Physics-Aware Convolutional Neural Networks for Computational Fluid Dynamics

Determining the behavior of fluids is of interest in many fields. In this work, we focus on incompressible, viscous, Newtonian fluids, which are well described by the incompressible Navier-Stokes equations. A common approach to solve them approximately is to perform Computational Fluid Dynamics (CFD) simulations. However, CFD simulations are very expensive and must be repeated if the geometry changes even slightly. We consider Convolutional Neural Networks (CNNs) as surrogate models for CFD simulations for various geometries. This can also be considered as operator learning. Typically, these models are trained on images of high-fidelity simulation results. The generation of this high-fidelity training data is expensive, and a fully data-driven approach usually requires a large data set. Therefore, we are interested in training a CNN in the absence of abundant training data. To this end, we leverage the underlying physics in the form of the governing equations to construct physical constraints that we then use to train a CNN. We present results for various model problems, including two- and three-dimensional flow in channels around obstacles of various sizes and in non-rectangular geometries, especially arteries and aneurysms. We compare our novel physics-aware approach to the state-of-the-art data-based approach and also to a combination of the two, a combined or hybrid approach. In addition, we present results for an extension of our approach to include variations in the boundary conditions

A short note on solving partial differential equations using convolutional neural networks

The approach of using physics-based machine learning to solve PDEs has recently become very popular. A recent approach to solve PDEs based on CNNs uses finite difference stencils to include the residual of the partial differential equation into the loss function. In this work, the relation between the network training and the solution of a respective finite difference linear system of equations using classical numerical solvers is discussed. It turns out that many beneficial properties of the linear equation system are neglected in the network training. Finally, numerical results which underline the benefits of classical numerical solvers are presented

New first line treatment options of clear cell renal cell cancer patients with PD-1 or PD-L1 immune-checkpoint inhibitor-based combination therapies

In metastatic renal cell carcinoma (mRCC) the PD-1 immune-checkpoint inhibitor (ICI) Nivolumab became a standard second line treatment option in 2015 based on a significant improvement of overall survival compared to Everolimus. Current pivotal phase 3 studies showed that PD-1 ICI-based combinations were more efficacious than the VEGFR-TKI Sunitinib, a previous standard of care, leading to approval of three new regimens as guideline-recommended first-line treatment. Nivolumab plus Ipilimumab is characterized by a survival advantage, a high rate of complete response and durable remissions in intermediate and poor prognosis patients. Despite frequent immune-mediated side effects, fewer symptoms and a better quality of life were observed compared to Sunitinib. Pembrolizumab or Avelumab plus Axitinib were characterized by an improved progression-free-survival and a high response rate with a low rate of intrinsic resistance. In addition, Pembrolizumab plus Axitinib reached a significant survival benefit. The side effect profile is driven by the chronic toxicity of Axitinib, but there is additional risk of immune-mediated side effects of the PD-1/PD-L1 ICIs. The quality of life data published so far do not suggest any improvement regarding patient-reported outcomes compared to the previous standard Sunitinib. The PD-1/PD-L1 ICIs thus form the backbone of the first-line therapy of mRCC

Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks

The course of an epidemic can be often successfully described mathematically using compartment models. These models result in a system of ordinary differential equations. Two well-known examples are the SIR and the SEIR models. The transition rates between the different compartments are defined by certain parameters which are specific for the respective virus. Often, these parameters can be taken from the literature or can be determined from statistics. However, the contact rate or the related effective reproduction number are in general not constant and thus cannot easily be determined. Here, a new machine learning approach based on physics-informed neural networks is presented that can learn the contact rate from given data for the dynamical systems given by the SIR and SEIR models. The new method generalizes an already known approach for the identification of constant parameters to the variable or time-dependent case. After introducing the new method, it is tested for synthetic data generated by the numerical solution of SIR and SEIR models. Here, the case of exact and perturbed data is considered. In all cases, the contact rate can be learned very satisfactorily. Finally, the SEIR model in combination with physics-informed neural networks is used to learn the contact rate for COVID-19 data given by the course of the epidemic in Germany. The simulation of the number of infected individuals over the course of the epidemic, using the learned contact rate, is very promising

Everolimus after failure of one prior VEGF-targeted therapy in metastatic renal cell carcinoma : Final results of the MARC-2 trial

