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Background and aimsThe quantitative retrieval of soil organic carbon (SOC) storage, particularly for soils with a large potential for carbon sequestration, is of global interest due to its link with the carbon cycle and the mitigation of climate change. However, complex ecosystems with good soil qualities for SOC storage are poorly studied.MethodsThe interrelation between SOC and various vegetation remote sensing drivers is understood to demonstrate the link between the carbon stored in the vegetation layer and SOC of the top soil layers. Based on the mapping of SOC in two horizons (0–30 cm and 30–60 cm) we predict SOC with high accuracy in the complex and mountainous heterogeneous páramo system in Ecuador. A large SOC database (in weight % and in Mg/ha) of 493 and 494 SOC sampling data points from 0–30 cm and 30–60 cm soil profiles, respectively, were used to calibrate GPR models using Sentinel-2 and GIS predictors (i.e., Temperature, Elevation, Soil Taxonomy, Geological Unit, Slope Length and Steepness (LS Factor), Orientation and Precipitation).ResultsIn the 0–30 cm soil profile, the models achieved a R2 of 0.85 (SOC%) and a R2 of 0.79 (SOC Mg/ha). In the 30–60 cm soil profile, models achieved a R2 of 0.86 (SOC%), and a R2 of 0.79 (SOC Mg/ha).ConclusionsThe used Sentinel-2 variables (FVC, CWC, LCC/Cab, band 5 (705 nm) and SeLI index) were able to improve the estimation accuracy between 3–21% compared to previous results of the same study area. CWC emerged as the most relevant biophysical variable for SOC prediction.

Multi-fidelity modelling enables accurate inference of quantities of interest by synergistically combining realizations of low-cost/low-fidelity models with a small set of high-fidelity observations. This is particularly effective when the low- and high-fidelity models exhibit strong correlations, and can lead to significant computational gains over approaches that solely rely on high-fidelity models. However, in many cases of practical interest, low-fidelity models can only be well correlated to their high-fidelity counterparts for a specific range of input parameters, and potentially return wrong trends and erroneous predictions if probed outside of their validity regime. Here we put forth a probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent cross-correlations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends. This introduces a new class of multi-fidelity information fusion algorithms that provide a fundamental extension to the existing linear autoregressive methodologies, while still maintaining the same algorithmic complexity and overall computational cost. The performance of the proposed methods is tested in several benchmark problems involving both synthetic and real multi-fidelity datasets from computational fluid dynamics simulations.

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto–Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM–LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.

A time series is a sequence of time-ordered data, and it is generally used to describe how a phenomenon evolves over time. Time series forecasting, estimating future values of time series, allows the implementation of decision-making strategies. Deep learning, the currently leading field of machine learning, applied to time series forecasting can cope with complex and high-dimensional time series that cannot be usually handled by other machine learning techniques. The aim of the work is to provide a review of state-of-the-art deep learning architectures for time series forecasting, underline recent advances and open problems, and also pay attention to benchmark data sets. Moreover, the work presents a clear distinction between deep learning architectures that are suitable for short-term and long-term forecasting. With respect to existing literature, the major advantage of the work consists in describing the most recent architectures for time series forecasting, such as Graph Neural Networks, Deep Gaussian Processes, Generative Adversarial Networks, Diffusion Models, and Transformers.

For market players and policy officials, commodity price forecasts are crucial problems that are challenging to address due to the complexity of price time series. Given its strategic importance, corn crops are hardly an exception. The current paper evaluates the forecasting issue for China’s weekly wholesale price index for yellow corn from January 1, 2010 to January 10, 2020. We develop a Gaussian process regression model using cross validation and Bayesian optimizations over various kernels and basis functions that could effectively handle this sophisticated commodity price forecast problem. The model provides precise out-of-sample forecasts from January 4, 2019 to January 10, 2020, with a relative root mean square error, root mean square error, and mean absolute error of 1.245%, 1.605, and 0.936, respectively. The models developed here might be used by market players for market evaluations and decision-making as well as by policymakers for policy creation and execution.

Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to reformulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, reformulation is not always workable and is difficult to apply to other distributions because not all matrix-variate distributions can be transformed to respective multivariate distributions, such as the case for matrix-variate Student- t distribution. In this paper, we propose a unified framework which is used not only to introduce a novel multivariate Student- t process regression model (MV-TPR) for multi-output prediction, but also to reformulate the multivariate Gaussian process regression (MV-GPR) that overcomes some limitations of the existing methods. Both MV-GPR and MV-TPR have closed-form expressions for the marginal likelihoods and predictive distributions under this unified framework and thus can adopt the same optimization approaches as used in the conventional GPR. The usefulness of the proposed methods is illustrated through several simulated and real-data examples. In particular, we verify empirically that MV-TPR has superiority for the datasets considered, including air quality prediction and bike rent prediction. At last, the proposed methods are shown to produce profitable investment strategies in the stock markets.

