Mobile robots are a key component for the automation of many tasks that either require high precision or are deemed too hazardous for human personnel. One of the typical duties for mobile robots in the industrial sector is to perform trajectory tracking, which involves pursuing a specific path through both space and time. In this paper, an iterative learning-based procedure for highly accurate tracking is proposed. This contribution shows how data-based techniques, namely Gaussian process regression, can be used to tailor a motion model to a specific reoccurring reference. The procedure is capable of explorative behavior meaning that the robot automatically explores states around the prescribed trajectory, enriching the data set for learning and increasing the robustness and practical training accuracy. The trade-off between highly accurate tracking and exploration is done automatically by an optimization-based reference generator using a suitable cost function minimizing the posterior variance of the underlying Gaussian process model. While this study focuses on omnidirectional mobile robots, the scheme can be applied to a wide range of mobile robots. The effectiveness of this approach is validated in meaningful real-world experiments on a custom-built omnidirectional mobile robot where it is shown that explorative behavior can outperform purely exploitative approaches.

Simulations of future climate contain variability arising from a number of sources, including internal stochasticity and external forcings. However, to the best of our abilities climate models and the true observed climate depend on the same underlying physical processes. In this paper, we simultaneously study the outputs of multiple climate simulation models and observed data, and we seek to leverage their mean structure as well as interdependencies that may reflect the climate’s response to shared forcings. Bayesian modeling provides a fruitful ground for the nuanced combination of multiple climate simulations. We introduce one such approach whereby a Gaussian process is used to represent a mean function common to all simulated and observed climates. Dependent random effects encode possible information contained within and between the plurality of climate model outputs and observed climate data. We propose an empirical Bayes approach to analyze such models in a computationally efficient way. This methodology is amenable to the CMIP6 model ensemble, and we demonstrate its efficacy at forecasting global average near-surface air temperature. Results suggest that this model and the extensions it engenders may provide value to climate prediction and uncertainty quantification.

Wind turbine towers are subjected to highly varying internal loads, characterized by large uncertainty. The uncertainty stems from many factors, including what the actual wind fields experienced over time will be, modeling uncertainties given the various operational states of the turbine with and without controller interaction, the influence of aerodynamic damping, and so forth. To monitor the true experienced loading and assess the fatigue, strain sensors can be installed at fatigue-critical locations on the turbine structure. A more cost-effective and practical solution is to predict the strain response of the structure based only on a number of acceleration measurements. In this contribution, an approach is followed where the dynamic strains in an existing onshore wind turbine tower are predicted using a Gaussian process latent force model. By employing this model, both the applied dynamic loading and strain response are estimated based on the acceleration data. The predicted dynamic strains are validated using strain gauges installed near the bottom of the tower. Fatigue is subsequently assessed by comparing the damage equivalent loads calculated with the predicted as opposed to the measured strains. The results confirm the usefulness of the method for continuous tracking of fatigue life consumption in onshore wind turbine towers.

Tree-ring chronologies encode interannual variability in forest growth rates over long time periods from decades to centuries or even millennia. However, each chronology is a highly localized measurement describing conditions at specific sites where wood samples have been collected. The question whether these local growth variabilites are representative for large geographical regions remains an open issue. To overcome the limitations of interpreting a sparse network of sites, we propose an upscaling approach for annual tree-ring indices that approximate forest growth variability and compute gridded data products that generalize the available information for multiple tree genera. Using regression approaches from machine learning, we predict tree-ring indices in space and time based on climate variables, but considering also species range maps as constraints for the upscaling. We compare various prediction strategies in cross-validation experiments to identify the best performing setup. Our estimated maps of tree-ring indices are the first data products that provide a dense view on forest growth variability at the continental level with 0.5° and 0.0083° spatial resolution covering the years 1902–2013. Furthermore, we find that different genera show very variable spatial patterns of anomalies. We have selected Europe as study region and focused on the six most prominent tree genera, but our approach is very generic and can easily be applied elsewhere. Overall, the study shows perspectives but also limitations for reconstructing spatiotemporal dynamics of complex biological processes. The data products are available at https://www.doi.org/10.17871/BACI.248.

Reduced-order models (ROMs) are computationally inexpensive simplifications of high-fidelity complex ones. Such models can be found in computational fluid dynamics where they can be used to predict the characteristics of multiphase flows. In previous work, we presented a ROM analysis framework that coupled compression techniques, such as autoencoders, with Gaussian process regression in the latent space. This pairing has significant advantages over the standard encoding–decoding routine, such as the ability to interpolate or extrapolate in the initial conditions’ space, which can provide predictions even when simulation data are not available. In this work, we focus on this major advantage and show its effectiveness by performing the pipeline on three multiphase flow applications. We also extend the methodology by using deep Gaussian processes as the interpolation algorithm and compare the performance of our two variations, as well as another variation from the literature that uses long short-term memory networks, for the interpolation.

Electromagnetic simulation software has become an important tool for antenna design. However, high-fidelity simulation of wideband or ultra-wideband antennas is very expensive. Therefore, antenna optimization design by using an electromagnetic solver may be limited due to its high computational cost. This problem can be alleviated by the utilization of fast and accurate surrogate models. Unfortunately, conventional surrogate models for antenna design are usually prohibitive because training data acquisition is time-consuming. In order to solve the problem, a modeling method named progressive Gaussian process (PGP) is proposed in this study. Specially, when a Gaussian process (GP) is trained, test sample with the largest predictive variance is inputted into an electromagnetic solver to simulate its results. After that, the test sample is added to the training set to train the GP progressively. The process can incrementally increase some important trusted training data and improve the model generalization performance. Based on the proposed PGP, two monopole antennas are optimized. The optimization results show effectiveness and efficiency of the method.

