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Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate image prior information in the forward model of iterative PET image reconstruction. Existing kernel methods construct the kernels commonly using an empirical process, which may lead to unsatisfactory performance. In this paper, we describe the equivalence between the kernel representation and a trainable neural network model. A deep kernel method is then proposed by exploiting a deep neural network to enable automated learning of an improved kernel model and is directly applicable to single subjects in dynamic PET. The training process utilizes available image prior data to form a set of robust kernels in an optimized way rather than empirically. The results from computer simulations and a real patient dataset demonstrate that the proposed deep kernel method can outperform the existing kernel method and neural network method for dynamic PET image reconstruction.

Machine learning (ML) methods are progressively gaining acceptance in the electron microscopy community for de-noising, semantic segmentation, and dimensionality reduction of data post-acquisition. The introduction of the application programming interfaces (APIs) by major instrument manufacturers now allows the deployment of ML workflows in microscopes, not only for data analytics but also for real-time decision-making and feedback for microscope operation. However, the number of use cases for real-time ML remains remarkably small. Here, we discuss some considerations in designing ML-based active experiments and pose that the likely strategy for the next several years will be human-in-the-loop automated experiments (hAE). In this paradigm, the ML learning agent directly controls beam position and image and spectroscopy acquisition functions, and a human operator monitors experiment progression in real and feature space of the system and tunes the policies of the ML agent to steer the experiment toward specific objectives. [ABSTRACT FROM AUTHOR]

Diabetic retinopathy (DR) is a leading cause of vision loss. Therefore, screening for early signs and assessment of the DR severity is crucial and extensively studied. To support clinicians, screening could be automated by algorithms that can, for example, refer difficult decisions to specialists for further investigation. However, frequently used neural networks (NNs) typically do not know when they do not know and approximate Bayesian NNs often equally do not suffice to provide well-calibrated uncertainty estimates. Thus, in this work, we investigate whether and how to use deep kernel learning (DKL) which we designed as a hybrid combination of the state-of-the-art EfficientNet-B0 and a Gaussian process (GP) layer to improve the quality of uncertainty estimates in referral-based DR screening. To this end, we first analyze the necessity for recently proposed extensions to the DKL framework to resolve miscalibrated uncertainties, despite the theoretical superiority of GPs to uncertainty quantification. Our subsequent comprehensive comparison of the curated DKL’s performance to that of the most common approximate Bayesian NNs shows our DKL models to particularly improve the detection of near out-of-distribution (OOD) samples containing other eye diseases through epistemic uncertainty information, but also enhance the calibration of aleatoric in-distribution uncertainty and diagnostic performance. Hence, it can provide a substantial benefit for safety-critical medical applications, like automated DR screening, particularly by potentially reducing the risk of missing diseases other than DR due to the improved near-OOD detection performance.

The retinal disease Diabetic retinopathy (DR) is one of the most probable causes of blindness. Automatic detection of DR is mostly done using convolutional neural networks (CNNs) on colour retinal images. This work in contrast uses stochastic variational deep kernel learning (SVDKL) for DR grading, combining a deep CNN with Gaussian processes (GPs) into a single end-to-end trainable model, which promises to provide predictions with a reliable uncertainty estimate exploiting approximate Bayesian inference. Evaluating the performance and uncertainty calibration of SVDKL on DR grading compared to a plain CNN, the EfficientNet-B0, preliminary results on a subset of the Kaggle DR dataset show a naturally enhanced uncertainty calibration for SVDKL over the plain CNN as well as a good diagnostic performance. Despite SVDKL achieving a slightly reduced accuracy, incorrect predictions were in closer proximity to the target stages, which is beneficial for clinical diagnosis due to minimizing the cost related to severe misclassifications.

The material removal rate (MRR) is an important variable but difficult to measure in the chemical–mechanical planarization (CMP) process. Most data-based virtual metrology (VM) methods ignore the large number of unlabeled samples, resulting in a waste of information. In this paper, the semi-supervised deep kernel active learning (SSDKAL) model is proposed. Clustering-based phase partition and phase-matching algorithms are used for the initial feature extraction, and a deep network is used to replace the kernel of Gaussian process regression so as to extract hidden deep features. Semi-supervised regression and active learning sample selection strategies are applied to make full use of information on the unlabeled samples. The experimental results of the CMP process dataset validate the effectiveness of the proposed method. Compared with supervised regression and co-training-based semi-supervised regression algorithms, the proposed model has a lower mean square error with different labeled sample proportions. Compared with other frameworks proposed in the literature, such as physics-based VM models, Gaussian-process-based regression models, and stacking models, the proposed method achieves better prediction results without using all the labeled samples. [ABSTRACT FROM AUTHOR]

