. Notably, we suggest a method for improving the robustness of the correlation matrix of gene expression data for improving the clustering results. The performance of the model is evaluated by applying to five cancer datasets obtained through TCGA and comparisons are performed with some state of the art methods of NEMO, RSC-OTRI and SNF with regard to log−rank test and Restricted Life Expectancy Difference. For example in GBM dataset, the minimum separation for any two discovered subtypes is 221 days which is significantly higher than the other methodologies. We also compared the results without using the robust correlation based estimate and observed that robust correlation improves separability between survival curves significantly. From the results we infer that our methodology performs better compared to other methodologies with regard to separating survival curves of patient sub-groups despite using single omics profiles of patients compared to multiple omics profiles of SNF and NEMO. Pathway over-representation analysis is performed on the final clustering results to investigate the biological underpinnings characterizing each subtype.

Connecting Vibrational Spectroscopy to Atomic Structure via Supervised Manifold Learning: Beyond Peak Analysis.

Vibrational spectroscopy is a nondestructive technique commonly used in chemical and physical analyses to determine atomic structures and associated properties. However, the evaluation and interpretation of spectroscopic profiles based on human-identifiable peaks can be difficult and convoluted. To address this challenge, we present a reliable protocol based on supervised manifold learning techniques meant to connect vibrational spectra to a variety of complex and diverse atomic structure configurations. As an illustration, we examined a large database of virtual vibrational spectroscopy profiles generated from atomistic simulations for silicon structures subjected to different stress, amorphization, and disordering states. We evaluated representative features in those spectra via various linear and nonlinear dimensionality reduction techniques and used the reduced representation of those features with decision trees to correlate them with structural information unavailable through classical human-identifiable peak analysis. We show that our trained model accurately (over 97% accuracy) and robustly (insensitive to noise) disentangles the contribution from the different material states, hence demonstrating a comprehensive decoding of spectroscopic profiles beyond classical (human-identifiable) peak analysis.

Model order reduction techniques to identify submarining risk in a simplified human body model

This work investigates linear and non-linear parametric reduced order models (ROM) capable of replacing computationally expensive high-fidelity simulations of human body models (HBM) through a non-intrusive approach. Conventional crash simulation methods pose a computational barrier that restricts profound analyses such as uncertainty quantification, sensitivity analysis, or optimization studies. The non-intrusive framework couples dimensionality reduction techniques with machine learning-based surrogate models that yield a fast responding data-driven black-box model. A comparative study is made between linear and non-linear dimensionality reduction techniques. Both techniques report speed-ups of a few orders of magnitude with an accurate generalization of the design space. These accelerations make ROMs a valuable tool for engineers.