Robust algebraic Schur complement preconditioners based on low rank corrections

In this paper we introduce LORASC, a robust algebraic preconditioner for solving sparse linear systems of equations involving symmetric and positive definite matrices. The graph of the input matrix is partitioned by using k-way partitioning with vertex separators into N disjoint domains and a separator formed by the vertices connecting the N domains. The obtained permuted matrix has a block arrow structure. The preconditioner relies on the Cholesky factorization of the first N diagonal blocks and on approximating the Schur complement corresponding to the separator block. The approximation of the Schur complement involves the factorization of the last diagonal block and a low rank correction obtained by solving a generalized eigenvalue problem or a randomized algorithm. The preconditioner can be build and applied in parallel. Numerical results on a set of matrices arising from the discretization by the finite element method of linear elasticity models illustrate the robusteness and the efficiency of our preconditioner

HMOE: Hypernetwork-based Mixture of Experts for Domain Generalization

Due to domain shift, machine learning systems typically fail to generalize well to domains different from those of training data, which is what domain generalization (DG) aims to address. Although various DG methods have been developed, most of them lack interpretability and require domain labels that are not available in many real-world scenarios. This paper presents a novel DG method, called HMOE: Hypernetwork-based Mixture of Experts (MoE), which does not rely on domain labels and is more interpretable. MoE proves effective in identifying heterogeneous patterns in data. For the DG problem, heterogeneity arises exactly from domain shift. HMOE uses hypernetworks taking vectors as input to generate experts' weights, which allows experts to share useful meta-knowledge and enables exploring experts' similarities in a low-dimensional vector space. We compare HMOE with other DG algorithms under a fair and unified benchmark-DomainBed. Our extensive experiments show that HMOE can divide mixed-domain data into distinct clusters that are surprisingly more consistent with human intuition than original domain labels. Compared to other DG methods, HMOE shows competitive performance and achieves SOTA results in some cases

Adaptive linear solution process for single-phase Darcy flow

International audienceThis article presents an adaptive approach for solving linear systems arising from self-adjoint partial differential equations (PDE) problems discretized by cell-centered finite volume method and stemming from single-phase flow simulations. This approach aims at reducing the algebraic error in targeted parts of the domain using a posteriori error estimates. Numerical results of a reservoir simulation example for heterogeneous porous media in two dimensions are discussed. Using the adaptive solve procedure, we obtain a significant gain in terms of the number of time steps and iterations compared to a standard solve.Cet article présente une approche adaptative pour la résolution de systèmes linéaires qui découlent de problèmes d’équations aux dérivées partielles (EDP) avec opérateurs auto-adjoints discrétisés par la méthode des volumes finis centrés en cellules et issus de simulations d’écoulement mono-phasique. Cette approche vise à réduire l’erreur algébrique dans des parties ciblées du domaine à l’aide d’estimateurs d’erreur a posteriori. Des résultats numériques d’un exemple de simulation de réservoir en milieux poreux hétérogènes en deux dimensions sont présentés. En utilisant la procédure adaptative de résolution, nous obtenons un gain significatif en termes de nombre de pas de temps et d’itérations par rapport à une résolution classique

Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality

International audienceWe develop in this work an adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality. As a model problem, we consider the contact problem between two membranes. Discretized with the finite volume method, this leads to a nonlinear algebraic system with complementarity constraints. The non-differentiability of the arising nonlinear discrete problem a priori requests the use of an iterative linearization algorithm in the semismooth class like, e.g., the Newton-min. In this work, we rather approximate the inequality constraints by a smooth nonlinear equality, involving a positive smoothing parameter that should be drawn down to zero. This makes it possible to directly apply any standard linearization like the Newton method. The solution of the ensuing linear system is then approximated by any iterative linear algebraic solver. In our approach, we carry out an a posteriori error analysis where we introduce potential reconstructions in discrete subspaces included in H1 (Ω), as well as H (div, Ω)-conforming discrete equilibrated flux reconstructions. With these elements, we design an a posteriori estimate that provides guaranteed upper bound on the energy error between the unavailable exact solution of the continuous level and a postprocessed, discrete, and available approximation, and this at any resolution step. It also offers a separation of the different error components, namely, discretization, smoothing, linearization, and algebraic. Moreover, we propose stopping criteria and design an adaptive algorithm where all the iterative procedures (smoothing, linearization, algebraic) are adaptively stopped; this is in particular our way to fix the smoothing parameter. Finally, we numerically assess the estimate and confirm the performance of the proposed adaptive algorithm, in particular in comparison with the semismooth Newton method