The ability of deep learning methods to perform classification and regression tasks relies heavily on their capacity to uncover manifolds in high-dimensional data spaces and project them into low-dimensional representation spaces. In this study, we investigate the structure and character of the manifolds generated by classical variational autoencoder (VAE) approaches and deep kernel learning (DKL). In the former case, the structure of the latent space is determined by the properties of the input data alone, while in the latter, the latent manifold forms as a result of an active learning process that balances the data distribution and target functionalities. We show that DKL with active learning can produce a more compact and smooth latent space which is more conducive to optimization compared to previously reported methods, such as the VAE. We demonstrate this behavior using a simple cards dataset and extend it to the optimization of domain-generated trajectories in physical systems. Our findings suggest that latent manifolds constructed through active learning have a more beneficial structure for optimization problems, especially in feature-rich target-poor scenarios that are common in domain sciences, such as materials synthesis, energy storage, and molecular discovery. The Jupyter Notebooks that encapsulate the complete analysis accompany the article.

Deep learning methods have achieved state-of-the-art performance on synthetic aperture radar (SAR) target recognition tasks in recent years. However, obtaining sufficient SAR images for training these deep learning methods is costly in time and labor. This paper focuses on recognizing targets with a few training samples, that is, few-shot target recognition. We combine deep neural networks’ powerful feature representation capabilities with the nonparametric flexibility of Gaussian processes (GPs) and propose a few-shot recognition model based on deep kernel learning. Deep neural networks map input samples into a low-dimensional embedding space. GPs employ a family of kernel functions to measure the similarity between embedded samples and classify them. During training, the model builds diverse related tasks to learn kernel functions with parameters shared across few-shot tasks. These learned kernel functions define common prior knowledge that can be transferred to unseen tasks. During testing, the model can recognize novel tasks with a few samples based on learned kernel functions. We conducted extensive experiments on a widely-used real SAR dataset to evaluate the model’s effectiveness. The test results demonstrate that our model is superior to several recently proposed few-shot recognition methods.

Remote sensing hyperspectral images are very useful for land cover classification because of their rich spatial and spectral information. However, hyperspectral image acquisition and pixel labeling are laborious and time-consuming, so few-shot learning methods are considered to solve this problem. Deep learning has gradually been used for few-shot hyperspectral classification, but there are some problems. The feature extraction network based on deep learning requires too many parameters to be trained, resulting in a huge network model, which is not conducive to deployment on remote sensing data acquisition equipment. Moreover, due to the lack of label samples, the algorithm based on deep learning is more prone to overfitting. To solve the above problems, considering the advanced characteristics of the kernel method in dealing with nonlinear, small sample, and high-dimensional data, we propose a small scale high precision network called 3-D convolution random Fourier features (3-DCRFF) based on the random Fourier feature (RFF) kernel approximation, which is the 3-DCRFF network. First, we combine 3-D convolution with RFF as the basic structure of the network to extract the spatial and spectral features of HSI cubes. Second, we use a classifier based on attention mechanism to classify feature vectors to obtain recognition probability. Finally, the network parameters are solved from the perspective of Bayesian optimization, and the synthetic gradient optimization method is designed and implemented to realize the fast learning of the network. A large number of experiments HSI classification experiments were performed on University of Pavia (UP), Pavia Center (PC), Indian Pines (IP), and Salinas standard remote sensing datasets, the results show that our algorithm outperforms most state-of-the-art algorithms on few-shot classification. [ABSTRACT FROM AUTHOR]

The material removal rate (MRR) is an important variable but difficult to measure in the chemical–mechanical planarization (CMP) process. Most data-based virtual metrology (VM) methods ignore the large number of unlabeled samples, resulting in a waste of information. In this paper, the semi-supervised deep kernel active learning (SSDKAL) model is proposed. Clustering-based phase partition and phase-matching algorithms are used for the initial feature extraction, and a deep network is used to replace the kernel of Gaussian process regression so as to extract hidden deep features. Semi-supervised regression and active learning sample selection strategies are applied to make full use of information on the unlabeled samples. The experimental results of the CMP process dataset validate the effectiveness of the proposed method. Compared with supervised regression and co-training-based semi-supervised regression algorithms, the proposed model has a lower mean square error with different labeled sample proportions. Compared with other frameworks proposed in the literature, such as physics-based VM models, Gaussian-process-based regression models, and stacking models, the proposed method achieves better prediction results without using all the labeled samples.

