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Brain–computer interfaces (BCIs) are essential in advancing medical diagnosis and treatment by providing non-invasive tools to assess neurological states. Among these, motor imagery (MI), in which patients mentally simulate motor tasks without physical movement, has proven to be an effective paradigm for diagnosing and monitoring neurological conditions. Electroencephalography (EEG) is widely used for MI data collection due to its high temporal resolution, cost-effectiveness, and portability. However, EEG signals can be noisy from a number of sources, including physiological artifacts and electromagnetic interference. They can also vary from person to person, which makes it harder to extract features and understand the signals. Additionally, this variability, influenced by genetic and cognitive factors, presents challenges for developing subject-independent solutions. To address these limitations, this paper presents a Multimodal and Explainable Deep Learning (MEDL) approach for MI-EEG classification and physiological interpretability. Our approach involves the following: (i) evaluating different deep learning (DL) models for subject-dependent MI-EEG discrimination; (ii) employing class activation mapping (CAM) to visualize relevant MI-EEG features; and (iii) utilizing a questionnaire–MI performance canonical correlation analysis (QMIP-CCA) to provide multidomain interpretability. On the GIGAScience MI dataset, experiments show that shallow neural networks are good at classifying MI-EEG data, while the CAM-based method finds spatio-frequency patterns. Moreover, the QMIP-CCA framework successfully correlates physiological data with MI-EEG performance, offering an enhanced, interpretable solution for BCIs.

To optimize growth and management, precision agriculture relies on a deep understanding of agricultural dynamics, particularly crop water status analysis. Leveraging unmanned aerial vehicles, we can efficiently acquire high-resolution spatiotemporal samples by utilizing remote sensors. However, non-linear relationships among data features, localized within specific subgroups, frequently emerge in agricultural data. Interpreting these complex patterns requires sophisticated analysis due to the presence of noise, high variability, and non-stationarity behavior in the collected samples. Here, we introduce Local Biplot, a methodological framework tailored for discerning meaningful data patterns in non-stationary contexts for precision agriculture. Local Biplot relies on the well-known uniform manifold approximation and projection method, such as UMAP, and local affine transformations to codify non-stationary and non-linear data patterns while maintaining interpretability. This lets us find important clusters for transformation and projection within a single global axis pair. Hence, our framework encompasses variable and observational contributions within individual clusters. At the same time, we provide a relevance analysis strategy to help explain why those clusters exist, facilitating the understanding of data dynamics while favoring interpretability. We demonstrated our method’s capabilities through experiments on both synthetic and real-world datasets, covering scenarios involving grass and rice crops. Moreover, we use random forest and linear regression models to predict water status variables from our Local Biplot-based feature ranking and clusters. Our findings revealed enhanced clustering and prediction capability while emphasizing the importance of input features in precision agriculture. As a result, Local Biplot is a useful tool to visualize, analyze, and compare the intricate underlying patterns and internal structures of complex agricultural datasets.

Nonlinear optimization (NOPT) is a meaningful tool for solving complex tasks in fields like engineering, economics, and operations research, among others. However, NOPT has problems when it comes to dealing with data variability and noisy input measurements that lead to incorrect solutions. Furthermore, nonlinear constraints may result in outcomes that are either infeasible or suboptimal, such as nonconvex optimization. This paper introduces a novel regularized physics-informed neural network (RPINN) framework as a new NOPT tool for both supervised and unsupervised data-driven scenarios. Our RPINN is threefold: By using custom activation functions and regularization penalties in an artificial neural network (ANN), RPINN can handle data variability and noisy inputs. Furthermore, it employs physics principles to construct the network architecture, computing the optimization variables based on network weights and learned features. In addition, it uses automatic differentiation training to make the system scalable and cut down on computation time through batch-based back-propagation. The test results for both supervised and unsupervised NOPT tasks show that our RPINN can provide solutions that are competitive compared to state-of-the-art solvers. In turn, the robustness of RPINN against noisy input measurements makes it particularly valuable in environments with fluctuating information. Specifically, we test a uniform mixture model and a gas-powered system as NOPT scenarios. Overall, with RPINN, its ANN-based foundation offers significant flexibility and scalability.

