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

A mixture deep neural network GARCH model for volatility forecasting

Recently, deep neural networks have been widely used to solve financial risk modeling and forecasting challenges. Following this hotspot, this paper presents a mixture model for conditional volatility probability forecasting based on the deep autoregressive network and the Gaussian mixture model under the GARCH framework. An efficient algorithm for the model is developed. Both simulation and empirical results show that our model predicts conditional volatilities with smaller errors than the classical GARCH and ANN-GARCH models

Soil Organic Carbon Pool and the Production of Goji Berry (Lycium barbarum L.) as Affected by Different Fertilizer Combinations Under Drip Fertigation

Goji berries (Lycium barbarum L.), widely planted in arid to semi-arid regions, are a functional resource characterized by a homology of medicine and food. Changing extensive water and fertilizer management practices to drip fertigation is one of the most cost-effective ways to achieve the sustainable development of the Goji berry industry. This study explores the effects of different fertilizer combinations on the soil organic carbon pool and L. barbarum yield under drip fertigation in Ningxia, northwestern China. A two-year field experiment (2017–2019) was conducted using different levels of drip nitrogen (40, 60, and 80 mg L−1) and phosphorus (10, 20, and 30 mg L−1) fertigation. Compared with traditional manual fertilization (control), soil organic carbon contents in the 0–20, 20–40, and 40–60 cm layers increased by 33.6–144.4, 39.6–136.8, and 14.0–73.6%, respectively, across all fertigation treatments. With increasing levels of fertigation, the easily oxidizable organic carbon content increased most prominently in the 0–20 cm soil layer and reached the highest value (538 mg kg−1) under treatment with 60 mg L−1 nitrogen plus 10 mg L−1 phosphorus. The microbial biomass carbon contents in the 20–60 cm soil layer was markedly higher under treatment with 60 mg L−1 nitrogen plus 30 mg L−1 phosphorus compared with other treatments. Fertigation increased the soil carbon pool management index and L. barbarum yield. The highest two-year average yield (13,890 kg ha−1) was obtained under treatment with 60 mg L−1 nitrogen plus 30 mg L−1 phosphorus. These findings suggest that drip fertigation with 60 mg L−1 nitrogen plus 30 mg L−1 phosphorus is the optimal practice for carbon sequestration and sustainable production of L. barbarum in arid regions

Berberine Moderates Glucose and Lipid Metabolism through Multipathway Mechanism

Berberine is known to improve glucose and lipid metabolism disorders, but the mechanism is still under investigation. In this paper, we explored the effects of berberine on the weight, glucose levels, lipid metabolism, and serum insulin of KKAy mice and investigated its possible glucose and lipid-regulating mechanism. We randomly divided KKAy mice into two groups: berberine group (treated with 250 mg/kg/d berberine) and control group. Fasting blood glucose (FBG), weight, total cholesterol (TC), triglyceride (TG), high-density lipoprotein-cholesterol (HDL-c), low-density lipoprotein-cholesterol (LDL-c), and fasting serum insulin were measured in both groups. The oral glucose tolerance test (OGTT) was performed. RT2 PCR array gene expression analysis was performed using skeletal muscle of KKAy mice. Our data demonstrated that berberine significantly decreased FBG, area under the curve (AUC), fasting serum insulin (FINS), homeostasis model assessment insulin resistance (HOMA-IR) index, TC, and TG, compared with those of control group. RT2 profiler PCR array analysis showed that berberine upregulated the expression of glucose transporter 4 (GLUT4), mitogen-activated protein kinase 14 (MAPK14), MAPK8(c-jun N-terminal kinase, JNK), peroxisome proliferator-activated receptor α (PPARα), uncoupling protein 2 (UCP2), and hepatic nuclear factor 4α(HNF4α), whereas it downregulated the expression of PPARγ, CCAAT/enhancer-binding protein (CEBP), PPARγ coactivator 1α(PGC 1α), and resistin. These results suggest that berberine moderates glucose and lipid metabolism through a multipathway mechanism that includes AMP-activated protein kinase-(AMPK-) p38 MAPK-GLUT4, JNK pathway, and PPARα pathway

Ammonia Gas Detection by Tannic Acid Functionalized and Reduced Graphene Oxide at Room Temperature

Reduced graphene oxide (rGO) based chemiresistor gas sensor has received much attention in gas sensing for high sensitivity, room temperature operation, and reversible. Here, for the first time, we present a promising chemiresistor for ammonia gas detection based on tannic acid (TA) functionalized and reduced graphene oxide (rGOTA functionalized). Green reductant of TA plays a major role in both reducing process and enhancing the gas sensing properties of rGOTA functionalized. Our results show rGOTA functionalized only selective to ammonia with excellent respond, recovery, respond time, and recovery times. rGOTA functionalized electrical resistance decreases upon exposure to NH3 where we postulated that it is due to n-doping by TA and charge transfer between rGOTA functionalized and NH3 through hydrogen bonding. Furthermore, rGOTA functionalized hinders the needs for stimulus for both recovery and respond. The combination of greener sensing material and simplicity in overall sensor design provides a new sight for green reductant approach of rGO based chemiresistor gas sensor