Remote sensing image target recognition is used in various fields, such as ships, tanks, airplanes, and vehicles, which are closed targets. The features of these targets include target outlines that are obvious and target discriminant features that are significantly different from the surrounding environment, and the targets are characterized as small and dense. Therefore, the recognition of these types of targets is a popular topic. We proposed a recognition framework consisting of a remote sensing image target recognition method based on deep saliency kernel learning analysis, which uses a target region extraction method based on the visual saliency mechanism and implements a nonlinear deep kernel learning saliency feature analysis method to realize target extraction and recognition. Experimental results show that a 95.9% recognition rate is achieved for SAR remote sensing target recognition on the public MSTAR data set, a 96% recognition rate on the UC Merced Land Use data set, and an 85% recognition rate on a self-built visible light remote sensing image data set. The recognition framework can be used for video recognition.

• A novel context-aware deep kernel network that learns context is proposed. • The learning algorithms for layerwise, stationary and classwise contexts are proposed. • The results on the ImageCLEF, COREL5k and NUS-WIDE benchmarks validate their effectiveness. Context plays a crucial role in visual recognition as it provides complementary clues for different learning tasks including image classification and annotation. As the performances of these tasks are currently reaching a plateau, any extra knowledge, including context, should be leveraged in ordficant leaps in these performances. In the particular scenario of kernel machines, context-aware kernel design aims at learning positive semi-definite similarity functions which return high values not only when data share similar contents, but also similar structures (a.k.a. contexts). However, the use of context in kernel design has not been fully explored; indeed, context in these solutions is handcrafted instead of being learned. In this paper, we introduce a novel deep network architecture that learns context in kernel design. This architecture is fully determined by the solution of an objective function mixing a content term that captures the intrinsic similarity between data, a context criterion which models their structure and a regularization term that helps designing smooth kernel network representations. The solution of this objective function defines a particular deep network architecture whose parameters correspond to different variants of learned contexts including layerwise, stationary and classwise; larger values of these parameters correspond to the most influencing contextual relationships between data. Extensive experiments conducted on the challenging ImageCLEF Photo Annotation, Corel5k and NUS-WIDE benchmarks show that our deep context networks are highly effective for image classification and the learned contexts further enhance the performance of image annotation. [ABSTRACT FROM AUTHOR]

We apply deep kernel learning (DKL), which can be viewed as a combination of a Gaussian process (GP) and a deep neural network (DNN), to compression ignition engine emissions and compare its performance to a selection of other surrogate models on the same dataset. Surrogate models are a class of computationally cheaper alternatives to physics-based models. High-dimensional model representation (HDMR) is also briefly discussed and acts as a benchmark model for comparison. We apply the considered methods to a dataset, which was obtained from a compression ignition engine and includes as outputs soot and NOx emissions as functions of 14 engine operating condition variables. We combine a quasi-random global search with a conventional grid-optimization method in order to identify suitable values for several DKL hyperparameters, which include network architecture, kernel, and learning parameters. The performance of DKL, HDMR, plain GPs, and plain DNNs is compared in terms of the root mean squared error (RMSE) of the predictions as well as computational expense of training and evaluation. It is shown that DKL performs best in terms of RMSE in the predictions whilst maintaining the computational cost at a reasonable level, and DKL predictions are in good agreement with the experimental emissions data.

Breast cancer is a pathological condition characterized by the abnormal proliferation of cells inside the breast tissue. The biggest challenge at the moment is determining the most optimal subset from large datasets. Numerous methodologies have been presented for the purpose of selecting the most suitable subset from datasets with high dimensions. However, the outcomes have proven to be insufficient in effectively addressing extensive quantities of multidimensional datasets. This publication presents a proposal for an efficient approach of selecting numerous feature subsets and performing classification on Multidimensional Datasets (MDD). In this study, the Moment Invariant Wavelet Feature Extraction (MI-WFE) approach is employed for the purpose of feature extraction. The New Adaptive Hybrid Levy Flight based Cuckoo Search Optimization Algorithm is employed to identify the most pertinent subset of features. This study presents a novel approach, referred to as H-RS-LVCSO, which aims to enhance the local search capability and optimization speed of the algorithm. This is achieved through the hybridization of the Rat Swarm Optimizer with the levy flight based cuckoo search optimization technique. In this study, it is suggested a hybridized approach for classifying breast cancer, utilizing a Multilayer Multiple Deep Kernel Learning (ML-MDKL) Classifier in conjunction with the standard Support Vector Machine (SVM) Classifier. The simulation of the suggested method is conducted using the MATLAB software. The approach under consideration is evaluated in comparison to two pre-existing methods. The suggested method demonstrates an accuracy improvement of 10.58% compared to existing methods. Furthermore, it outperforms these methods by 17.5% in terms of accuracy. The proposed method exhibits a precision improvement of 6.52% and 14.23% compared to the existing methods. [ABSTRACT FROM AUTHOR]

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.