The demand for thermal power generation from natural gas has increased globally due to its cleaner burning properties compared to other fossil fuels. Optimizing the gas flow through the network to meet this demand is challenging due to the nonconvex Weymouth equation constraining gas flow and nodal pressures in pipelines. Traditional methods for addressing this nonconvexity lead to significant approximation errors or high operational costs. This study poses the Weymouth constraint as a Mathematical Programming with Complementarity Constraints (MPCC) for an optimal gas flow problem. The complementarity constraints reformulate the discontinuous sign function using binary-behaving continuous variables. This MPCC-based approach avoids solving mixed-integer programming problems while enhancing the accuracy of conventional linear and second-order approximations. Testing the approach on various interconnected systems, including Colombia’s national gas transportation grid, demonstrated significant reductions in Weymouth approximation errors, thereby supporting effective optimization for interconnected networks.

Magnetic resonance imaging and computed tomography produce three-dimensional volumetric medical images. While a scalar value represents each individual volume element, or voxel, volumetric data are characterized by features derived from groups of neighboring voxels and their inherent relationships, which may vary depending on the specific clinical application. Labeled samples are also required in most applications, which can be problematic for large datasets such as medical images. We propose a direct volume rendering (DVR) framework based on multi-scale dimensionality reduction neighbor embedding that generates two-dimensional transfer function (TF) domains. In this way, we present FSS.t-SNE, a fast semi-supervised version of the t-distributed stochastic neighbor embedding (t-SNE) method that works over hundreds of thousands of voxels without the problem of crowding and with better separation in a 2D histogram compared to traditional TF domains. Our FSS.t-SNE scatters voxels of the same sub-volume in a wider region through multi-scale neighbor embedding, better preserving both local and global data structures and allowing for its internal exploration based on the original features of the multi-dimensional space, taking advantage of the partially provided labels. Furthermore, FSS.t-SNE untangles sample paths among sub-volumes, allowing us to explore edges and transitions. In addition, our approach employs a Barnes–Hut approximation to reduce computational complexity from O(N2) (t-SNE) to O(NlogN). Although we require the additional step of generating the 2D TF domain from multiple features, our experiments show promising performance in volume segmentation and visual inspection.

Brain–computer interfaces (BCIs) from electroencephalography (EEG) provide a practical approach to support human–technology interaction. In particular, motor imagery (MI) is a widely used BCI paradigm that guides the mental trial of motor tasks without physical movement. Here, we present a deep learning methodology, named kernel-based regularized EEGNet (KREEGNet), leveled on centered kernel alignment and Gaussian functional connectivity, explicitly designed for EEG-based MI classification. The approach proactively tackles the challenge of intrasubject variability brought on by noisy EEG records and the lack of spatial interpretability within end-to-end frameworks applied for MI classification. KREEGNet is a refinement of the widely accepted EEGNet architecture, featuring an additional kernel-based layer for regularized Gaussian functional connectivity estimation based on CKA. The superiority of KREEGNet is evidenced by our experimental results from binary and multiclass MI classification databases, outperforming the baseline EEGNet and other state-of-the-art methods. Further exploration of our model’s interpretability is conducted at individual and group levels, utilizing classification performance measures and pruned functional connectivities. Our approach is a suitable alternative for interpretable end-to-end EEG-BCI based on deep learning.

