arXiv subjects

Mario Teixeira Parente

Publications and source records attributed to Mario Teixeira Parente.

8 recordsLinked to original sources

arXiv2025

Nicht-algebraische Didaktik nicht-diagonalisierbarer Matrizen

This article offers a motivating travel guide towards the Jordan normal form, one of the highlights in courses on linear algebra or advanced mathematics. Its itinerary is characterized by a focus on core geometric aspects and the avoidance of algebraic tools. In this way, it attempts to encourage academic lecturers from more applied mathematical contexts to devote more time to one of the most exciting structures of linear algebra in their courses, rather than rushing through it, often using just a definition. -- -- Dieser Artikel bietet einen motivierenden Reiseführer zur Jordanschen Normalform, einem der Höhepunkte in Lehrveranstaltungen zu Linearer Algebra oder Höherer Mathematik, an. Seine Reiseroute zeichnet sich durch die Besinnung auf geometrische Kernaspekte und den Verzicht auf algebraische Hilfsmittel aus. Er versucht so, Hochschuldozenten aus mathematisch angewandteren Kontexten zu ermutigen, einer der spannendsten Strukturen der Linearen Algebra mehr Zeit in ihren Lehrveranstaltungen einzuräumen, anstatt allzu hastig, und nicht selten nur mittels einer Definition, über sie hinweg zu gehen.

math.HO↗

arXiv2023

Active learning-assisted neutron spectroscopy with log-Gaussian processes

Neutron scattering experiments at three-axes spectrometers (TAS) investigate magnetic and lattice excitations by measuring intensity distributions to understand the origins of materials properties. The high demand and limited availability of beam time for TAS experiments however raise the natural question whether we can improve their efficiency and make better use of the experimenter's time. In fact, there are a number of scientific problems that require searching for signals, which may be time consuming and inefficient if done manually due to measurements in uninformative regions. Here, we describe a probabilistic active learning approach that not only runs autonomously, i.e., without human interference, but can also directly provide locations for informative measurements in a mathematically sound and methodologically robust way by exploiting log-Gaussian processes. Ultimately, the resulting benefits can be demonstrated on a real TAS experiment and a benchmark including numerous different excitations.

physics.data-an↗

arXiv2021

Autonomous Experiments for Neutron Three-Axis Spectrometers (TAS) with Log-Gaussian Processes

Autonomous experiments are excellent tools to increase the efficiency of material discovery. Indeed, AI and ML methods can help optimizing valuable experimental resources as, for example, beam time in neutron scattering experiments, in addition to scientists' knowledge and experience. Active learning methods form a particular class of techniques that acquire knowledge on a specific quantity of interest by autonomous decisions on what or where to investigate next based on previous measurements. For instance, Gaussian Process Regression (GPR) is a well-known technique that can be exploited to accomplish active learning tasks for scattering experiments as was recently demonstrated. Gaussian processes are not only capable to approximate functions by their posterior mean function, but can also quantify uncertainty about the approximation itself. Hence, if we perform function evaluations at locations of highest uncertainty, the function can be "optimally" learned in an iterative manner. We suggest the use of log-Gaussian processes, being a natural approach to successfully conduct autonomous neutron scattering experiments in general and TAS experiments with the instrument PANDA at MLZ in particular.

physics.data-an↗

arXiv2020

Generalized bounds for active subspaces

In this article, we consider scenarios in which traditional estimates for the active subspace method based on probabilistic Poincaré inequalities are not valid due to unbounded Poincaré constants. Consequently, we propose a framework that allows to derive generalized estimates in the sense that it enables to control the trade-off between the size of the Poincaré constant and a weaker order of the final error bound. In particular, we investigate independently exponentially distributed random variables in dimension two or larger and give explicit expressions for corresponding Poincaré constants showing their dependence on the dimension of the problem. Finally, we suggest possibilities for future work that aim for extending the class of distributions applicable to the active subspace method as we regard this as an opportunity to enlarge its usability.

math.PR↗

arXiv2019

Bayesian calibration and sensitivity analysis for a karst aquifer model using active subspaces

