Showing papers on "Gaussian process published in 2022"

Predicting elemental stiffness matrix of FG nanoplates using Gaussian Process Regression based surrogate model in framework of layerwise model

Abstract: The accuracy of predicting the behaviour of structure using finite element (FE) depends widely on the precision of the evaluation of the stiffness matrix. In the present article, an attempt has been made to evaluate the stiffness matrix of functionally graded (FG) nanoplate using Gaussian process regression (GPR) based surrogate model in the framework of the layerwise theory. The stiffness matrix comprises various matrix terms corresponding to the membrane, membrane-bending, bending-membrane, and bending and shear. Following two different methodologies are adopted for predicting the stiffness matrix at the elemental level, one in which the final elemental stiffness matrix is evaluated, and the second one in which all the matrix terms as stated are evaluated separately using the GPR surrogate model and then are added to get the final stiffness matrix at the elemental level. The effectiveness of both approaches has been worked out by comparing the present results with those available in the literature. Both the proposed methodologies can predict the behaviour of FG nanoplates with good accuracy. However, the second one is found to be outstanding.

A proficient approach to forecast COVID-19 spread via optimized dynamic machine learning models

Abstract: Abstract This study aims to develop an assumption-free data-driven model to accurately forecast COVID-19 spread. Towards this end, we firstly employed Bayesian optimization to tune the Gaussian process regression (GPR) hyperparameters to develop an efficient GPR-based model for forecasting the recovered and confirmed COVID-19 cases in two highly impacted countries, India and Brazil. However, machine learning models do not consider the time dependency in the COVID-19 data series. Here, dynamic information has been taken into account to alleviate this limitation by introducing lagged measurements in constructing the investigated machine learning models. Additionally, we assessed the contribution of the incorporated features to the COVID-19 prediction using the Random Forest algorithm. Results reveal that significant improvement can be obtained using the proposed dynamic machine learning models. In addition, the results highlighted the superior performance of the dynamic GPR compared to the other models (i.e., Support vector regression, Boosted trees, Bagged trees, Decision tree, Random Forest, and XGBoost) by achieving an averaged mean absolute percentage error of around 0.1%. Finally, we provided the confidence level of the predicted results based on the dynamic GPR model and showed that the predictions are within the 95% confidence interval. This study presents a promising shallow and simple approach for predicting COVID-19 spread.

A proficient approach to forecast COVID-19 spread via optimized dynamic machine learning models

Abstract: Abstract This study aims to develop an assumption-free data-driven model to accurately forecast COVID-19 spread. Towards this end, we firstly employed Bayesian optimization to tune the Gaussian process regression (GPR) hyperparameters to develop an efficient GPR-based model for forecasting the recovered and confirmed COVID-19 cases in two highly impacted countries, India and Brazil. However, machine learning models do not consider the time dependency in the COVID-19 data series. Here, dynamic information has been taken into account to alleviate this limitation by introducing lagged measurements in constructing the investigated machine learning models. Additionally, we assessed the contribution of the incorporated features to the COVID-19 prediction using the Random Forest algorithm. Results reveal that significant improvement can be obtained using the proposed dynamic machine learning models. In addition, the results highlighted the superior performance of the dynamic GPR compared to the other models (i.e., Support vector regression, Boosted trees, Bagged trees, Decision tree, Random Forest, and XGBoost) by achieving an averaged mean absolute percentage error of around 0.1%. Finally, we provided the confidence level of the predicted results based on the dynamic GPR model and showed that the predictions are within the 95% confidence interval. This study presents a promising shallow and simple approach for predicting COVID-19 spread.

A Multioutput Convolved Gaussian Process for Capacity Forecasting of Li-Ion Battery Cells

Abstract: A latent function decomposition method is proposed for forecasting the capacity of lithium-ion battery cells. The method uses the multioutput convolved Gaussian process (MCGP), a machine learning framework for multitask and transfer learning. The MCGP decomposes the available capacity trends from multiple battery cells into latent functions. The latent functions are then convolved with optimized kernel smoothers to reconstruct and forecast the capacity trends. The latent functions capture nontrivial cross correlations between the capacity trends of the available battery cells. The MCGP also provides uncertainty quantification for its predictions. These two merits make the proposed MCGP a very reliable and practical solution for applications that use battery cell packs. The MCGP is derived and compared to benchmark methods on two experimental lithium-ion battery cells datasets. The results show the effectiveness of the proposed MCGP for long-term capacity forecasting.

The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running

Abstract: Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert spaces, and graph based models. This article describes how the stochastic partial differential equation approach to generalising Matérn covariance models via Hilbert space projections connects with several of these approaches, with each connection being useful in different situations. In addition to an overview of the main ideas, some important extensions, theory, applications, and other recent developments are discussed. The methods include both Markovian and non-Markovian models, non-Gaussian random fields, non-stationary fields and space–time fields on arbitrary manifolds, and practical computational considerations.

Robust Deep Gaussian Process-Based Probabilistic Electrical Load Forecasting Against Anomalous Events

Abstract: The abnormal events, such as the unprecedented COVID-19 pandemic, can significantly change the load behaviors, leading to huge challenges for traditional short-term forecasting methods. This article proposes a robust deep Gaussian processes (DGP)-based probabilistic load forecasting method using a limited number of data. Since the proposed method only requires a limited number of training samples for load forecasting, it allows us to deal with extreme scenarios that cause short-term load behavior changes. In particular, the load forecasting at the beginning of abnormal event is cast as a regression problem with limited training samples and solved by double stochastic variational inference DGP. The mobility data are also utilized to deal with the uncertainties and pattern changes and enhance the flexibility of the forecasting model. The proposed method can quantify the uncertainties of load forecasting outcomes, which would be essential under uncertain inputs. Extensive comparison results with other state-of-the-art point and probabilistic forecasting methods show that our proposed approach can achieve high forecasting accuracies with only a limited number of data while maintaining the excellent performance of capturing the forecasting uncertainties.