Environmental demands around the world have led to an increasing interest in natural gas due to its advantages over other hydrocarbons used in power generation, which has led to the search for the best way to solve the transportation problem associated with this resource. In this paper, we propose a methodology that allows us to address the non-convexity related to the Weymouth equation that makes the optimization problem so difficult. The mentioned equation, in charge of relating the flows through the pipelines and the pressures at the nodes, is characterized by having a discontinuity in the form of a sign function. The proposal of this work is based on the use of Mathematical Programs with Complementarity Constraints (MPCC) to achieve a good approximation since it allows make certain continuous variables to behave as discrete variables in such a way that it is possible to avoid having to pose a mixed integer programming problem and this one. This approach showed a smaller approximation error (or at least equal) with other approximations used in the state of the art when tested in three different networks: one of 8 nodes, one of 48 nodes tested in other related works, and one of 63 nodes representing the Colombian natural gas transportation system.

Regional neuraxial analgesia for pain relief during labor is a universally accepted, safe, and effective procedure involving administering medication into the epidural. Still, an adequate assessment requires continuous patient monitoring after catheter placement. This research introduces a cutting-edge semantic thermal image segmentation method emphasizing superior interpretability for regional neuraxial analgesia monitoring. Namely, we propose a novel Convolutional Random Fourier Features-based approach, termed CRFFg, and custom-designed layer-wise weighted class-activation maps created explicitly for foot segmentation. Our method aims to enhance three well-known semantic segmentation (FCN, UNet, and ResUNet). We have rigorously evaluated our methodology on a challenging dataset of foot thermal images from pregnant women who underwent epidural anesthesia. Its limited size and significant variability distinguish this dataset. Furthermore, our validation results indicate that our proposed methodology not only delivers competitive results in foot segmentation but also significantly improves the explainability of the process.

Sound synthesis refers to the creation of original acoustic signals with broad applications in artistic innovation, such as music creation for games and videos. Nonetheless, machine learning architectures face numerous challenges when learning musical structures from arbitrary corpora. This issue involves adapting patterns borrowed from other contexts to a concrete composition objective. Using Labeled Correlation Alignment (LCA), we propose an approach to sonify neural responses to affective music-listening data, identifying the brain features that are most congruent with the simultaneously extracted auditory features. For dealing with inter/intra-subject variability, a combination of Phase Locking Value and Gaussian Functional Connectivity is employed. The proposed two-step LCA approach embraces a separate coupling stage of input features to a set of emotion label sets using Centered Kernel Alignment. This step is followed by canonical correlation analysis to select multimodal representations with higher relationships. LCA enables physiological explanation by adding a backward transformation to estimate the matching contribution of each extracted brain neural feature set. Correlation estimates and partition quality represent performance measures. The evaluation uses a Vector Quantized Variational AutoEncoder to create an acoustic envelope from the tested Affective Music-Listening database. Validation results demonstrate the ability of the developed LCA approach to generate low-level music based on neural activity elicited by emotions while maintaining the ability to distinguish between the acoustic outputs.

An Open Brain–Computer Interface (OpenBCI) provides unparalleled freedom and flexibility through open-source hardware and firmware at a low-cost implementation. It exploits robust hardware platforms and powerful software development kits to create customized drivers with advanced capabilities. Still, several restrictions may significantly reduce the performance of OpenBCI. These limitations include the need for more effective communication between computers and peripheral devices and more flexibility for fast settings under specific protocols for neurophysiological data. This paper describes a flexible and scalable OpenBCI framework for electroencephalographic (EEG) data experiments using the Cyton acquisition board with updated drivers to maximize the hardware benefits of ADS1299 platforms. The framework handles distributed computing tasks and supports multiple sampling rates, communication protocols, free electrode placement, and single marker synchronization. As a result, the OpenBCI system delivers real-time feedback and controlled execution of EEG-based clinical protocols for implementing the steps of neural recording, decoding, stimulation, and real-time analysis. In addition, the system incorporates automatic background configuration and user-friendly widgets for stimuli delivery. Motor imagery tests the closed-loop BCI designed to enable real-time streaming within the required latency and jitter ranges. Therefore, the presented framework offers a promising solution for tailored neurophysiological data processing.