MARC-2, a prospective, multicenter phase IV trial, aimed to investigate clinical outcomes in patients with metastatic renal cell carcinoma (mRCC) treated with everolimus after failure of one initial vascular endothelial growth factor receptor tyrosine kinase inhibitor (VEGFR-TKI) therapy and to identify subgroups benefiting most, based on clinical characteristics and biomarkers. Patients with clear cell mRCC failing one initial VEGFR-TKI received everolimus until progression or unacceptable toxicity. Primary endpoint was 6-month progression-free survival rate (6moPFS). Secondary endpoints were overall response rate (ORR), PFS, overall survival (OS), and safety. Between 2011 and 2015, 63 patients were enrolled. Median age was 65.4 years (range 43.3-81.1). 6moPFS was 39.3% (95% confidence interval [CI], 27.0-51.3) overall, 54.4% (95% CI, 35.2-70.1) vs 23.7% (95% CI, 10.5-39.9) for patients aged ≥65 vs 25 vs ≤25 kg/m2. A Cox proportional hazards model confirmed a longer PFS for patients aged ≥65 years (hazard ratio [HR] 0.46; 95% CI, 0.26-0.80) and a longer OS for patients with BMI >25 kg/m2 (HR 0.36; 95% CI, 0.18-0.71). Median PFS and median OS were 3.8 months (95% CI, 3.2-6.2) and 16.8 months (95% CI, 14.3-24.3). ORR was 7.9% and disease control rate was 60.3%. No new safety signals emerged. Most common adverse events were stomatitis (31.7%), fatigue (31.7%), and anemia (30.2%). One patient died from treatment-related upper gastrointestinal hemorrhage. Everolimus remains a safe and effective treatment option for mRCC patients after one prior VEGFR-TKI therapy. Patients aged ≥65 years and patients with BMI >25 kg/m2 benefited most

Thrombospondin-2 and LDH Are Putative Predictive Biomarkers for Treatment with Everolimus in Second-Line Metastatic Clear Cell Renal Cell Carcinoma (MARC-2 Study)

There is an unmet need for predictive biomarkers in metastatic renal cell carcinoma (mRCC) therapy. The phase IV MARC-2 trial searched for predictive blood biomarkers in patients with predominant clear cell mRCC who benefit from second-line treatment with everolimus. In an exploratory approach, potential biomarkers were assessed employing proteomics, ELISA, and polymorphism analyses. Lower levels of angiogenesis-related protein thrombospondin-2 (TSP-2) at baseline (≤665 parts per billion, ppb) identified therapy responders with longer median progressionfree survival (PFS; ≤665 ppb at baseline: 6.9 months vs. 1.8, p = 0.005). Responders had higher lactate dehydrogenase (LDH) levels in serum two weeks after therapy initiation (>27.14 nmol/L), associated with a longer median PFS (3.8 months vs. 2.2, p = 0.013) and improved overall survival (OS; 31.0 months vs. 14.0 months, p < 0.001). Baseline TSP-2 levels had a stronger relation to PFS (HR 0.36, p = 0.008) than baseline patient parameters, including IMDC score. Increased serum LDH levels two weeks after therapy initiation were the best predictor for OS (HR 0.21, p < 0.001). mTOR polymorphisms appeared to be associated with therapy response but were not significant. Hence, we identified TSP-2 and LDH as promising predictive biomarkers for therapy response on everolimus after failure of one VEGF-targeted therapy in patients with clear cell mRCC

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Is a Federal European Constitution for an Enlarged European Union Necessary? Some Preliminary Suggestions Using Public Choice Analysis

In order to guarantee a further successful functioning of the enlarged European Union a Federal European Constitution is proposed. Six basic elements of a future European federal constitution are developed: the European commission should be turned into an European government and the European legislation should consist of a two chamber system with full responsibility over all federal items. Three further key elements are the subsidiarity principle, federalism and the secession right, which are best suited to limiting the domain of the central European authority to which certain tasks are given, such as defense, foreign and environmental policy. Another important feature is direct democracy, which provides the possibility for European voters to participate actively in the political decision making, to break political and interest group cartels, and to prevent an unwanted shifting of responsibilities from EU member states to the European federal level