In this article, we perform a parameter study for a recently developed karst hydrological model. The study consists of a high-dimensional Bayesian inverse problem and a global sensitivity analysis. For the first time in karst hydrology, we use the active subspace method to find directions in the parameter space that dominate the Bayesian update from the prior to the posterior distribution in order to effectively reduce the dimension of the problem and for computational efficiency. Additionally, the calculated active subspace can be exploited to construct sensitivity metrics on each of the individual parameters and be used to construct a natural model surrogate. The model consists of 21 parameters to reproduce the hydrological behavior of spring discharge in a karst aquifer located in the Kerschbaum spring recharge area at Waidhofen a.d. Ybbs in Austria. The experimental spatial and time series data for the inference process were collected by the water works in Waidhofen. We show that this case study has implicit low-dimensionality, and we run an adjusted Markov chain Monte Carlo algorithm in a low-dimensional subspace to construct samples of the posterior distribution. The results are visualized and verified by plots of the posterior's push-forward distribution displaying the uncertainty in predicting discharge values due to the experimental noise in the data. Finally, a discussion provides hydrological interpretation of these results for the Kerschbaum area.

stat.CO↗

arXiv2019

A probabilistic framework for approximating functions in active subspaces

This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational problems. It can be seen as an attempt to approximate a high-dimensional function of interest $f$ by a low-dimensional one. To do this, a common approach is to integrate $f$ over the inactive, i.e. non-dominant, directions with a suitable conditional density function. In practice, this can be done with a finite Monte Carlo sum, making not only the resulting approximation random in the inactive variable for each fixed input from the active subspace, but also its expectation, i.e. the integral of the low-dimensional function weighted with a probability measure on the active variable. In this regard we develop a fully probabilistic framework extending results from (Constantine et al., 2014, 2016). The results are supported by a simple numerical example.

math.PR↗

arXiv2019

On the relation between parameters and discharge data for a lumped karst aquifer model

Hydrological models of karst aquifers are often semi-distributed, and physical processes such as infiltration and spring discharge generation are described in a lumped way. Several works have previously addressed the problems associated with the calibration of such models, highlighting in particular the issue of model parameter estimation and model equifinality. In this work, we investigate the problem of model calibration using the active subspace (AS) method, a novel tool for model parameter dimension reduction. We apply the method to a newly proposed hydrological model for karst aquifers, LuKARS, to investigate if the AS framework identifies catchment-specific characteristics or if the results only depend on the chosen model structure. Therefore, we consider four different case studies, three synthetic and one real case (Kerschbaum springshed in Waidhofen a.d. Ybbs, Austria), with varying hydrotope distributions and properties. We find that both the hydrotope area coverage and the catchment characteristics have major impacts on parameter sensitivities. While model parameters are similarly informed in scenarios with less varying catchment characteristics, we find significant differences in parameter sensitivities when the applied hydrotopes were different from each other. Our results show that the AS method can be used to investigate the relation between the model structure, the area of a hydrotope, the physical properties of a catchment and the discharge data. Finally, we successfully effectively reduce the parameter dimensions of the LuKARS model for the Kerschbaum case study using the AS method. The model with reduced parameter dimensions is able to reproduce the observed impacts of land use changes in the Kerschbaum springshed, highlighting the robustness of the hydrotope-based modeling approach of LuKARS and its applicability for land use change impact studies in karstic systems.

physics.geo-ph↗

arXiv2018

Efficient parameter estimation for a methane hydrate model with active subspaces

Methane gas hydrates have increasingly become a topic of interest because of their potential as a future energy resource. There are significant economical and environmental risks associated with extraction from hydrate reservoirs, so a variety of multiphysics models have been developed to analyze prospective risks and benefits. These models generally have a large number of empirical parameters which are not known a priori. Traditional optimization-based parameter estimation frameworks may be ill-posed or computationally prohibitive. Bayesian inference methods have increasingly been found effective for estimating parameters in complex geophysical systems. These methods often are not viable in cases of computationally expensive models and high-dimensional parameter spaces. Recently, methods have been developed to effectively reduce the dimension of Bayesian inverse problems by identifying low-dimensional structures that are most informed by data. Active subspaces is one of the most generally applicable methods of performing this dimension reduction. In this paper, Bayesian inference of the parameters of a state-of-the-art mathematical model for methane hydrates based on experimental data from a triaxial compression test with gas hydrate-bearing sand is performed in an efficient way by utilizing active subspaces. Active subspaces are used to identify low-dimensional structure in the parameter space which is exploited by generating a cheap regression-based surrogate model and implementing a modified Markov chain Monte Carlo algorithm. Posterior densities having means that match the experimental data are approximated in a computationally efficient way.

math.NA↗