In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for the analysis of machine learning algorithms based on compositions of functions. As a direct consequence in the finitesample case, the corresponding infinite-dimensional minimization problems can be recast into (nonlinear) finite-dimensional minimization problems, which can be tackled with nonlinear optimization algorithms. Moreover, we show how concatenated machine learning problems can be reformulated as neural networks and how our representer theorem applies to a broad class of state-of-the-art deep learning methods. [ABSTRACT FROM AUTHOR]

Ion-selective electrodes (ISEs) have recently become the most attractive tools for the development of efficient hydroponic systems. Nevertheless, some inherent shortcomings such as signal drifts, secondary ion interferences, and effected high ionic strength make them difficult to apply in a hydroponic system. To minimize these deficiencies, we combined the multivariate standard addition (MSAM) sampling technique with the deep kernel learning (DKL) model for a six ISEs array to increase the prediction accuracy and precision of eight ions, including NO3−, NH4+, K+, Ca2+, Na+, Cl−, H2PO4−, and Mg2+. The enhanced data feature based on feature enrichment (FE) of the MSAM technique provided more useful information to DKL for improving the prediction reliability of the available ISE ions and enhanced the detection of unavailable ISE ions (phosphate and magnesium). The results showed that the combined MSAM–feature enrichment (FE)–DKL sensing structure for validating ten real hydroponic samples achieved low root mean square errors (RMSE) of 63.8, 8.3, 29.2, 18.5, 11.8, and 8.8 mg·L−1 with below 8% coefficients of variation (CVs) for predicting nitrate, ammonium, potassium, calcium, sodium, and chloride, respectively. Moreover, the prediction of phosphate and magnesium in the ranges of 5–275 mg·L−1 and 10–80 mg·L−1 had RMSEs of 29.6 and 8.7 mg·L−1 respectively. The results prove that the proposed approach can be applied successfully to improve the accuracy and feasibility of ISEs in a closed hydroponic system.

The broad adoption of machine learning (ML)-based autonomous experiments (AEs) in material characterization and synthesis requires strategies development for understanding and intervention in the experimental workflow. Here, we introduce and realize a post-experimental analysis strategy for deep kernel learning-based autonomous scanning probe microscopy. This approach yields real-time and post-experimental indicators for the progression of an active learning process interacting with an experimental system. We further illustrate how this approach can be applied to human-in-the-loop AEs, where human operators make high-level decisions at high latencies setting the policies for AEs, and the ML algorithm performs low-level, fast decisions. The proposed approach is universal and can be extended to other techniques and applications such as combinatorial library analysis., Competing Interests: The authors declare no conflict of interest., (© 2023 The Author(s), Oak Ridge National Laboratory.)

Recent progress in machine learning methods and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs) have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. The discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods and can be particularly impactful for destructive or irreversible measurements.

The standard kernel method is computationally expensive because it needs to store and compute the inverse of the Gram matrix. Furthermore, the classification accuracy of the single kernel method is not effective or efficient as the method's ability to extract features. The random Fourier feature method establishes a connection between the kernel method and deep learning to solve the above problems. In this paper, we propose a novel slim deep random Fourier feature network named Slim-RFFNet, which introduces convolution into kernel learning. We use the hierarchical strategy and skip connection to construct a deep network structure and lighten the model by using quantization. Experiments conducted on classification benchmarks MNIST and CIFAR10 demonstrate that the proposed Slim-RFFNet significantly outperforms current state-of-the-art deep kernel learning methods. Our algorithm also achieves a trade-off between accuracy and latency. The proposed network can be applied to resource-constrained embedded AI devices. The experimental results on the edge computing system show that our algorithm has a small memory footprint and fast inference speed on small edge devices, and thus meets the requirements for practical applications. [ABSTRACT FROM AUTHOR]

Automated experiments in 4D scanning transmission electron microscopy (STEM) are implemented for rapid discovery of local structures, symmetry-breaking distortions, and internal electric and magnetic fields in complex materials. Deep kernel learning enables active learning of the relationship between local structure and 4D-STEM-based descriptors. With this, efficient and "intelligent" probing of dissimilar structural elements to discover desired physical functionality is made possible. This approach allows effective navigation of the sample in an automated fashion guided by either a predetermined physical phenomenon, such as strongest electric field magnitude, or in an exploratory fashion. We verify the approach first on preacquired 4D-STEM data and further implement it experimentally on an operational STEM. The experimental discovery workflow is demonstrated using graphene and subsequently extended toward a lesser-known layered 2D van der Waals material, MnPS 3 . This approach establishes a pathway for physics-driven automated 4D-STEM experiments that enable probing the physics of strongly correlated systems and quantum materials and devices, as well as exploration of beam-sensitive materials.

