scholarly journals Deep learning of mixing by two ‘atoms’ of stratified turbulence

2019 ◽  
Vol 861 ◽  
Author(s):  
Hesam Salehipour ◽  
W. R. Peltier
Keyword(s):  
Deep Learning ◽  
Ad Hoc ◽  
Training Data ◽  
Global Ocean ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Diapycnal Mixing ◽  
Ocean Turbulence ◽  
High Level

Current global ocean models rely on ad hoc parameterizations of diapycnal mixing, in which the efficiency of mixing is globally assumed to be fixed at 20 %, despite increasing evidence that this assumption is questionable. As an ansatz for small-scale ocean turbulence, we may focus on stratified shear flows susceptible to either Kelvin–Helmholtz (KHI) or Holmboe wave (HWI) instability. Recently, an unprecedented volume of data has been generated through direct numerical simulation (DNS) of these flows. In this paper, we describe the application of deep learning methods to the discovery of a generic parameterization of diapycnal mixing using the available DNS dataset. We furthermore demonstrate that the proposed model is far more universal compared to recently published parameterizations. We show that a neural network appropriately trained on KHI- and HWI-induced turbulence is capable of predicting mixing efficiency associated with unseen regions of the parameter space well beyond the range of the training data. Strikingly, the high-level patterns learned based on the KHI and weakly stratified HWI are ‘transferable’ to predict HWI-induced mixing efficiency under much more strongly stratified conditions, suggesting that through the application of appropriate networks, significant universal abstractions of density-stratified turbulent mixing have been recognized.

Time-dependent, non-monotonic mixing in stratified turbulent shear flows: implications for oceanographic estimates of buoyancy flux

2013 ◽  
Vol 736 ◽  
pp. 570-593 ◽  
Author(s):  
A. Mashayek ◽  
C. P. Caulfield ◽  
W. R. Peltier
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Buoyancy Flux ◽  
Shear Instability ◽  
Turbulent Shear ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Flow Evolution

AbstractWe employ direct numerical simulation to investigate the efficiency of diapycnal mixing by shear-induced turbulence in stably stratified free shear layers for flows with bulk Richardson numbers in the range $0. 12\leq R{i}_{0} \leq 0. 2$ and Reynolds number $Re= 6000$. We show that mixing efficiency depends non-monotonically upon $R{i}_{0} $, peaking in the range 0.14–0.16, which coincides closely with the range in which both the buoyancy flux and the dissipation rate are maximum. By detailed analyses of the energetics of flow evolution and the underlying dynamics, we show that the existence of high mixing efficiency in the range $0. 14\lt R{i}_{0} \lt 0. 16$ is due to the emergence of a large number of small-scale instabilities which do not exist at lower Richardson numbers and are stabilized at high Richardson numbers. As discussed in Mashayek & Peltier (J. Fluid Mech., vol. 725, 2013, pp. 216–261), the existence of such a well-populated ‘zoo’ of secondary instabilities at intermediate Richardson numbers and the subsequent high mixing efficiency is realized only if the Reynolds number is higher than a critical value which is generally higher than that achievable in laboratory settings, as well as that which was achieved in the majority of previous numerical studies of shear-induced stratified turbulence. We furthermore show that the primary assumptions upon which the widely employed Osborn (J. Phys. Oceanogr. vol. 10, 1980, pp. 83–89) formula is based, as well as its counterparts and derivatives, which relate buoyancy flux to dissipation rate through a (constant) flux coefficient ($\Gamma $), fail at higher Richardson numbers provided that the Reynolds number is sufficiently high. Specifically, we show that the assumptions of fully developed, stationary, and isotropic turbulence all break down at high Richardson numbers. We show that the breakdown of these assumptions occurs most prominently at Richardson numbers above that corresponding to the maximum mixing efficiency, a fact that highlights the importance of the non-monotonicity of the dependence of mixing efficiency upon Richardson number, which we establish to be characteristic of stratified shear-induced turbulence. At high $R{i}_{0} $, the lifecycle of the turbulence is composed of a rapidly growing phase followed by a phase of rapid decay. Throughout the lifecycle, there is considerable exchange of energy between the small-scale turbulence and larger coherent structures which survive the various stages of flow evolution. Since shear instability is one of the most prominent mechanisms for turbulent dissipation of energy at scales below hundreds of metres and at various depths of the ocean, our results have important implications for the inference of turbulent diffusivities on the basis of microstructure measurements in the oceanic environment.

