Adjoint-based variational optimal mixed models for large-eddy simulation of turbulence

An adjoint-based variational optimal mixed model (VOMM) is proposed for subgrid-scale (SGS) closure in large-eddy simulation (LES) of turbulence. The stabilized adjoint LES equations are formulated by introducing a minimal regularization to address the numerical instabilities of the long-term gradient evaluations in chaotic turbulent flows. The VOMM model parameters are optimized by minimizing the discrepancy of energy dissipation spectra between LES calculations and a priori knowledge of direct numerical simulation (DNS) using the gradient-based optimization. The a posteriori performance of the VOMM model is comprehensively examined in LES of three turbulent flows, including the forced homogeneous isotropic turbulence, decaying homogenous isotropic turbulence, and temporally evolving turbulent mixing layer. The VOMM model outperforms the dynamic Smagorinsky model (DSM), dynamic mixed model (DMM) and approximate deconvolution model (ADM) in predictions of various turbulence statistics, including the velocity spectrum, structure functions, statistics of velocity increments and vorticity, temporal evolutions of the turbulent kinetic energy, dissipation rate, momentum thickness and Reynolds stress, as well as the instantaneous vortex structures at different grid resolutions and times. In addition, the VOMM model only takes up 30% time of the DMM model for all flow scenarios. These results demonstrate that the proposed VOMM model improves the numerical stability of LES and has high a posteriori accuracy and computational efficiency by incorporating the a priori information of turbulence statistics, highlighting that the VOMM model has a great potential to develop advanced SGS models in the LES of turbulence.Comment: 48 pages, 23 figures, 8 table

The discrete direct deconvolution model in the large eddy simulation of turbulence

The discrete direct deconvolution model (D3M) is developed for the large-eddy simulation (LES) of turbulence. The D3M is a discrete approximation of previous direct deconvolution model studied by Chang et al. ["The effect of sub-filter scale dynamics in large eddy simulation of turbulence," Phys. Fluids 34, 095104 (2022)]. For the first type model D3M-1, the original Gaussian filter is approximated by local discrete formulation of different orders, and direct inverse of the discrete filter is applied to reconstruct the unfiltered flow field. The inverse of original Gaussian filter can be also approximated by local discrete formulation, leading to a fully local model D3M-2. Compared to traditional models including the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM), the D3M-1 and D3M-2 exhibit much larger correlation coefficients and smaller relative errors in the a priori studies. In the a posteriori validations, both D3M-1 and D3M-2 can accurately predict turbulence statistics, including velocity spectra, probability density functions (PDFs) of sub-filter scale (SFS) stresses and SFS energy flux, as well as time-evolving kinetic energy spectra, momentum thickness, and Reynolds stresses in turbulent mixing layer. Moreover, the proposed model can also well capture spatial structures of the Q-criterion iso surfaces. Thus, the D3M holds potential as an effective SFS modeling approach in turbulence simulations.Comment: 57 pages, 17 figure

Temperature Effect on Interactions of Oil Droplet with Water-wetted Shale Kerogen at Reservoir Temperatures: Linear Relationships between Temperature, Free Energy, and Contact Angle

Detailed knowledge about the interfacial interactions between oil and kerogen at nanoscales is imperative for unlocking adsorbed hydrocarbon in tight reservoirs, especially in unconventional shale that retain abundant hydrocarbon in kerogen nanopores. In this study, the temperature effect on interactions of light oil with a type II kerogen in water was investigated using molecular dynamics simulation. Non-polar and polar light oil droplets were modeled by clusters of 30 octane molecules and 30 octanethiol molecules, respectively. The free energy calculations were performed with umbrella sampling at constant temperatures in the range 300-500 $K$, that are comparable to the reservoir conditions of common shale plays. Our result shows that the adsorption/desorption energy of an oil droplet is a linear function of temperature ($T$), which can be described by $f(T) = c_1\times T + c_2$ where $c_1$ and $c_2$ are constant. Comparative simulations show that a single oil molecule cannot qualitatively describe oil droplet. In addition, the most stable contact angles of oil droplets, which are associated with the global energy minimum, were identified by computing free energy across a wide range of distance between the oil droplet and the kerogen surface. The cosine of the contact angle can be linearly correlated with the free energy of oil adsorption/desorption. This study provides a thermodynamic insight at the molecular level on how temperature affects the oil interactions with kerogen, providing valuable implications to improve unconventional oil recovery.Comment: 30 pages, 10 figures, 6 table