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference. [ABSTRACT FROM AUTHOR]

Rapid emergence of multimodal imaging in scanning probe, electron, and optical microscopies has brought forth the challenge of understanding the information contained in these complex data sets, targeting the intrinsic correlations between different channels, and further exploring the underpinning causal physical mechanisms. Here, we develop such an analysis framework for Piezoresponse Force Microscopy. We argue that under certain conditions, we can bootstrap experimental observations with the prior knowledge of materials structure to get information on certain nonobserved properties, and demonstrate linear causal analysis for PFM observables. We further demonstrate that the strength of individual causal links between complex descriptors can be ascertained using the deep kernel learning (DKL) model. In this DKL analysis, we use the prior information on domain structure within the image to predict the physical properties. This analysis demonstrates the correlative relationships between morphology, piezoresponse, elastic property, etc., at nanoscale. The prediction of morphology and other physical parameters illustrates a mutual interaction between surface condition and physical properties in ferroelectric materials. This analysis is universal and can be extended to explore the correlative relationships of other multichannel data sets, and allow for high-fidelity reconstruction of underpinning functionalities and physical mechanisms.

Ion-selective electrodes (ISEs) have recently become the most attractive tools for the development of efficient hydroponic systems. Nevertheless, some inherent shortcomings such as signal drifts, secondary ion interferences, and effected high ionic strength make them difficult to apply in a hydroponic system. To minimize these deficiencies, we combined the multivariate standard addition (MSAM) sampling technique with the deep kernel learning (DKL) model for a six ISEs array to increase the prediction accuracy and precision of eight ions, including N O 3 − , N H 4 + , K + , C a 2 + , N a + , C l − , H 2 P O 4 − , and M g 2 + . The enhanced data feature based on feature enrichment (FE) of the MSAM technique provided more useful information to DKL for improving the prediction reliability of the available ISE ions and enhanced the detection of unavailable ISE ions (phosphate and magnesium). The results showed that the combined MSAM–feature enrichment (FE)–DKL sensing structure for validating ten real hydroponic samples achieved low root mean square errors (RMSE) of 63.8, 8.3, 29.2, 18.5, 11.8, and 8.8 mg · L − 1 with below 8% coefficients of variation (CVs) for predicting nitrate, ammonium, potassium, calcium, sodium, and chloride, respectively. Moreover, the prediction of phosphate and magnesium in the ranges of 5–275 mg·L−1 and 10–80 mg · L − 1 had RMSEs of 29.6 and 8.7 mg · L − 1 respectively. The results prove that the proposed approach can be applied successfully to improve the accuracy and feasibility of ISEs in a closed hydroponic system. [ABSTRACT FROM AUTHOR]

Ion-selective electrodes (ISEs) have recently become the most attractive tools for the development of efficient hydroponic systems. Nevertheless, some inherent shortcomings such as signal drifts, secondary ion interferences, and effected high ionic strength make them difficult to apply in a hydroponic system. To minimize these deficiencies, we combined the multivariate standard addition (MSAM) sampling technique with the deep kernel learning (DKL) model for a six ISEs array to increase the prediction accuracy and precision of eight ions, including NO3-, NH4+, K+, Ca2+, Na+, Cl-, H2PO4-, and Mg2+. The enhanced data feature based on feature enrichment (FE) of the MSAM technique provided more useful information to DKL for improving the prediction reliability of the available ISE ions and enhanced the detection of unavailable ISE ions (phosphate and magnesium). The results showed that the combined MSAM-feature enrichment (FE)-DKL sensing structure for validating ten real hydroponic samples achieved low root mean square errors (RMSE) of 63.8, 8.3, 29.2, 18.5, 11.8, and 8.8 mg·L-1 with below 8% coefficients of variation (CVs) for predicting nitrate, ammonium, potassium, calcium, sodium, and chloride, respectively. Moreover, the prediction of phosphate and magnesium in the ranges of 5-275 mg·L -1 and 10-80 mg·L-1 had RMSEs of 29.6 and 8.7 mg·L-1 respectively. The results prove that the proposed approach can be applied successfully to improve the accuracy and feasibility of ISEs in a closed hydroponic system.