Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize the paradigm of turbulence modeling. However, due to the black-box essence of most ML methods, it is currently hard to extract interpretable information and knowledge from data-driven models. To address this critical limitation, this work leverages deep learning with symbolic regression methods to discover hidden governing equations of Reynolds stress models. Specifically, the Reynolds stress tensor is decomposed into linear and non-linear parts. While the linear part is taken as the regular linear eddy viscosity model, a long short-term memory neural network is employed to generate symbolic terms on which tractable mathematical expressions for the non-linear counterpart are built. A novel reinforcement learning algorithm is employed to train the neural network to produce best-fitted symbolic expressions. Within the proposed framework, the Reynolds stress closure is explicitly expressed in algebraic forms, thus allowing for direct functional inference. On the other hand, the Galilean and rotational invariance are craftily respected by constructing the training feature space with independent invariants and tensor basis functions. The performance of the present methodology is validated through numerical simulations of three different canonical flows that deviate in geometrical configurations. The results demonstrate promising accuracy improvements over traditional RANS models, showing the generalization ability of the proposed method. Moreover, with the given explicit model equations, it can be easier to interpret the influence of input features on generated models

A Systematic Review on Different Treatment Methods of Bone Metastasis from Cancers

Background and objective Skeletal metastase is one of the most common complications related to advanced cancer. The aim of this study is to analyze the effectiveness and safety of radiotherapy plus intravenous bisphosphonates versus radiotherapy alone for treating bone metastasis. Methods We searched the Cochrane Library, PubMed, EMBASE, CBM, CNKI and VIP, as well as the reference lists of reports and reviews. The quality of included trials was evaluated by the Cochrane Handbook. Data were extracted and evaluated by two reviewers independently. The Cochrane Collaboration’s Rev-Man 5.0 was used for data analysis. Results Twenty-two trials involving 1 585 patients were included. Compared with radiotherapy alone, radiotherapy plus intravenous bisphosphonates was more effective in total effective rate of pain relive (RR=1.21, 95%CI: 1.13-1.30, P < 0.001), average abated time (WMD=16.00, 95%CI: 10.12-21.88, P < 0.001), and quality of life (RR=1.25, 95%CI: 1.08-1.45, P=0.003, with significant differences. Side effects have no significant differences between the two groups except fever (RR=5.61, 95%CI: 3.11-10.13, P < 0.001). Conclusion Current evidence supports more effective of radiotherapy plus intravenous bisphosphonates for bone metastases. The combine treatment is safe and effective

Synthesis and Formation Mechanism of CuInS\u3csub\u3e2\u3c/sub\u3e Nanocrystals with a Tunable Phase

Chalcopyrite CuInS2 (CIS) hierarchical structures composed of nanoflakes with a thickness of about 5 nm were synthesized by a facial solvothermal method. The thermodynamically metastable wurtzite phase CIS would be obtained by using InCl3 instead of In(NO3)3 as In precursor. The effects of the In precursor and the volume of concentrated HCl aqueous solution on the phases and morphologies of CIS nanocrystals have been systematically investigated. Experimental results indicated that the obtained phases of CIS nanocrystals were predominantly determined by precursor-induced intermediate products. The photocatalytic properties of chalcopyrite and wurtzite CIS in visible-light-driven degradation of organic dye were also compared