Motor Imagery (MI) refers to imagining the mental representation of motor movements without overt motor activity, enhancing physical action execution and neural plasticity with potential applications in medical and professional fields like rehabilitation and education. Currently, the most promising approach for implementing the MI paradigm is the Brain-Computer Interface (BCI), which uses Electroencephalogram (EEG) sensors to detect brain activity. However, MI-BCI control depends on a synergy between user skills and EEG signal analysis. Thus, decoding brain neural responses recorded by scalp electrodes poses still challenging due to substantial limitations, such as non-stationarity and poor spatial resolution. Also, an estimated third of people need more skills to accurately perform MI tasks, leading to underperforming MI-BCI systems. As a strategy to deal with BCI-Inefficiency, this study identifies subjects with poor motor performance at the early stages of BCI training by assessing and interpreting the neural responses elicited by MI across the evaluated subject set. Using connectivity features extracted from class activation maps, we propose a Convolutional Neural Network-based framework for learning relevant information from high-dimensional dynamical data to distinguish between MI tasks while preserving the post-hoc interpretability of neural responses. Two approaches deal with inter/intra-subject variability of MI EEG data: (a) Extracting functional connectivity from spatiotemporal class activation maps through a novel kernel-based cross-spectral distribution estimator, (b) Clustering the subjects according to their achieved classifier accuracy, aiming to find common and discriminative patterns of motor skills. According to the validation results obtained on a bi-class database, an average accuracy enhancement of 10% is achieved compared to the baseline EEGNet approach, reducing the number of “poor skill” subjects from 40% to 20%. Overall, the proposed method can be used to help explain brain neural responses even in subjects with deficient MI skills, who have neural responses with high variability and poor EEG-BCI performance.

This paper uses EEG data to introduce an approach for classifying right and left-hand classes in Motor Imagery (MI) tasks. The Kernel Cross-Spectral Functional Connectivity Network (KCS-FCnet) method addresses these limitations by providing richer spatial-temporal-spectral feature maps, a simpler architecture, and a more interpretable approach for EEG-driven MI discrimination. In particular, KCS-FCnet uses a single 1D-convolutional-based neural network to extract temporal-frequency features from raw EEG data and a cross-spectral Gaussian kernel connectivity layer to model channel functional relationships. As a result, the functional connectivity feature map reduces the number of parameters, improving interpretability by extracting meaningful patterns related to MI tasks. These patterns can be adapted to the subject’s unique characteristics. The validation results prove that introducing KCS-FCnet shallow architecture is a promising approach for EEG-based MI classification with the potential for real-world use in brain–computer interface systems.

Supervised learning requires the accurate labeling of instances, usually provided by an expert. Crowdsourcing platforms offer a practical and cost-effective alternative for large datasets when individual annotation is impractical. In addition, these platforms gather labels from multiple labelers. Still, traditional multiple-annotator methods must account for the varying levels of expertise and the noise introduced by unreliable outputs, resulting in decreased performance. In addition, they assume a homogeneous behavior of the labelers across the input feature space, and independence constraints are imposed on outputs. We propose a Generalized Cross-Entropy-based framework using Chained Deep Learning (GCECDL) to code each annotator’s non-stationary patterns regarding the input space while preserving the inter-dependencies among experts through a chained deep learning approach. Experimental results devoted to multiple-annotator classification tasks on several well-known datasets demonstrate that our GCECDL can achieve robust predictive properties, outperforming state-of-the-art algorithms by combining the power of deep learning with a noise-robust loss function to deal with noisy labels. Moreover, network self-regularization is achieved by estimating each labeler’s reliability within the chained approach. Lastly, visual inspection and relevance analysis experiments are conducted to reveal the non-stationary coding of our method. In a nutshell, GCEDL weights reliable labelers as a function of each input sample and achieves suitable discrimination performance with preserved interpretability regarding each annotator’s trustworthiness estimation.

