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We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equation in engineering and physics, the stochastic Landau-Lifshitz-Gilbert equation poses many interesting challenges that do not appear simultaneously in previous works on uncertainty quantification: The equation is strongly non-linear, time-dependent, and has a non-convex side constraint. Moreover, the parametrization of the stochastic noise features countably many unbounded parameters and low regularity compared to other elliptic and parabolic problems studied in uncertainty quantification. We use a novel technique to establish uniform holomorphic regularity of the parameter-to-solution map based on a Gronwall-type estimate and the implicit function theorem. This method is very general and based on a set of abstract assumptions. Thus, it can be applied beyond the Landau-Lifshitz-Gilbert equation as well. We demonstrate numerically the feasibility of approximating with sparse grid and show a clear advantage of a multi-level sparse grid scheme., Comment: 36 pages, 4 figures

The European Space Agency is well known as a powerful force for scientific discovery in numerous areas related to Space. The amount and depth of the knowledge produced throughout the different missions carried out by ESA and their contribution to scientific progress is enormous, involving large collections of documents like scientific publications, feasibility studies, technical reports, and quality management procedures, among many others. Through initiatives like the Open Space Innovation Platform, ESA also acts as a hub for new ideas coming from the wider community across different challenges, contributing to a virtuous circle of scientific discovery and innovation. Handling such wealth of information, of which large part is unstructured text, is a colossal task that goes beyond human capabilities, hence requiring automation. In this paper, we present a methodological framework based on artificial intelligence and natural language processing and understanding to automatically extract information from Space documents, generating value from it, and illustrate such framework through several case studies implemented across different functional areas of ESA, including Mission Design, Quality Assurance, Long-Term Data Preservation, and the Open Space Innovation Platform. In doing so, we demonstrate the value of these technologies in several tasks ranging from effortlessly searching and recommending Space information to automatically determining how innovative an idea can be, answering questions about Space, and generating quizzes regarding quality procedures. Each of these accomplishments represents a step forward in the application of increasingly intelligent AI systems in Space, from structuring and facilitating information access to intelligent systems capable to understand and reason with such information.

ESA's INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) was launched on 17 Oct 2002 at 06:41 CEST. Since then, it has been providing long, uninterrupted observations (up to about 47 hr, or 170 ksec, per satellite orbit of 2.7 days) with a large field-of-view (fully coded: 100 deg^2), msec time resolution, keV energy resolution, polarization measurements, as well as additional coverage in the optical. This is realized by two main instruments in the 15 keV to 10 MeV range, the spectrometer SPI (spectral resolution 3 keV at 1.8 MeV) and the imager IBIS (angular resolution 12 arcmin FWHM), complemented by X-ray (JEM-X; 3-35 keV) and optical (OMC; Johnson V-band) monitors. All instruments are co-aligned to simultaneously observe the target region. A particle radiation monitor (IREM) measures charged particle fluxes near the spacecraft. The Anti-coincidence subsystems of the main instruments are also efficient all-sky gamma-ray detectors, which provide omni-directional monitoring above ~75 keV. INTEGRAL can also rapidly (within a couple of hours) re-point and conduct Target of Opportunity observations. INTEGRAL has build an impressive legacy: e.g. discovery of >600 new high-energy sources; first-ever direct detection of 56Ni and 56Co radio-active decay lines from a Type Ia supernova; new insights on positron annihilation in the Galactic bulge and disk; pioneering gamma-ray polarization studies. INTEGRAL is also a successful in multi-messenger astronomy: INTEGRAL found the first prompt electromagnetic radiation in coincidence with a binary neutron star merger. More than 1750 papers based on INTEGRAL data have been published in refereed journals. Here we give a comprehensive update of the satellite status after more than 18 years of operations in a harsh space environment, and an account of the successful Ground Segment., Comment: 29 pages, 20 figures, accepted for publication in special issue of New Astronomy Reviews

We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an adaptive algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.