A novel error estimation method for the parametric non-intrusive reduced order model (P-NIROM) based on machine learning is presented. This method relies on constructing a set of response functions ...for the errors between the high fidelity full model solutions and P-NIROM using machine learning method, particularly, Gaussian process regression method. This yields closer solutions agreement with the high fidelity full model. The novelty of this work is that it is the first time to use machine learning method to derive error estimate for the P-NIROM. The capability of the new error estimation method is demonstrated using three numerical simulation examples: flow past a cylinder, dam break and 3D fluvial channel. It is shown that the results are closer to those of the high fidelity full model when considering error terms. In addition, the interface between two phases of dam break case is captured well if the error estimator is involved in the P-NIROM.
•An error estimator for parametric non-intrusive reduced order model (P-NIROM) is presented.•The error estimator is based on machine learning methods.•The error estimator constructs a set of functions to represent the errors.•The error estimator is demonstrated to capture the interface between two phases of dam break.
Summary
This paper presents a novel model reduction method: deep learning reduced order model, which is based on proper orthogonal decomposition and deep learning methods. The deep learning approach ...is a recent technological advancement in the field of artificial neural networks. It has the advantage of learning the nonlinear system with multiple levels of representation and predicting data. In this work, the training data are obtained from high fidelity model solutions at selected time levels. The long short‐term memory network is used to construct a set of hypersurfaces representing the reduced fluid dynamic system. The model reduction method developed here is independent of the source code of the full physical system.
The reduced order model based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new reduced order model is evaluated using 2 numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.
This paper presents a novel model reduction method: deep learning reduced order model, which is based on proper orthogonal decomposition and deep learning methods. The reduced order model based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new reduced order model is evaluated using 2 numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.
Bone defect repair is challenging in orthopaedic clinics. For treatment of large bone defects, bone grafting remains the method of choice for the majority of surgeons, as it fills spaces and provides ...support to enhance biological bone repair. As therapeutic agents are desirable for enhancing bone healing, this study was designed to develop such a bioactive composite scaffold (PLGA/TCP/ICT) made of polylactide-co-glycolide (PLGA) and tricalcium phosphate (TCP) as a basic carrier, incorporating a phytomolecule icaritin (ICT), i.e., a novel osteogenic exogenous growth factor. PLGA/TCP/ICT scaffolds were fabricated as PLGA/TCP (control group) and PLGA/TCP in tandem with low/mid/high-dose ICT (LICT/MICT/HICT groups, respectively). To evaluate the in vivo osteogenic and angiogenic potentials of these bioactive scaffolds with slow release of osteogenic ICT, the authors established a 12mm ulnar bone defect model in rabbits. X-ray and high-resolution peripheral quantitative computed tomography results at weeks 2, 4 and 8 post-surgery showed more newly formed bone within bone defects implanted with PLGA/TCP/ICT scaffolds, especially PLGA/TCP/MICT scaffold. Histological results at weeks 4 and 8 also demonstrated more newly mineralized bone in PLGA/TCP/ICT groups, especially in the PLGA/TCP/MICT group, with correspondingly more new vessel ingrowth. These findings may form a good foundation for potential clinical validation of this innovative bioactive scaffold incorporated with the proper amount of osteopromotive phytomolecule ICT as a ready product for clinical applications.
AbstractThe off-axis embedment behaviors of unidirectional and multidirectional laminated engineered bamboo panels used for glued-laminated bamboo (glubam) structures under dowel-type bolts with ...three different diameters, 12, 14, and 16 mm, were experimentally studied in this research. The half-hole loading method given by current standards was adopted to perform the embedment tests. Seven different off-axis loading directions from 0° to 90° related to the main bamboo fiber direction at an interval of 15° in the panel plane were considered. The different failure patterns, stress-displacement curves, and the corresponding full-field surface strain measured through the digital image correlation (DIC) method are reported. The loading angles significantly influenced the embedment performance of unidirectional bamboo panel specimens, and the strength values decreased with the increasing off-axis loading angles. A difference of 35% in the strength values between 0° and 90° loading specimens was observed. However, quasi-isotropic embedment properties were noticed for the multidirectional laminated engineered bamboo panels. The capacity functions were provided to predict the mean off-axis embedment strength and characteristic strength values by inputting the characteristic density values into the functions. Compared with the characteristic strength values estimated through the statistical method, with a 95% probability of exceedance and 75% significant level, the conventional capacity-function method underestimated the off-axis embedment strength values, and thus may leading to an overconservative design. The statistical characteristic embedment strength values are suggested to be used to calibrate the safety factor of capacity equations given by wood standards. Results from this research can be used to predict the ultimate strength of glubam joints under complex loading conditions and obtain reliable design values for engineering applications.