scholarly journals A statistical mechanics approach to mixing in stratified fluids

2016 ◽  
Vol 810 ◽  
pp. 554-583 ◽  
Author(s):  
A. Venaille ◽  
L. Gostiaux ◽  
J. Sommeria
Keyword(s):  
Potential Energy ◽  
Statistical Mechanics ◽  
Richardson Number ◽  
Degrees Of Freedom ◽  
Coarse Grained ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Adiabatic Dynamics ◽  
Boussinesq Fluid

Predicting how much mixing occurs when a given amount of energy is injected into a Boussinesq fluid is a long-standing problem in stratified turbulence. The huge number of degrees of freedom involved in these processes renders extremely difficult a deterministic approach to the problem. Here we present a statistical mechanics approach yielding a prediction for a cumulative, global mixing efficiency as a function of a global Richardson number and the background buoyancy profile. Assuming random evolution through turbulent stirring, the theory predicts that the inviscid, adiabatic dynamics is attracted irreversibly towards an equilibrium state characterised by a smooth, stable buoyancy profile at a coarse-grained level, upon which are fine-scale fluctuations of velocity and buoyancy. The convergence towards a coarse-grained buoyancy profile different from the initial one corresponds to an irreversible increase of potential energy, and the efficiency of mixing is quantified as the ratio of this potential energy increase to the total energy injected into the system. The remaining part of the energy is lost into small-scale fluctuations. We show that for sufficiently large Richardson number, there is equipartition between potential and kinetic energy, provided that the background buoyancy profile is strictly monotonic. This yields a mixing efficiency of 0.25, which provides statistical mechanics support for previous predictions based on phenomenological kinematics arguments. In the general case, the cumulative, global mixing efficiency predicted by the equilibrium theory can be computed using an algorithm based on a maximum entropy production principle. It is shown in particular that the variation of mixing efficiency with the Richardson number strongly depends on the background buoyancy profile. This approach could be useful to the understanding of mixing in stratified turbulence in the limit of large Reynolds and Péclet numbers.

scholarly journals Robust deep learning classification of adamantinomatous craniopharyngioma from limited preoperative radiographic images

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Eric W. Prince ◽  
Ros Whelan ◽  
David M. Mirsky ◽  
Nicholas Stence ◽  
Susan Staulcup ◽  
...  
Keyword(s):  
Deep Learning ◽  
Model Performance ◽  
Pediatric Brain Tumor ◽  
Training Data ◽  
Small Scale ◽  
Radiographic Images ◽  
Non Invasive ◽  
Magnetic Resonance Imaging Mri ◽  
Adamantinomatous Craniopharyngioma

Abstract Deep learning (DL) is a widely applied mathematical modeling technique. Classically, DL models utilize large volumes of training data, which are not available in many healthcare contexts. For patients with brain tumors, non-invasive diagnosis would represent a substantial clinical advance, potentially sparing patients from the risks associated with surgical intervention on the brain. Such an approach will depend upon highly accurate models built using the limited datasets that are available. Herein, we present a novel genetic algorithm (GA) that identifies optimal architecture parameters using feature embeddings from state-of-the-art image classification networks to identify the pediatric brain tumor, adamantinomatous craniopharyngioma (ACP). We optimized classification models for preoperative Computed Tomography (CT), Magnetic Resonance Imaging (MRI), and combined CT and MRI datasets with demonstrated test accuracies of 85.3%, 83.3%, and 87.8%, respectively. Notably, our GA improved baseline model performance by up to 38%. This work advances DL and its applications within healthcare by identifying optimized networks in small-scale data contexts. The proposed system is easily implementable and scalable for non-invasive computer-aided diagnosis, even for uncommon diseases.

scholarly journals Exploiting self-organized criticality in strongly stratified turbulence

2021 ◽  
Vol 933 ◽  
Author(s):  
Gregory P. Chini ◽  
Guillaume Michel ◽  
Keith Julien ◽  
Cesar B. Rocha ◽  
Colm-cille P. Caulfield
Keyword(s):  
Large Scale ◽  
Ad Hoc ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Marginal Stability ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Self Organized ◽  
Reduced Equations ◽  
Self Organized Criticality