Deep CNN Frameworks for Comparison for Malaria Diagnosis

Abstract We compare Deep Convolutional Neural Networks (DCNN) frameworks, namely AlexNet and VGGNet, for the classification of healthy and malaria-infected cells in large, grayscale, low quality and low resolution microscopic images, in the case only a small training set is available. Experimental results deliver promising results on the path to quick, automatic and precise classification in unstrained images

Linear attention coupled Fourier neural operator for simulation of three-dimensional turbulence

Modeling three-dimensional (3D) turbulence by neural networks is difficult because 3D turbulence is highly-nonlinear with high degrees of freedom and the corresponding simulation is memory-intensive. Recently, the attention mechanism has been shown as a promising approach to boost the performance of neural networks on turbulence simulation. However, the standard self-attention mechanism uses $O(n^2)$ time and space with respect to input dimension $n$, and such quadratic complexity has become the main bottleneck for attention to be applied on 3D turbulence simulation. In this work, we resolve this issue with the concept of linear attention network. The linear attention approximates the standard attention by adding two linear projections, reducing the overall self-attention complexity from $O(n^2)$ to $O(n)$ in both time and space. The linear attention coupled Fourier neural operator (LAFNO) is developed for the simulation of 3D turbulence. Numerical simulations show that the linear attention mechanism provides 40\% error reduction at the same level of computational cost, and LAFNO can accurately reconstruct a variety of statistics and instantaneous spatial structures of 3D turbulence. The linear attention method would be helpful for the improvement of neural network models of 3D nonlinear problems involving high-dimensional data in other scientific domains.Comment: 28 pages, 14 figure

Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator

Long-term predictions of nonlinear dynamics of three-dimensional (3D) turbulence are very challenging for machine learning approaches. In this paper, we propose an implicit U-Net enhanced Fourier neural operator (IU-FNO) for stable and efficient predictions on the long-term large-scale dynamics of turbulence. The IU-FNO model employs implicit recurrent Fourier layers for deeper network extension and incorporates the U-net network for the accurate prediction on small-scale flow structures. The model is systematically tested in large-eddy simulations of three types of 3D turbulence, including forced homogeneous isotropic turbulence (HIT), temporally evolving turbulent mixing layer, and decaying homogeneous isotropic turbulence. The numerical simulations demonstrate that the IU-FNO model is more accurate than other FNO-based models including vanilla FNO, implicit FNO (IFNO) and U-Net enhanced FNO (U-FNO), and dynamic Smagorinsky model (DSM) in predicting a variety of statistics including the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and instantaneous spatial structures of flow field. Moreover, IU-FNO improves long-term stable predictions, which has not been achieved by the previous versions of FNO. Besides, the proposed model is much faster than traditional LES with DSM model, and can be well generalized to the situations of higher Taylor-Reynolds numbers and unseen flow regime of decaying turbulence.Comment: 45 pages, 21 figure

Label Mask for Multi-Label Text Classification

One of the key problems in multi-label text classification is how to take advantage of the correlation among labels. However, it is very challenging to directly model the correlations among labels in a complex and unknown label space. In this paper, we propose a Label Mask multi-label text classification model (LM-MTC), which is inspired by the idea of cloze questions of language model. LM-MTC is able to capture implicit relationships among labels through the powerful ability of pre-train language models. On the basis, we assign a different token to each potential label, and randomly mask the token with a certain probability to build a label based Masked Language Model (MLM). We train the MTC and MLM together, further improving the generalization ability of the model. A large number of experiments on multiple datasets demonstrate the effectiveness of our method