Multi-Fidelity Data Assimilation For Physics Inspired Machine Learning In Uncertainty Quantification Of Fluid Turbulence Simulations

Reliable prediction of turbulent flows is an important necessity across different fields of science and engineering. In Computational Fluid Dynamics (CFD) simulations, the most common type of models are eddy viscosity models that are computationally inexpensive but introduce a high degree of epistemic error. The Eigenspace Perturbation Method (EPM) attempts to quantify this predictive uncertainty via physics based perturbation in the spectral representation of the predictions. While the EPM outlines how to perturb, it does not address how much or even where to perturb. We address this need by introducing machine learning models to predict the details of the perturbation, thus creating a physics inspired machine learning (ML) based perturbation framework. In our choice of ML models, we focus on incorporating physics based inductive biases while retaining computational economy. Specifically we use a Convolutional Neural Network (CNN) to learn the correction between turbulence model predictions and true results. This physics inspired machine learning based perturbation approach is able to modulate the intensity and location of perturbations and leads to improved estimates of turbulence model errors.Comment: arXiv admin note: substantial text overlap with arXiv:2301.1184

Multi-fidelity Deep Learning-based methodology for epistemic uncertainty quantification of turbulence models

Computational Fluid Dynamics (CFD) simulations using turbulence models are commonly used in engineering design. Of the different turbulence modeling approaches that are available, eddy viscosity based models are the most common for their computational economy. Eddy viscosity based models utilize many simplifications for this economy such as the gradient diffusion and the isotropic eddy viscosity hypotheses. These simplifications limit the degree to which eddy viscosity models can replicate turbulence physics and lead to model form uncertainty. The Eigenspace Perturbation Method (EPM) has been developed for purely physics based estimates of this model form uncertainty in turbulence model predictions. Due to its physics based nature, the EPM weighs all physically possible outcomes equally leading to overly conservative uncertainty estimates in many cases. In this investigation we use data driven Machine Learning (ML) approaches to address this limitation. Using ML models, we can weigh the physically possible outcomes by their likelihood leading to better calibration of the uncertainty estimates. Specifically, we use ML models to predict the degree of perturbations in the EPM over the flow domain. This work focuses on a Convolutional Neural Network (CNN) based model to learn the discrepancy between Reynolds Averaged Navier Stokes (RANS) and Direct Numerical Simulation (DNS) predictions. This model acts as a marker function, modulating the degree of perturbations in the EPM. We show that this physics constrained machine learning framework performs better than the purely physics or purely ML alternatives, and leads to less conservative uncertainty bounds with improved calibration.Comment: arXiv admin note: text overlap with arXiv:2301.1184

Machine learning based uncertainty quantification of turbulence model for airfoils

Reynolds-averaged Navier-Stokes (RANS)-based transition modeling is widely used in aerospace applications but suffers inaccuracies due to the Boussinesq turbulent viscosity hypothesis. The eigenspace perturbation method can estimate the accuracy of a RANS model by injecting perturbations to its predicted Reynolds stresses. However, there lacks a reliable method for choosing the strength of the injected perturbation, while existing machine learning models are often complex and data craving. We examined two light-weighted machine learning models to help select the strength of the injected perturbation for estimating the RANS uncertainty of flows undergoing the transition to turbulence over a Selig-Donovan 7003 airfoil. On the one hand, we examined polynomial regression to construct a marker function augmented with eigenvalue perturbations to estimate the uncertainty bound for the predicted skin friction coefficient. On the other hand, we trained a convolutional neural network (CNN) to predict high-fidelity turbulence kinetic energy. The trained CNN acts as a marker function that can be integrated into the eigenspace perturbation method to quantify the RANS uncertainty. Our findings suggest that the light-weighted machine learning models are effective in constructing an appropriate marker function that is promising to enrich the existing eigenspace perturbation method to quantify the RANS uncertainty more precisely

Spatial Pattern of the oasis landscape Ecotone in Ebinur Lake, Xinjiang, northwest of China

[ABSTRACT]Based on methods of lanscape ecology and TM images of the Ebinur lake during the diffierent period, This paper studies the characteristics of landscape pattern, function and its variation. The ecological process, mechanism and intensity of variation influenced by the human activities and physical factors are analyzed in order to offer the countermeasure and references for restoring and reconstructing destroyed ecological function in the study areas. The results showed that (!)Landscape ecotone of Ebinur Lake, with higher complex spatial heterogeneity in ecological system,was fragile and unstable to disturbance of the human activities and environment factors, which mainly include rainfall variation, frequency and intensity of wind as well as population,agriculture and livestock changes. (2)The grassland is a dominant type of land use; The proportion of grassland, woodland and the unutilized land is nearly 80% while the agricultural land and inhabitant location is_less, less than ~%. Thus, the land use structure should be adijusted to sustain the stability of oasis in Ebinur Lake .Especially three farms near the lake should control the increase of agricutural lands and livestock. (3)The land that not to utilize and the patches of woodlands are 94. 78%, but this two kinds of landscape\u27s average area is small, landscape fragment is obvious. ( 4 )The shapes of grassland patches are not regulations and complicated,the bend level of boundary is distinct.The index of the landscape diversity and homogeneity is high, dominant is small, the distribution of landscape patches is symmetrical The results indicate the landscape the landscape is complete, and have not - 170 - phenomenon of obvious fragment. (S)Study on ecological restoration of the unutilized lands should be strenthen, which is important for optimizing the composition structure and spatial pattern of landscape ecotone of Ebinur Lake. The unutilized lands including salina land , wind-erode land and water corrisive land, were distributed in areas with large population. Therefore, it is essential that we should prevent desertification and protect present vegetation and improve vegetation coverage. (6)The landacape ecology system was charactered by complicated and landscape patches fragment and higher diversity and homogenecity, which is related climate change, human activities, groundwater level and lake volume ・change. Thus,we need ensure the water supply for lake, which provide references and information for bionomical resources, agrichuture and railroad security

Valley Contrasting Magnetoluminescence in Monolayer MoS2_{2} Quantum Hall Systems

The valley dependent optical selection rules in recently discovered monolayer group-VI transition metal dichalcogenides (TMDs) make possible optical control of valley polarization, a crucial step towards valleytronic applications. However, in presence of Landaul level(LL) quantization such selection rules are taken over by selection rules between the LLs, which are not necessarily valley contrasting. Using MoS$_{2}$ as an example we show that the spatial inversion-symmetry breaking results in unusual valley dependent inter-LL selection rules, which directly locks polarization to valley. We find a systematic valley splitting for all Landau levels (LLs) in the quantum Hall regime, whose magnitude is linearly proportional to the magnetic field and in comparable with the LL spacing. Consequently, unique plateau structures are found in the optical Hall conductivity, which can be measured by the magneto-optical Faraday rotations