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The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational grids for such problems often remains one of the main bottlenecks. The use of a domain partitioning with non-conforming grids is a possible solution, which, however, requires the development of robust and efficient inter-grid interpolation operators to transfer a scalar or a vector field from one domain to another. This work presents a novel approach for interpolating quantities across non-conforming meshes within the framework of the classical mortar method, where weak continuity conditions are enforced. The key contribution is the introduction of a novel strategy that uses mesh-free Radial Basis Function (RBF) interpolations to compute the mortar integral, offering a compelling alternative to traditional projection-based methods. We propose an efficient algorithm tailored for complex three-dimensional settings allowing for potentially significant savings in the overall computational cost and ease of implementation, with no detrimental effects on the numerical accuracy. The formulation, analysis, and validation of the proposed RBF-based algorithm is discussed with the aid of a set of numerical examples, demonstrating its effectiveness. Furthermore, the details of the implementation are discussed and a test case involving a complex geometry is presented, to illustrate the applicability and advantages of our approach in real-world problems., Comment: 36 pages, 20 figures, 2 tables

Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of governing parameters, and data errors challenge the reliability of predictions. In the absence of direct measurements, inverse modeling and stochastic data assimilation methods can offer reliable solutions, but in complex and large-scale settings, the computational expense can become prohibitive. To address these challenges, this paper presents a deep learning-based surrogate model (SurMoDeL) designed for seismic data assimilation in fault activation modeling. The surrogate model leverages neural networks to provide simplified yet accurate representations of complex geophysical systems, enabling faster simulations and analyses essential for uncertainty quantification. The work proposes two different methods to integrate an understanding of fault behavior into the model, thereby enhancing the accuracy of its predictions. The application of the proxy model to integrate seismic data through effective data assimilation techniques efficiently constrains the uncertain parameters, thus bridging the gap between theoretical models and real-world observations.

Underground gas storage is a versatile tool for managing energy resources and addressing pressing environmental concerns. While natural gas is stored in geological formations since the beginning of the 20th century, hydrogen has recently been considered as a potential candidate toward a more flexible and sustainable energy infrastructure. Furthermore, these formations can also be used to sequester environmentally harmful gases such as CO2. When such operations are implemented in faulted basins, however, safety concerns may arise due to the possible reactivation of pre-existing faults, which could result in (micro)-seismicity events. In the Netherlands, it has been recently noted that fault reactivation can occur "unexpectedly" during the life of an underground gas storage (UGS) site, even when stress conditions are not expected to cause a failure. The present two-part work aims to develop a modeling framework to investigate the physical mechanisms causing such occurrences and define a safe operational bandwidth for pore pressure variation for UGS operations in the faulted reservoirs of the Rotliegend formation, the Netherlands. In this follow-up paper, we investigate in detail the mechanisms and crucial factors that result in fault reactivation at various stages of a UGS. The mathematical and numerical model described in Part I is used, also accounting for the effect of geochemical dissolution on reservoir and caprock weakening. TThe study investigates the risks of fault activation caused by the storage of different fluids for various purposes, such as long-term CO2 sequestration, CH4 and N2 injection and extraction cycles, and N2 permanent storage. The results show how geomechanical properties and reservoir operating conditions may increase the risk of fault reactivation at various UGS stages. Finally, operational guidelines for improving secure storage operations are presented., Comment: 31 pages, 24 figures, 4 tables

Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics during an epidemic. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to change in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and provide an estimate of the model state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the COVID-19 Italian pandemic. Our results show that the split implementation of PINNs outperforms the standard approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%).