Peripheral nerve blocking (PNB) is a standard procedure to support regional anesthesia. Still, correct localization of the nerve’s structure is needed to avoid adverse effects; thereby, ultrasound images are used as an aid approach. In addition, image-based automatic nerve segmentation from deep learning methods has been proposed to mitigate attenuation and speckle noise ultrasonography issues. Notwithstanding, complex architectures highlight the region of interest lacking suitable data interpretability concerning the learned features from raw instances. Here, a kernel-based deep learning enhancement is introduced for nerve structure segmentation. In a nutshell, a random Fourier features-based approach was utilized to complement three well-known semantic segmentation architectures, e.g., fully convolutional network, U-net, and ResUnet. Moreover, two ultrasound image datasets for PNB were tested. Obtained results show that our kernel-based approach provides a better generalization capability from image segmentation-based assessments on different nerve structures. Further, for data interpretability, a semantic segmentation extension of the GradCam++ for class-activation mapping was used to reveal relevant learned features separating between nerve and background. Thus, our proposal favors both straightforward (shallow) and complex architectures (deeper neural networks).

Nowadays, bearings installed in industrial electric motors are constituted as the primary mode of a failure affecting the global energy consumption. Since industries’ energy demand has a growing tendency, interest for efficient maintenance in electric motors is decisive. Vibration signals from bearings are employed commonly as a non-invasive approach to support fault diagnosis and severity evaluation of rotating machinery. However, vibration-based diagnosis poses a challenge concerning the signal properties, e.g., highly dynamic and non-stationary. Here, we introduce a knowledge-based tool to analyze multiple health conditions in bearings. Our approach includes a stochastic feature selection method, termed Stochastic Feature Selection (SFS), highlighting and interpreting relevant multi-domain attributes (time, frequency, and time–frequency) related to the bearing faults discriminability. In particular, a relief-F-based ranking and a Hidden Markov Model are trained under a windowing scheme to achieve our SFS. Obtained results in a public database demonstrate that our proposal is competitive compared to state-of-the-art algorithms concerning both the number of features selected and the classification accuracy.

Condition monitoring of Internal Combustion Engines (ICE) benefits cost-effective operations in the modern industrial sector. Because of this, vibration signals are commonly monitored as part of a non-invasive approach to ICE analysis. However, vibration-based ICE monitoring poses a challenge due to the properties of this kind of signals. They are highly dynamic and non-stationary, let alone the diverse sources involved in the combustion process. In this paper, we propose a feature relevance estimation strategy for vibration-based ICE analysis. Our approach is divided into three main stages: signal decomposition using an Ensemble Empirical Mode Decomposition algorithm, multi-domain parameter estimation from time and frequency representations, and a supervised feature selection based on the Relief-F technique. Accordingly, we decomposed the vibration signals by using self-adaptive analysis to represent nonlinear and non-stationary time series. Afterwards, time and frequency-based parameters were calculated to code complex and/or non-stationary dynamics. Subsequently, we computed a relevance vector index to measure the contribution of each multi-domain feature to the discrimination of different fuel blend estimation/diagnosis categories for ICE. In particular, we worked with an ICE dataset collected from fuel blends under normal and fault scenarios at different engine speeds to test our approach. Our classification results presented nearly 98% of accuracy after using a k-Nearest Neighbors machine. They reveal the way our approach identifies a relevant subset of features for ICE condition monitoring. One of the benefits is the reduced number of parameters.

Inmersión localmente lineal (LLE) es una técnica de reducción de dimensión no lineal que permite conservar la geometría local del espacio de alta dimensión, al realizar una inmersión de los datos a un espacio de baja dimensión. El algoritmo posee 3 parámetros libres que deben ser definidos por el usuario al momento de realizar la inmersión, el número de vecinos más cercanos k, la dimensión de salida de los datos m y el parámetro de regularización a. Este último sólo es necesario determinarlo cuando el número de vecinos elegido es mayor que la dimensión original de los datos, o cuando los puntos (datos) no están ubicados en posición general, pero juega un papel muy importante en el resultado de la inmersión. En este trabajo se propone un par de criterios que permiten encontrar el valor óptimo para los parámetros k y a, de manera que se obtenga una inmersión que represente de manera fiel los datos del espacio de entrada. Con el fin de comprobar la eficacia de los criterios propuestos, se realizaron pruebas sobre dos bases de datos artificiales y dos bases de datos reales. Además, se realiza una comparación de los resultados contra métodos encontrados en el estado del arte.