An a posteriori-based adaptive preconditioner for controlling a local algebraic error norm

International audienceThis paper introduces an adaptive preconditioner for iterative solution of sparse linear systems arising from partial differential equations with self-adjoint operators. This preconditioner allows to control the growth rate of a dominant part of the algebraic error within a fixed point iteration scheme. Several numerical results that illustrate the efficiency of this adaptive preconditioner with a PCG solver are presented and the preconditioner is also compared with a previous variant in the literature

A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media

ABSTRACT In this paper we derive a posteriori error estimates for the compositional model of multiphase Darcy flow in porous media REFERENCE

A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media

International audienceIn this paper we derive a posteriori error estimates for the compositional model of multiphase Darcy flow in porous media, consisting of a system of strongly coupled nonlinear unsteady partial differential and algebraic equations. We show how to control the dual norm of the residual augmented by a nonconformity evaluation term by fully computable estimators. We then decompose the estimators into the space, time, linearization, and algebraic error components. This allows to formulate criteria for stopping the iterative algebraic solver and the iterative linearization solver when the corresponding error components do not affect significantly the overall error. Moreover, the spatial and temporal error components can be balanced by time step and space mesh adaptation. Our analysis applies to a broad class of standard numerical methods, and is independent of the linearization and of the iterative algebraic solvers employed. We exemplify it for the two-point finite volume method with fully implicit Euler time stepping, the Newton linearization, and the GMRes algebraic solver. Numerical results on two real-life reservoir engineering examples confirm that significant computational gains can be achieved thanks to our adaptive stopping criteria, already on fixed meshes, without any noticeable loss of precision

The unfinished agenda of communicable diseases among children and adolescents before the COVID-19 pandemic, 1990-2019: a systematic analysis of the Global Burden of Disease Study 2019

BACKGROUND: Communicable disease control has long been a focus of global health policy. There have been substantial reductions in the burden and mortality of communicable diseases among children younger than 5 years, but we know less about this burden in older children and adolescents, and it is unclear whether current programmes and policies remain aligned with targets for intervention. This knowledge is especially important for policy and programmes in the context of the COVID-19 pandemic. We aimed to use the Global Burden of Disease (GBD) Study 2019 to systematically characterise the burden of communicable diseases across childhood and adolescence. METHODS: In this systematic analysis of the GBD study from 1990 to 2019, all communicable diseases and their manifestations as modelled within GBD 2019 were included, categorised as 16 subgroups of common diseases or presentations. Data were reported for absolute count, prevalence, and incidence across measures of cause-specific mortality (deaths and years of life lost), disability (years lived with disability [YLDs]), and disease burden (disability-adjusted life-years [DALYs]) for children and adolescents aged 0-24 years. Data were reported across the Socio-demographic Index (SDI) and across time (1990-2019), and for 204 countries and territories. For HIV, we reported the mortality-to-incidence ratio (MIR) as a measure of health system performance. FINDINGS: In 2019, there were 3·0 million deaths and 30·0 million years of healthy life lost to disability (as measured by YLDs), corresponding to 288·4 million DALYs from communicable diseases among children and adolescents globally (57·3% of total communicable disease burden across all ages). Over time, there has been a shift in communicable disease burden from young children to older children and adolescents (largely driven by the considerable reductions in children younger than 5 years and slower progress elsewhere), although children younger than 5 years still accounted for most of the communicable disease burden in 2019. Disease burden and mortality were predominantly in low-SDI settings, with high and high-middle SDI settings also having an appreciable burden of communicable disease morbidity (4·0 million YLDs in 2019 alone). Three cause groups (enteric infections, lower-respiratory-tract infections, and malaria) accounted for 59·8% of the global communicable disease burden in children and adolescents, with tuberculosis and HIV both emerging as important causes during adolescence. HIV was the only cause for which disease burden increased over time, particularly in children and adolescents older than 5 years, and especially in females. Excess MIRs for HIV were observed for males aged 15-19 years in low-SDI settings. INTERPRETATION: Our analysis supports continued policy focus on enteric infections and lower-respiratory-tract infections, with orientation to children younger than 5 years in settings of low socioeconomic development. However, efforts should also be targeted to other conditions, particularly HIV, given its increased burden in older children and adolescents. Older children and adolescents also experience a large burden of communicable disease, further highlighting the need for efforts to extend beyond the first 5 years of life. Our analysis also identified substantial morbidity caused by communicable diseases affecting child and adolescent health across the world. FUNDING: The Australian National Health and Medical Research Council Centre for Research Excellence for Driving Investment in Global Adolescent Health and the Bill & Melinda Gates Foundation