Underground gas storage (UGS) is a worldwide well-established technology that is becoming even more important to cope with seasonal peaks of gas consumption due to the growing uncertainties of the energy market. Safety issues concerning the reactivation of pre-existing faults might arise if the target reservoir is located in a faulted basin, where human activities can trigger (micro-)seismicity events. In the Netherlands, it has been observed that fault activation can occur somehow "unexpectedly" after the primary production (PP), i.e., during cushion gas injection (CGI) and UGS cycles, when the stress regime should be in the unloading/reloading path. To understand the physical mechanisms responsible for such occurrences, a 3D mathematical model coupling frictional contact mechanics in faulted porous rocks with fluid flow is developed, implemented and tested. The final aim of this two-part work is to define a safe operational bandwidth for the pore pressure range for UGS activities in the faulted reservoirs of the Rotliegend formation. Part I of this work concerns the development of the mathematical and numerical model of frictional contact mechanics and flow in faulted porous rocks. A mixed discretization of the governing PDEs under frictional contact constraints along the faults is used. A slip-weakening constitutive law governing the fault macroscopic behavior is also presented. The model is tested in the setting of an ideal reservoir located in the Rotliegend formation. The analyses point out how fault reactivation during PP can lead to a stress redistribution, giving rise to a new equilibrium configuration. When the fault is reloaded in the opposite direction during the CGI and/or UGS stages, further activation events can occur even if the stress range does not exceed either the undisturbed initial value or the maximum strength ever experienced by the formation., Comment: 22 pages, 20 figures

This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a $3 \times 3$ block-structured Jacobian matrix with a $2 \times 2$ inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner $2 \times 2$ structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.

We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling parameter aimed at avoiding unwanted clustering of eigenvalues of the preconditioned matrices at the extrema of the spectrum. We use this preconditioned framework to solve a $3 \times 3$ block system arising in the simulation of fluid flow in large-size discrete fractured networks. We apply our polynomial preconditioner to a suitable Schur complement related with this system, which can not be explicitly computed because of its size and density. Numerical results confirm the excellent properties of the proposed preconditioner up to very high polynomial degrees. The parallel implementation achieves satisfactory scalability by taking advantage from the reduced number of scalar products and hence of global communications.

The AMS-02 collaboration recently released cosmic-ray F/Si data of unprecedented accuracy. Cosmic-ray (CR) fluorine is predominantly produced by fragmentation of heavier progenitors, while silicon is mostly accelerated at source. This ratio is thus maximally sensitive to CR propagation. We study the compatibility of the transport parameters derived from the F/Si ratio with those obtained from the lighter (Li,Be,B)/C ratios. We also inspect the CR source abundance of F, one of the few elements with a high first ionisation potential but only moderately volatile, and a potentially key element to study the acceleration mechanism of CRs. We use the 1D diffusion model implemented in the USINE code and perform $\chi^2$ analyses accounting for several systematic effects (energy correlations in data, nuclear cross sections and solar modulation uncertainties). We also take advantage of the EXFOR nuclear database to update the F production cross sections for its most important progenitors (identified to be 56Fe, 32S, 28Si, 27Al, 24Mg, 22Ne, and 20Ne). The transport parameters obtained from AMS-02 F/Si data are compatible with those obtained from AMS-02 (Li,Be,B)/C data. The combined fit of all these ratios leads to a chi2/dof$\approx 1.1$, with $\lesssim 10\%$ adjustments of the B and F production cross sections (the latter are based on very few nuclear data points, and would strongly benefit from new measurements). The F/Si ratio is compatible with a pure secondary origin of F, with a best-fit relative source abundance (19F/28Si)$\sim 10^{-3}$ and an upper limit of $\sim 5\times 10^{-3}$. Unfortunately, this limit is not sufficient to test global acceleration models of CR nuclei, for which values at the level of $\sim 10^{-4}$ are required. Such levels could be attained with F/Si data of a few percent accuracy at a few tens of TV, possibly within reach of the next generation of CR experiments., Comment: 18 pages, 14 figures, 4 tables (1 new): more re-organisation (for referees), but results and conclusions still unchanged (matching accepted A&A version)

The AMS-02 and HELIX experiments should soon provide $\mathrm{^{10}Be/^9Be}$ cosmic-ray data of unprecedented precision. We propose an analytical formula to quickly and accurately determine $L$ from these data. Our formula is validated against the full calculation performed with the propagation code \usine{}. We compare the constraints on $L$ set by Be/B and $\mathrm{^{10}Be/^9Be}$, relying on updated sets of production cross-sections. The best-fit $L$ from AMS-02 Be/B data is shifted from 5 kpc to 3.8 kpc when using the updated cross-sections. We obtained consistent results from the Be/B analysis with USINE, $L=3.8^{+2.8}_{-1.6}$ kpc (data and cross-section uncertainties), and from the analysis of $\mathrm{^{10}Be/^9Be}$ data with the simplified formula, $L=4.7\pm0.6$ (data uncertainties) $\pm2$ (cross-section uncertainties) kpc. The analytical formula indicates that improvements on $L$ thanks to future data will be limited by production cross-section uncertainties, unless either $\mathrm{^{10}Be/^9Be}$ measurements are extended up to several tens of GeV/n, or nuclear data for the production of $\mathrm{^{10}Be}$ and $\mathrm{^9Be}$ are improved; new data for the production cross-section of $\mathrm{^{16}O}$ into Be isotopes above a few GeV/n are especially desired., Comment: 9 pages, 2 tables, 5 figures (matches accepted A&A version): comparison to [De21] moved to appendix (also highlight impact of reacceleration)