Projections of commodity prices have long been a significant source of dependence for investors and the government. This study investigates the challenging topic of forecasting the daily regional steel price index in the northeast Chinese market from January 1, 2010, to April 15, 2021. The projection of this significant commodity price indication has not received enough attention in the literature. The forecasting model that is used is Gaussian process regressions, which are trained using a mix of cross-validation and Bayesian optimizations. The models that were built precisely predicted the price indices between January 8, 2019, and April 15, 2021, with an out-of-sample relative root mean square error of 0.5432%. Investors and government officials can use the established models to study pricing and make judgments. Forecasting results can help create comparable commodity price indices when reference data on the price trends suggested by these models are used.

The main objective of this research is to investigate the potential combination of Sentinel-2A and ALOS-2 PALSAR-2 (Advanced Land Observing Satellite -2 Phased Array type L-band Synthetic Aperture Radar-2) imagery for improving the accuracy of the Aboveground Biomass (AGB) measurement. According to the current literature, this kind of investigation has rarely been conducted. The Hyrcanian forest area (Iran) is selected as the case study. For this purpose, a total of 149 sample plots for the study area were documented through fieldwork. Using the imagery, three datasets were generated including the Sentinel-2A dataset, the ALOS-2 PALSAR-2 dataset, and the combination of the Sentinel-2A dataset and the ALOS-2 PALSAR-2 dataset (Sentinel-ALOS). Because the accuracy of the AGB estimation is dependent on the method used, in this research, four machine learning techniques were selected and compared, namely Random Forests (RF), Support Vector Regression (SVR), Multi-Layer Perceptron Neural Networks (MPL Neural Nets), and Gaussian Processes (GP). The performance of these AGB models was assessed using the coefficient of determination (R2), the root-mean-square error (RMSE), and the mean absolute error (MAE). The results showed that the AGB models derived from the combination of the Sentinel-2A and the ALOS-2 PALSAR-2 data had the highest accuracy, followed by models using the Sentinel-2A dataset and the ALOS-2 PALSAR-2 dataset. Among the four machine learning models, the SVR model (R2 = 0.73, RMSE = 38.68, and MAE = 32.28) had the highest prediction accuracy, followed by the GP model (R2 = 0.69, RMSE = 40.11, and MAE = 33.69), the RF model (R2 = 0.62, RMSE = 43.13, and MAE = 35.83), and the MPL Neural Nets model (R2 = 0.44, RMSE = 64.33, and MAE = 53.74). Overall, the Sentinel-2A imagery provides a reasonable result while the ALOS-2 PALSAR-2 imagery provides a poor result of the forest AGB estimation. The combination of the Sentinel-2A imagery and the ALOS-2 PALSAR-2 imagery improved the estimation accuracy of AGB compared to that of the Sentinel-2A imagery only.

Multi-output Gaussian processes (MOGPs) can help to improve predictive performance for some output variables, by leveraging the correlation with other output variables. In this paper, our main motivation is to use multiple-output Gaussian processes to exploit correlations between outputs where each output is a multi-class classification problem. MOGPs have been mostly used for multi-output regression. There are some existing works that use MOGPs for other types of outputs, e.g., multi-output binary classification. However, MOGPs for multi-class classification has been less studied. The reason is twofold: 1) when using a softmax function, it is not clear how to scale it beyond the case of a few outputs; 2) most common type of data in multi-class classification problems consists of image data, and MOGPs are not specifically designed to image data. We thus propose a new MOGPs model called Multi-output Gaussian Processes with Augment & Reduce (MOGPs-AR) that can deal with large scale classification and downsized image input data. Large scale classification is achieved by subsampling both training data sets and classes in each output whereas downsized image input data is handled by incorporating a convolutional kernel into the new model. We show empirically that our proposed model outperforms single-output Gaussian processes in terms of different performance metrics and multi-output Gaussian processes in terms of scalability, both in synthetic and in real classification problems. We include an example with the Ommiglot dataset where we showcase the properties of our model.

Laser Powder-Bed Fusion (L-PBF) metal-based additive manufacturing (AM) is complex and not fully understood. Successful processing for one material, might not necessarily apply to a different material. This paper describes a workflow process that aims at creating a material data sheet standard that describes regimes where the process can be expected to be robust. The procedure consists of building a Gaussian process-based surrogate model of the L-PBF process that predicts melt pool depth in single-track experiments given a laser power, scan speed, and laser beam size combination. The predictions are then mapped onto a power versus scan speed diagram delimiting the conduction from the keyhole melting controlled regimes. This statistical framework is shown to be robust even for cases where experimental training data might be suboptimal in quality, if appropriate physics-based filters are applied. Additionally, it is demonstrated that a high-fidelity simulation model of L-PBF can equally be successfully used for building a surrogate model, which is beneficial since simulations are getting more efficient and are more practical to study the response of different materials, than to re-tool an AM machine for new material powder.