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Rock formations are very often characterized by the presence of fractures that have grown subcritically over geological time scales and under evolving stress fields. In mechanically layered systems, such fractures can either become layer-bound or penetrate into adjacent strata. The growth of fractures in brittle materials is generally dependent on the energy release rate, however no closed form analytical solutions exist for these when a crack tip is in the proximity of a material interface. In this study, we present new empirical formulas for calculating the energy release rate at the tip of a crack perpendicular to a material interface in a symmetric 3-layer system. In these formulas, the normalized energy release rate is expressed as the product of a base term that integrates the normalized stiffness modulus over the crack length, and a correction factor that accounts for the presence of a material interface. The latter is assumed to be dependent on two quantities: the ratio of the crack length to the inner layer thickness, and the contrast in material stiffness between the inner and outer layers. The correction factors are obtained by fitting the parameters of carefully chosen expressions to a set of finite element solutions in order to yield predictions that are accurate to within one percent of the numerical results., Comment: 16 pages, 15 figures, 2 tables

Nonlinear model predictive control (NMPC) requires accurate and computationally efficient plant models. Our previous work has shown that the classical compartmentalization model reduction approach for distillation columns can be enhanced by replacing parts of the system of equations by artificial neural networks (ANNs) trained on offline solved solutions to improve computational performance. In real-life applications, the absence of a high-fidelity model for data generation can, however, prevent the deployment of this approach. Therefore, we propose a method that utilizes solely plant measurement data, starting from a small initial data set and then continuously adapting to newly measured data. The efficacy of the proposed approach is examined in silico for a distillation column from literature. To this end, we first adjust our reduced hybrid mechanistic/data-driven modeling approach that originally builds on compartmentalization to a stage-aggregation procedure, tailoring it for the application within the adaptive learning framework. Second, we apply an adaptive learning algorithm that trains the ANNs replacing the stationary stage-to-stage calculations on newly available data. We apply the adaptive learning of the hybrid model within a regulatory NMPC framework and conduct closed-loop simulations. We demonstrate that by using the proposed method, the control performance can be steadily improved over time compared to a non-adaptive approach while being real-time applicable. Moreover, we show that the performance when using either a model trained on excessive amounts of offline generated data or the original high-fidelity model can be approached in the limit., Comment: 9 pages, 4 figures

BACKGROUND. The clinical effectiveness of primary prevention implantable cardioverter defibrillator (ICD) therapy is under debate. It is urgently needed to better identify patients who benefit from prophylactic ICD therapy. The EUropean Comparative Effectiveness Research to Assess the Use of Primary ProphylacTic Implantable Cardioverter Defibrillators (EU-CERT-ICD) completed in 2019 will assess this issue. SUMMARY. The EU-CERT-ICD is a prospective investigator-initiated non-randomized, controlled, multicenter observational cohort study done in 44 centers across 15 European countries. A total of 2327 patients with heart failure due to ischemic heart disease or dilated cardiomyopathy indicated for primary prophylactic ICD implantation were recruited between 2014 and 2018 (>1500 patients at first ICD implantation, >750 patients non-randomized non-ICD control group). The primary endpoint was all-cause mortality, first appropriate shock was co-primary endpoint. At baseline, all patients underwent 12-lead ECG and Holter-ECG analysis using multiple advanced methods for risk stratification as well as documentation of clinical characteristics and laboratory values. The EU-CERT-ICD data will provide much needed information on the survival benefit of preventive ICD therapy and expand on previous prospective risk stratification studies which showed very good applicability of clinical parameters and advanced risk stratifiers in order to define patient subgroups with above or below average ICD benefit. CONCLUSION. The EU-CERT-ICD study will provide new and current data about effectiveness of primary prophylactic ICD implantation. The study also aims for improved risk stratification and patient selection using clinical risk markers in general, and advanced ECG risk markers in particular., Comment: 22 pages, 3 figures

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrical signals, contain significant information in the phase of the signal. We explore complex-valued deep convolutional networks to leverage non-linear feature maps. Seismic data commonly has a lowcut filter applied, to attenuate noise from ocean waves and similar long wavelength contributions. Discarding the phase information leads to low-frequency aliasing analogous to the Nyquist-Shannon theorem for high frequencies. In non-stationary data, the phase content can stabilize training and improve the generalizability of neural networks. While it has been shown that phase content can be restored in deep neural networks, we show how including phase information in feature maps improves both training and inference from deterministic physical data. Furthermore, we show that the reduction of parameters in a complex network outperforms larger real-valued networks., Comment: 17 pages total, 15 pages, 2 pages references, paper, 11 figures, 28 networks

Geoscience data often have to rely on strong priors in the face of uncertainty. Additionally, we often try to detect or model anomalous sparse data that can appear as an outlier in machine learning models. These are classic examples of imbalanced learning. Approaching these problems can benefit from including prior information from physics models or transforming data to a beneficial domain. We show an example of including physical information in the architecture of a neural network as prior information. We go on to present noise injection at training time to successfully transfer the network from synthetic data to field data., Comment: 5 pages, 5 figures, workshop, extended abstract, EAGE 2019 Workshop Programme, European Association of Geoscientists and Engineers

Contrary to the recently published results by Daerden and Vanderzande [Phys. Rev. E 53, 4723 (1996)], we show that the time correlation function in the random-neighbor version of the Bak-Sneppen model can be well approximated by an exponential giving rise to a 1/f2 power spectrum., Comment: 2 pages, 2 figures