High-precision data from AMS-02 on Li, Be, and B provide the best constraints on Galactic cosmic-ray transport parameters. We re-evaluate the impact of Fe fragmentation on the Li, Be, and B modelling. We discuss the consequences on the transport parameter determination and reassess whether a primary source of Li is needed to match AMS-02 data. We renormalised several cross-section parametrisations to existing data for the most important reactions producing Li, Be, and B. We used the USINE code with these new cross-section sets to re-analyse Li/C, Be/C, and B/C AMS-02 data. We built three equally plausible cross-section sets. Compared to the initial cross-section sets, they lead to an average enhanced production of Li ($\sim20-50\%$) and Be ($\sim5-15\%$), while leaving the B flux mostly unchanged. In particular, Fe fragmentation is found to contribute to up to 10\% of the Li and Be fluxes. Used in the combined analysis of AMS-02 Li/C, Be/C, and B/C data, the fit is significantly improved, with an enhanced diffusion coefficient ($\sim 20\%)$. The three updated cross-section sets are found to either slightly undershoot or overshoot the Li/C and B/C ratios: this strongly disfavours evidence for a primary source of Li in cosmic rays. We stress that isotopic cosmic-ray ratios of Li (and to a lesser extent Be), soon to be released by AMS-02, are also impacted by the use of these updated sets. Almost no nuclear data exist for the production of Li and B isotopes from Ne, Mg, Si, and Fe, whereas these reactions are estimated to account for $\sim 20\%$ of the total production. New nuclear measurements would be appreciated and help to better exploit the high-precision AMS-02 cosmic-ray data., Comment: 20 pages, 16 figures, 2 tables (matches accepted A&A version): corrected sign for $\delta_l$ (typo in plotting script) + couple of sentences added (XS modelling, results for various propagation configurations)

A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered Lagrange multipliers and pressure unknowns used to impose the constraints and solve the fluid flow in the fractures, respectively. This formulation does not require any interpolation between different fields, but is not uniformly inf-sup stable and requires a stabilization. For the resulting 3 x 3 block Jacobian matrix, we design scalable preconditioning strategies, based on the physically-informed block partitioning of the unknowns and state-of-the-art multigrid preconditioners. The key idea is to restrict the system to a single-physics problem, approximately solve it by an inner algebraic multigrid approach, and finally prolong it back to the fully-coupled problem. Two different techniques are presented, analyzed and compared by changing the ordering of the restrictions. Numerical results illustrate the algorithmic scalability, the impact of the relative number of fracture-based unknowns, and the performance on a real-world problem., Comment: 25 pages, 11 figures, 7 tables

Frictional contact is one of the most challenging problems in computational mechanics. Typically, it is a tough nonlinear problem often requiring several Newton iterations to converge and causing troubles also in the solution to the related linear systems. When contact is modeled with the aid of Lagrange multipliers, the impenetrability condition is enforced exactly, but the associated Jacobian matrix is indefinite and needs a special treatment for a fast numerical solution. In this work, a constraint preconditioner is proposed where the primal Schur complement is computed after augmenting the zero block. The name Reverse is used in contrast to the traditional approach where only the structural block undergoes an augmentation. Besides being able to address problems characterized by singular structural blocks, often arising in contact mechanics, it is shown that the proposed approach is significantly cheaper than traditional constraint preconditioning for this class of problems and it is suitable for an efficient HPC implementation through the Chronos parallel package. Our conclusions are supported by several numerical experiments on mid- and large-size problems from various applications. The source files implementing the proposed algorithm are freely available on GitHub., Comment: 20 pages, 12 figures, 4 tables