The global burden of cancer attributable to risk factors, 2010-19 : a systematic analysis for the Global Burden of Disease Study 2019

Background Understanding the magnitude of cancer burden attributable to potentially modifiable risk factors is crucial for development of effective prevention and mitigation strategies. We analysed results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 to inform cancer control planning efforts globally. Methods The GBD 2019 comparative risk assessment framework was used to estimate cancer burden attributable to behavioural, environmental and occupational, and metabolic risk factors. A total of 82 risk-outcome pairs were included on the basis of the World Cancer Research Fund criteria. Estimated cancer deaths and disability-adjusted life-years (DALYs) in 2019 and change in these measures between 2010 and 2019 are presented. Findings Globally, in 2019, the risk factors included in this analysis accounted for 4.45 million (95% uncertainty interval 4.01-4.94) deaths and 105 million (95.0-116) DALYs for both sexes combined, representing 44.4% (41.3-48.4) of all cancer deaths and 42.0% (39.1-45.6) of all DALYs. There were 2.88 million (2.60-3.18) risk-attributable cancer deaths in males (50.6% [47.8-54.1] of all male cancer deaths) and 1.58 million (1.36-1.84) risk-attributable cancer deaths in females (36.3% [32.5-41.3] of all female cancer deaths). The leading risk factors at the most detailed level globally for risk-attributable cancer deaths and DALYs in 2019 for both sexes combined were smoking, followed by alcohol use and high BMI. Risk-attributable cancer burden varied by world region and Socio-demographic Index (SDI), with smoking, unsafe sex, and alcohol use being the three leading risk factors for risk-attributable cancer DALYs in low SDI locations in 2019, whereas DALYs in high SDI locations mirrored the top three global risk factor rankings. From 2010 to 2019, global risk-attributable cancer deaths increased by 20.4% (12.6-28.4) and DALYs by 16.8% (8.8-25.0), with the greatest percentage increase in metabolic risks (34.7% [27.9-42.8] and 33.3% [25.8-42.0]). Interpretation The leading risk factors contributing to global cancer burden in 2019 were behavioural, whereas metabolic risk factors saw the largest increases between 2010 and 2019. Reducing exposure to these modifiable risk factors would decrease cancer mortality and DALY rates worldwide, and policies should be tailored appropriately to local cancer risk factor burden. Copyright (C) 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license.Peer reviewe

Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BackgroundDisorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021.MethodsWe estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined.FindingsGlobally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer.InterpretationAs the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed