Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks

This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush-Kuhn-Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer-Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time

Impact of primary kidney disease on the effects of empagliflozin in patients with chronic kidney disease: secondary analyses of the EMPA-KIDNEY trial

Background: The EMPA KIDNEY trial showed that empagliflozin reduced the risk of the primary composite outcome of kidney disease progression or cardiovascular death in patients with chronic kidney disease mainly through slowing progression. We aimed to assess how effects of empagliflozin might differ by primary kidney disease across its broad population. Methods: EMPA-KIDNEY, a randomised, controlled, phase 3 trial, was conducted at 241 centres in eight countries (Canada, China, Germany, Italy, Japan, Malaysia, the UK, and the USA). Patients were eligible if their estimated glomerular filtration rate (eGFR) was 20 to less than 45 mL/min per 1·73 m2, or 45 to less than 90 mL/min per 1·73 m2 with a urinary albumin-to-creatinine ratio (uACR) of 200 mg/g or higher at screening. They were randomly assigned (1:1) to 10 mg oral empagliflozin once daily or matching placebo. Effects on kidney disease progression (defined as a sustained ≥40% eGFR decline from randomisation, end-stage kidney disease, a sustained eGFR below 10 mL/min per 1·73 m2, or death from kidney failure) were assessed using prespecified Cox models, and eGFR slope analyses used shared parameter models. Subgroup comparisons were performed by including relevant interaction terms in models. EMPA-KIDNEY is registered with ClinicalTrials.gov, NCT03594110. Findings: Between May 15, 2019, and April 16, 2021, 6609 participants were randomly assigned and followed up for a median of 2·0 years (IQR 1·5–2·4). Prespecified subgroupings by primary kidney disease included 2057 (31·1%) participants with diabetic kidney disease, 1669 (25·3%) with glomerular disease, 1445 (21·9%) with hypertensive or renovascular disease, and 1438 (21·8%) with other or unknown causes. Kidney disease progression occurred in 384 (11·6%) of 3304 patients in the empagliflozin group and 504 (15·2%) of 3305 patients in the placebo group (hazard ratio 0·71 [95% CI 0·62–0·81]), with no evidence that the relative effect size varied significantly by primary kidney disease (pheterogeneity=0·62). The between-group difference in chronic eGFR slopes (ie, from 2 months to final follow-up) was 1·37 mL/min per 1·73 m2 per year (95% CI 1·16–1·59), representing a 50% (42–58) reduction in the rate of chronic eGFR decline. This relative effect of empagliflozin on chronic eGFR slope was similar in analyses by different primary kidney diseases, including in explorations by type of glomerular disease and diabetes (p values for heterogeneity all >0·1). Interpretation: In a broad range of patients with chronic kidney disease at risk of progression, including a wide range of non-diabetic causes of chronic kidney disease, empagliflozin reduced risk of kidney disease progression. Relative effect sizes were broadly similar irrespective of the cause of primary kidney disease, suggesting that SGLT2 inhibitors should be part of a standard of care to minimise risk of kidney failure in chronic kidney disease. Funding: Boehringer Ingelheim, Eli Lilly, and UK Medical Research Council

Vorhersagbarkeit und Beurteilung der aquatischen Toxizitaet von Stoffgemischen - Binaere Kombinationen von unaehnlich wirkenden Substanzen unter Bedingungen akuter und chronischer Exposition

Die Belastungssituation in Gewaessern ist durch eine Exposition aquatischer Organismen gegenueber einer Vielzahl von Substanzen gekennzeichnet. Da die Zahl moeglicher Stoffkombinationen unuebersehbar ist, wird im Rahmen der Riskikoabschaetzung die Toxizitaet von Gemischen auf Grundlage der Einzelstoffoxizitaeten abgeschaetzt. In diesem Vorhaben wurde die Toxizitaet binaerer Gemische unaehnlich wirkender Substanzen im akuten und chronischen Daphnientest untersucht. Auf der Basis der ermittelten Konzentrations-Wirkungsbeziehungen der Einzelstoffe wurde die Toxizitaet der Gemische nach den Konzepten Konzentrations-Additivitaet und Unabhaengige Wirkung prognostiziert und mit den experimentell ermittelten Mischungstoxitaeten verglichen. Die akute und chronische Toxizitaet der untersuchten binaeren Gemische wurde von beiden Konzepten gut vorhergesagt. Unter akuter Exposition unterschieden sich die Vorhersagen beider Konzepte hinsichtlich Genauigkeit nicht. Im chronischen Daphnientest erbrachte jedoch das Konzept der Unabhaengigen Wirkung eine bessere Vorhersagegenauigkeit. Die vorliegende Studie hat gezeigt, dass der Effekt binaerer Mischungen unaehnlich wirkender Substanzen unter akuter und chronischer Exposition auf Daphnia magna meist groesser ist als der Effekt der jeweilig wirksamsten Einzelsubstanz und durch beide Konzepte angemessen vorhersagbar ist. Daher sollten Kombinationswirkungen unter Vorsorgegesichtspunkten in umweltpolitischen Regelungen zum Schutz aquatischer Systeme beruecksichtigt werden. (orig.)Aquatic organisms in surface waters are exposed towards a multitude of chemical substances. As the number of possible combinations is incalculable, the prediction of mixture toxicities bases on the toxicities of the single components. In this study the toxicity of binary mixtures of dissimilarly acting chemicals under acute and long-term exposure on Daphnia magna was investigated. The mixture toxicity predicted by the concepts Concentration Addition and Independent Action bases on the toxicities of the individual components. Experimental data were compared with both concepts. The observed toxicities under acute and long-term exposure were in good agreement with the predicted toxicity by both concepts. Under long-term exposure the predictive accuracy of Independent Action was higher. This study shows, that almost all toxicities of binary mixtures of dissimilarly acting chemicals under acute and long-term exposure on Daphnia magna was higher than the toxicity of the most effective single component. The mixture toxicities predicted by both concepts were in good agreement to the observed toxicities. For establishing environmental standards mixture toxicities should be taken into account for the future. (orig.)Available from TIB Hannover: F98B1952+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEBundesministerium fuer Bildung, Wissenschaft, Forschung und Technologie, Bonn (Germany)DEGerman

Interlaboratory comparison of a standardized toxicity test using the nematode Caenorhabditis elegans (ISO 10872)

Höss S, Ahlf W, Bergtold M, et al. Interlaboratory comparison of a standardized toxicity test using the nematode Caenorhabditis elegans (ISO 10872). Environmental Toxicology and Chemistry. 2012;31(7):1525-1535