This paper studies the joint tail asymptotics of extrema of the multi-dimensional Gaussian process over random intervals defined as $P(u)\;:\!=\; \mathbb{P}\{\cap_{i=1}^n (\sup_{t\in[0,\mathcal{T}_i]} ( X_{i}(t) +c_i t )>a_i u )\}$ , $u\rightarrow\infty$ , where $X_i(t)$ , $t\ge0$ , $i=1,2,\ldots,n$ , are independent centered Gaussian processes with stationary increments, $\boldsymbol{\mathcal{T}}=(\mathcal{T}_1, \ldots, \mathcal{T}_n)$ is a regularly varying random vector with positive components, which is independent of the Gaussian processes, and $c_i\in \mathbb{R}$ , $a_i>0$ , $i=1,2,\ldots,n$ . Our result shows that the structure of the asymptotics of P(u) is determined by the signs of the drifts $c_i$ . We also discuss a relevant multi-dimensional regenerative model and derive the corresponding ruin probability.

We present a hierarchical Dirichlet regression model with Gaussian process priors that enables accurate and well-calibrated forecasts for U.S. Senate elections at varying time horizons. This Bayesian model provides a balance between predictions based on time-dependent opinion polls and those made based on fundamentals. It also provides uncertainty estimates that arise naturally from historical data on elections and polls. Experiments show that our model is highly accurate and has a well calibrated coverage rate for vote share predictions at various forecasting horizons. We validate the model with a retrospective forecast of the 2018 cycle as well as a true out-of-sample forecast for 2020. We show that our approach achieves state-of-the art accuracy and coverage despite relying on few covariates.

We study, under mild conditions, the weak approximation constructed from a standard Poisson process for a class of Gaussian processes, and establish its sample path moderate deviations. The techniques consist of a good asymptotic exponential approximation in moderate deviations, the Besov–Lèvy modulus embedding, and an exponential martingale technique. Moreover, our results are applied to the weak approximations associated with the moving average of Brownian motion, fractional Brownian motion, and an Ornstein–Uhlenbeck process.

We investigate joint modelling of longevity trends using the spatial statistical framework of Gaussian process (GP) regression. Our analysis is motivated by the Human Mortality Database (HMD) that provides unified raw mortality tables for nearly 40 countries. Yet few stochastic models exist for handling more than two populations at a time. To bridge this gap, we leverage a spatial covariance framework from machine learning that treats populations as distinct levels of a factor covariate, explicitly capturing the cross-population dependence. The proposed multi-output GP models straightforwardly scale up to a dozen populations and moreover intrinsically generate coherent joint longevity scenarios. In our numerous case studies, we investigate predictive gains from aggregating mortality experience across nations and genders, including by borrowing the most recently available “foreign” data. We show that in our approach, information fusion leads to more precise (and statistically more credible) forecasts. We implement our models in R, as well as a Bayesian version in Stan that provides further uncertainty quantification regarding the estimated mortality covariance structure. All examples utilise public HMD datasets.

For a zero-mean, unit-variance stationary univariate Gaussian process we derive the probability that a record at the time n, say $X_n$ , takes place, and derive its distribution function. We study the joint distribution of the arrival time process of records and the distribution of the increments between records. We compute the expected number of records. We also consider two consecutive and non-consecutive records, one at time j and one at time n, and we derive the probability that the joint records $(X_j,X_n)$ occur, as well as their distribution function. The probability that the records $X_n$ and $(X_j,X_n)$ take place and the arrival time of the nth record are independent of the marginal distribution function, provided that it is continuous. These results actually hold for a strictly stationary process with Gaussian copulas.

We obtain an asymptotic formula for the persistence probability in the positive real line of a random polynomial arising from evolutionary game theory. It corresponds to the probability that a multi-player two-strategy random evolutionary game has no internal equilibria. The key ingredient is to approximate the sequence of random polynomials indexed by their degrees by an appropriate centered stationary Gaussian process.

Let Xn(k) be the number of vertices at level k in a random recursive tree with n+1 vertices. We are interested in the asymptotic behavior of Xn(k) for intermediate levels k=kn satisfying kn→∞ and kn=o(logn) as n→∞. In particular, we prove weak convergence of finite-dimensional distributions for the process (Xn ([knu]))u>0, properly normalized and centered, as n→∞. The limit is a centered Gaussian process with covariance (u,v)↦(u+v)−1. One-dimensional distributional convergence of Xn(kn), properly normalized and centered, was obtained with the help of analytic tools by Fuchs et al. (2006). In contrast, our proofs, which are probabilistic in nature, exploit a connection of our model with certain Crump–Mode–Jagers branching processes.

Brown‒Resnick processes are max-stable processes that are associated to Gaussian processes. Their simulation is often based on the corresponding spectral representation which is not unique. We study to what extent simulation accuracy and efficiency can be improved by minimizing the maximal variance of the underlying Gaussian process. Such a minimization is a difficult mathematical problem that also depends on the geometry of the simulation domain. We extend Matheron's (1974) seminal contribution in two directions: (i) making his description of a minimal maximal variance explicit for convex variograms on symmetric domains, and (ii) proving that the same strategy also reduces the maximal variance for a huge class of nonconvex variograms representable through a Bernstein function. A simulation study confirms that our noncostly modification can lead to substantial improvements among Gaussian representations. We also compare it with three other established algorithms.