Locally Linear Embedding (LLE) is a nonlinear dimensionality reduction technique, which preserves the local geometry of high dimensional space performing an embedding to low dimensional space. LLE algorithm has 3 free parameters that must be set to calculate the embedding: the number of nearest neighbors k, the output space dimensionality m and the regularization parameter a. The last one only is necessary when the value of k is greater than the dimensionality of input space or data are not located in general position, and it plays an important role in the embedding results. In this paper we propose a pair of criteria to find the optimum value for the parameters kand a, to obtain an embedding that faithfully represent the input data space. Our approaches are tested on 2 artificial data sets and 2 real world data sets to verify the effectiveness of the proposed criteria, besides the results are compared against methods found in the state of art.

Brain–computer interfaces (BCIs) are essential in advancing medical diagnosis and treatment by providing non-invasive tools to assess neurological states. Among these, motor imagery (MI), in which patients mentally simulate motor tasks without physical movement, has proven to be an effective paradigm for diagnosing and monitoring neurological conditions. Electroencephalography (EEG) is widely used for MI data collection due to its high temporal resolution, cost-effectiveness, and portability. However, EEG signals can be noisy from a number of sources, including physiological artifacts and electromagnetic interference. They can also vary from person to person, which makes it harder to extract features and understand the signals. Additionally, this variability, influenced by genetic and cognitive factors, presents challenges for developing subject-independent solutions. To address these limitations, this paper presents a Multimodal and Explainable Deep Learning (MEDL) approach for MI-EEG classification and physiological interpretability. Our approach involves the following: (i) evaluating different deep learning (DL) models for subject-dependent MI-EEG discrimination; (ii) employing class activation mapping (CAM) to visualize relevant MI-EEG features; and (iii) utilizing a questionnaire–MI performance canonical correlation analysis (QMIP-CCA) to provide multidomain interpretability. On the GIGAScience MI dataset, experiments show that shallow neural networks are good at classifying MI-EEG data, while the CAM-based method finds spatio-frequency patterns. Moreover, the QMIP-CCA framework successfully correlates physiological data with MI-EEG performance, offering an enhanced, interpretable solution for BCIs. [ABSTRACT FROM AUTHOR]

To optimize growth and management, precision agriculture relies on a deep understanding of agricultural dynamics, particularly crop water status analysis. Leveraging unmanned aerial vehicles, we can efficiently acquire high-resolution spatiotemporal samples by utilizing remote sensors. However, non-linear relationships among data features, localized within specific subgroups, frequently emerge in agricultural data. Interpreting these complex patterns requires sophisticated analysis due to the presence of noise, high variability, and non-stationarity behavior in the collected samples. Here, we introduce Local Biplot, a methodological framework tailored for discerning meaningful data patterns in non-stationary contexts for precision agriculture. Local Biplot relies on the well-known uniform manifold approximation and projection method, such as UMAP, and local affine transformations to codify non-stationary and non-linear data patterns while maintaining interpretability. This lets us find important clusters for transformation and projection within a single global axis pair. Hence, our framework encompasses variable and observational contributions within individual clusters. At the same time, we provide a relevance analysis strategy to help explain why those clusters exist, facilitating the understanding of data dynamics while favoring interpretability. We demonstrated our method's capabilities through experiments on both synthetic and real-world datasets, covering scenarios involving grass and rice crops. Moreover, we use random forest and linear regression models to predict water status variables from our Local Biplot-based feature ranking and clusters. Our findings revealed enhanced clustering and prediction capability while emphasizing the importance of input features in precision agriculture. As a result, Local Biplot is a useful tool to visualize, analyze, and compare the intricate underlying patterns and internal structures of complex agricultural datasets. [ABSTRACT FROM AUTHOR]