This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of the method lies in its treatment of the ...equation's non-linear operator, for which a new method is proposed that provides accurate simulations within an efficient framework. The method itself is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM), that have already been developed to treat non-linear operators within reduced order models. The method proposed applies the quadratic expansion to provide a first approximation of the non-linear operator, and DEIM is then used as a corrector to improve its representation. In addition to the treatment of the non-linear operator the POD model is stabilized using a Petrov–Galerkin method. This adds artificial dissipation to the solution of the reduced order model which is necessary to avoid spurious oscillations and unstable solutions.
A demonstration of the capabilities of this new approach is provided by solving the incompressible Navier–Stokes equations for simulating a flow past a cylinder and gyre problems. Comparisons are made with other treatments of non-linear operators, and these show the new method to provide significant improvements in the solution's accuracy.
In order to find good candidate materials for degradable fracturing ball applications, the microstructure, mechanical behavior and corrosion properties of as‐cast Mg‐17Al‐3Zn‐xCu alloys were ...investigated using optical microscope, scanning electronic microscope equipped with energy dispersive spectroscope, compression tests, electrochemical measurements, and immersion tests. The results show that Cu addition affects not only the amount but also the morphology and distribution of T‐phases. The distribution of Al also has a large dependence on Cu concentration. These modifications of the microstructures accordingly affect the mechanical and corrosion properties of the investigated alloys. Mg‐17Al‐3Zn‐5Cu alloy can be used as degradable fracturing ball.
The microRNA-371-373 (miR-371-373) cluster is specifically expressed in human embryonic stem cells (ESCs) and is thought to be involved in stem cell maintenance. Recently, microRNAs (miRNAs) of this ...cluster were shown to be frequently upregulated in several human tumors. However, the regulatory mechanism for the involvement of the miR-371-373 cluster in human ESCs or cancer cells remains unclear. In this study, we explored the relationship between this miRNA cluster and the Wnt/β-catenin-signaling pathway, which has been shown to be involved in both stem cell maintenance and tumorigenesis. We show that miR-371-373 expression is induced by lithium chloride and is positively correlated with Wnt/β-catenin-signaling activity in several human cancer cell lines. Mechanistically, three TCF/LEF1-binding elements (TBEs) were identified in the promoter region and shown to be required for Wnt-dependent activation of miR-371-373. Interestingly, we also found that miR-372&373, in turn, activate Wnt/β-catenin signaling. In addition, four protein genes related to the Wnt/β-catenin-signaling pathway were identified as direct targets of miR-372&373, including Dickkopf-1 (DKK1), a well-known inhibitor of Wnt/β-catenin signaling. Using a lentiviral system, we showed that overexpression of miR-372 or miR-373 promotes cell growth and the invasive activity of tumor cells as knockdown of DKK1. Taken together, our study demonstrates a novel β-catenin/LEF1-miR-372&373-DKK1 regulatory feedback loop, which may have a critical role in regulating the activity of Wnt/β-catenin signaling in human cancer cells.
A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model ...reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced order models (P-ROM) (most of them are based on the reduced basis method), it is non-intrusive and independent on partial differential equations and computational codes. During the training process, the Smolyak sparse grid method is used to select a set of parameters over a specific parameterized space (Ωp∈RP). For each selected parameter, the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function sets for any parameters over Ωp can be obtained using an interpolation method. The P-NIROM can then be constructed by using our recently developed technique (Xiao et al., 2015 41,42) where either the Smolyak or radial basis function (RBF) methods are used to generate a set of hyper-surfaces representing the underlying dynamical system over the reduced space.
The new P-NIROM technique has been applied to parameterized Navier–Stokes equations and implemented with an unstructured mesh finite element model. The capability of this P-NIROM has been illustrated numerically by two test cases: flow past a cylinder and lock exchange case. The prediction capabilities of the P-NIROM have been evaluated by varying the viscosity, initial and boundary conditions. The results show that this P-NIROM has captured the quasi-totality of the details of the flow with CPU speedup of three orders of magnitude. An error analysis for the P-NIROM has been carried out.
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