Vecchia-approximated Deep Gaussian Processes for Computer Experiments

Abstract: Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent literature. A “big data” regime, prevalent in machine learning, favors approximate, optimization-based inference for fast, high-fidelity prediction. A “small data” regime, preferred for computer surrogate modeling, deploys posterior integration for enhanced uncertainty quantification (UQ). We aim to bridge this gap by expanding the capabilities of Bayesian DGP posterior inference through the incorporation of the Vecchia approximation, allowing linear computational scaling without compromising accuracy or UQ. We are motivated by surrogate modeling of simulation campaigns with upwards of 100,000 runs – a size too large for previous fully-Bayesian implementations – and demonstrate prediction and UQ superior to that of “big data” competitors. All methods are implemented in the deepgp package on CRAN.

Physics-informed machine learning modeling for predictive control using noisy data

Abstract: Due to the occurrence of over-fitting at the learning phase, the modeling of chemical processes via artificial neural networks (ANN) by using corrupted data (i.e., noisy data) is an ongoing challenge. Therefore, this work investigates the effect of both Gaussian and non-Gaussian noise on the performance of process-structure based recurrent neural networks (RNN) models, which take the form of partially-connected RNN models in this work, that are used to approximate a class of multi-input-multi-outputs nonlinear systems. Furthermore, two different techniques, specifically Monte Carlo dropout and co-teaching, are utilized in the development of partially-connected RNN models. These two techniques are employed to reduce the over-fitting in ANNs when noisy data is used in the training process and, hence, to improve the open-loop accuracy as well as the closed-loop performance under a Lyapunov-based model predictive controller (MPC). Aspen Plus Dynamics, a well-known high-fidelity process simulator, is used to simulate a large-scale chemical process application in order to demonstrate the anticipated improvements in both open-loop approximation and closed-loop controller performance in the presence of Gaussian and non-Gaussian noise in the data set using physics-informed RNNs. • ML model structure is determined by process structure. • Measurement data noise is handled via data dropout in training. • ML model is used in model predictive control. • Comparisons with existing approaches are carried out to evaluate the approach.

A Survey of Uncertainty Quantification in Machine Learning for Space Weather Prediction

Abstract: With the availability of data and computational technologies in the modern world, machine learning (ML) has emerged as a preferred methodology for data analysis and prediction. While ML holds great promise, the results from such models are not fully unreliable due to the challenges introduced by uncertainty. An ML model generates an optimal solution based on its training data. However, if the uncertainty in the data and the model parameters are not considered, such optimal solutions have a high risk of failure in actual world deployment. This paper surveys the different approaches used in ML to quantify uncertainty. The paper also exhibits the implications of quantifying uncertainty when using ML by performing two case studies with space physics in focus. The first case study consists of the classification of auroral images in predefined labels. In the second case study, the horizontal component of the perturbed magnetic field measured at the Earth’s surface was predicted for the study of Geomagnetically Induced Currents (GICs) by training the model using time series data. In both cases, a Bayesian Neural Network (BNN) was trained to generate predictions, along with epistemic and aleatoric uncertainties. Finally, the pros and cons of both Gaussian Process Regression (GPR) models and Bayesian Deep Learning (DL) are weighed. The paper also provides recommendations for the models that need exploration, focusing on space weather prediction.

Scalable Gaussian Processes for Data-Driven Design Using Big Data With Categorical Factors

Abstract: Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have difficulties in accommodating big datasets, categorical inputs, and multiple responses, which has become a common challenge for a growing number of data-driven design applications. In this paper, we propose a GP model that utilizes latent variables and functions obtained through variational inference to address the aforementioned challenges simultaneously. The method is built upon the latent variable Gaussian process (LVGP) model where categorical factors are mapped into a continuous latent space to enable GP modeling of mixed-variable datasets. By extending variational inference to LVGP models, the large training dataset is replaced by a small set of inducing points to address the scalability issue. Output response vectors are represented by a linear combination of independent latent functions, forming a flexible kernel structure to handle multiple responses that might have distinct behaviors. Comparative studies demonstrate that the proposed method scales well for large datasets with over 10^4 data points, while outperforming state-of-the-art machine learning methods without requiring much hyperparameter tuning. In addition, an interpretable latent space is obtained to draw insights into the effect of categorical factors, such as those associated with building blocks of architectures and element choices in metamaterial and materials design. Our approach is demonstrated for machine learning of ternary oxide materials and topology optimization of a multiscale compliant mechanism with aperiodic microstructures and multiple materials.

A Multioutput Convolved Gaussian Process for Capacity Forecasting of Li-Ion Battery Cells

Abstract: A latent function decomposition method is proposed for forecasting the capacity of lithium-ion battery cells. The method uses the Multi-Output Gaussian Process, a generative machine learning framework for multi-task and transfer learning. The MCGP decomposes the available capacity trends from multiple battery cells into latent functions. The latent functions are then convolved over kernel smoothers to reconstruct and/or forecast capacity trends of the battery cells. Besides the high prediction accuracy the proposed method possesses, it provides uncertainty information for the predictions and captures nontrivial cross-correlations between capacity trends of different battery cells. These two merits make the proposed MCGP a very reliable and practical solution for applications that use battery cell packs. The MCGP is derived and compared to benchmark methods on an experimental lithium-ion battery cells data. The results show the effectiveness of the proposed method.