The demand for thermal power generation from natural gas has increased globally due to its cleaner burning properties compared to other fossil fuels. Optimizing the gas flow through the network to meet this demand is challenging due to the nonconvex Weymouth equation constraining gas flow and nodal pressures in pipelines. Traditional methods for addressing this nonconvexity lead to significant approximation errors or high operational costs. This study poses the Weymouth constraint as a Mathematical Programming with Complementarity Constraints (MPCC) for an optimal gas flow problem. The complementarity constraints reformulate the discontinuous sign function using binary-behaving continuous variables. This MPCC-based approach avoids solving mixed-integer programming problems while enhancing the accuracy of conventional linear and second-order approximations. Testing the approach on various interconnected systems, including Colombia's national gas transportation grid, demonstrated significant reductions in Weymouth approximation errors, thereby supporting effective optimization for interconnected networks. [ABSTRACT FROM AUTHOR]

Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning. [ABSTRACT FROM AUTHOR]

Nonlinear optimization (NOPT) is a meaningful tool for solving complex tasks in fields like engineering, economics, and operations research, among others. However, NOPT has problems when it comes to dealing with data variability and noisy input measurements that lead to incorrect solutions. Furthermore, nonlinear constraints may result in outcomes that are either infeasible or suboptimal, such as nonconvex optimization. This paper introduces a novel regularized physics-informed neural network (RPINN) framework as a new NOPT tool for both supervised and unsupervised data-driven scenarios. Our RPINN is threefold: By using custom activation functions and regularization penalties in an artificial neural network (ANN), RPINN can handle data variability and noisy inputs. Furthermore, it employs physics principles to construct the network architecture, computing the optimization variables based on network weights and learned features. In addition, it uses automatic differentiation training to make the system scalable and cut down on computation time through batch-based back-propagation. The test results for both supervised and unsupervised NOPT tasks show that our RPINN can provide solutions that are competitive compared to state-of-the-art solvers. In turn, the robustness of RPINN against noisy input measurements makes it particularly valuable in environments with fluctuating information. Specifically, we test a uniform mixture model and a gas-powered system as NOPT scenarios. Overall, with RPINN, its ANN-based foundation offers significant flexibility and scalability. [ABSTRACT FROM AUTHOR]

Magnetic resonance imaging and computed tomography produce three-dimensional volumetric medical images. While a scalar value represents each individual volume element, or voxel, volumetric data are characterized by features derived from groups of neighboring voxels and their inherent relationships, which may vary depending on the specific clinical application. Labeled samples are also required in most applications, which can be problematic for large datasets such as medical images. We propose a direct volume rendering (DVR) framework based on multi-scale dimensionality reduction neighbor embedding that generates two-dimensional transfer function (TF) domains. In this way, we present FSS.t-SNE, a fast semi-supervised version of the t-distributed stochastic neighbor embedding (t-SNE) method that works over hundreds of thousands of voxels without the problem of crowding and with better separation in a 2D histogram compared to traditional TF domains. Our FSS.t-SNE scatters voxels of the same sub-volume in a wider region through multi-scale neighbor embedding, better preserving both local and global data structures and allowing for its internal exploration based on the original features of the multi-dimensional space, taking advantage of the partially provided labels. Furthermore, FSS.t-SNE untangles sample paths among sub-volumes, allowing us to explore edges and transitions. In addition, our approach employs a Barnes–Hut approximation to reduce computational complexity from O (N 2) (t-SNE) to O (N l o g N) . Although we require the additional step of generating the 2D TF domain from multiple features, our experiments show promising performance in volume segmentation and visual inspection. [ABSTRACT FROM AUTHOR]