A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large Reynolds numbers. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporal scales, yielding simplified partial differential equations governing the coupled evolution of slow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internal waves. The dynamics captured by the coupled reduced equations is illustrated in the context of two-dimensional strongly stratified Kolmogorov flow. A noteworthy feature of the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL) dynamics about the comparably slowly varying large-scale fields. Crucially, this QL reduction is not invoked as an ad hoc closure approximation, but rather is derived in a physically relevant and mathematically consistent distinguished limit. Further analysis of the resulting slow–fast QL system shows how the amplitude of the fast stratified-shear instabilities is slaved to the slowly evolving mean fields to ensure the marginal stability of the latter. Physically, this marginal stability condition appears to be compatible with recent evidence of self-organized criticality in both observations and simulations of stratified turbulence. Algorithmically, the slaving of the fluctuation fields enables numerical simulations to be time-evolved strictly on the slow time scale of the hydrostatic flow. The reduced equations thus provide a solid mathematical foundation for future studies of three-dimensional strongly stratified turbulence in extreme parameter regimes of geophysical relevance and suggest avenues for new sub-grid-scale parametrizations.

scholarly journals On regularization properties of artificial datasets for deep learning

2019 ◽  
Vol 0 (9/2019) ◽  
pp. 13-18
Author(s):  
Karol Antczak
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Deep Neural Networks ◽  
Real Data ◽  
Training Data ◽  
Generation Process ◽  
Data Generation ◽  
Artificial Data ◽  
High Level ◽  
Artificial Datasets

The paper discusses regularization properties of artificial data for deep learning. Artificial datasets allow to train neural networks in the case of a real data shortage. It is demonstrated that the artificial data generation process, described as injecting noise to high-level features, bears several similarities to existing regularization methods for deep neural networks. One can treat this property of artificial data as a kind of “deep” regularization. It is thus possible to regularize hidden layers of the network by generating the training data in a certain way.

scholarly journals Anomaly Detection Neural Network with Dual Auto-Encoders GAN and Its Industrial Inspection Applications

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3336 ◽  
Author(s):  
Ta-Wei Tang ◽  
Wei-Han Kuo ◽  
Jauh-Hsiang Lan ◽  
Chien-Fang Ding ◽  
Hakiem Hsu ◽  
...  
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Anomaly Detection ◽  
Training Data ◽  
Labor Costs ◽  
Generative Adversarial Network ◽  
Detection Ability ◽  
Adversarial Network ◽  
Automated Optical Inspection ◽  
High Level

Recently, researchers have been studying methods to introduce deep learning into automated optical inspection (AOI) systems to reduce labor costs. However, the integration of deep learning in the industry may encounter major challenges such as sample imbalance (defective products that only account for a small proportion). Therefore, in this study, an anomaly detection neural network, dual auto-encoder generative adversarial network (DAGAN), was developed to solve the problem of sample imbalance. With skip-connection and dual auto-encoder architecture, the proposed method exhibited excellent image reconstruction ability and training stability. Three datasets, namely public industrial detection training set, MVTec AD, with mobile phone screen glass and wood defect detection datasets, were used to verify the inspection ability of DAGAN. In addition, training with a limited amount of data was proposed to verify its detection ability. The results demonstrated that the areas under the curve (AUCs) of DAGAN were better than previous generative adversarial network-based anomaly detection models in 13 out of 17 categories in these datasets, especially in categories with high variability or noise. The maximum AUC improvement was 0.250 (toothbrush). Moreover, the proposed method exhibited better detection ability than the U-Net auto-encoder, which indicates the function of discriminator in this application. Furthermore, the proposed method had a high level of AUCs when using only a small amount of training data. DAGAN can significantly reduce the time and cost of collecting and labeling data when it is applied to industrial detection.

scholarly journals New Machine Learning Developments in ROOT/TMVA

2019 ◽  
Vol 214 ◽  
pp. 06014
Author(s):  
Kim Albertsson ◽  
Sergei Gleyzer ◽  
Marc Huwiler ◽  
Vladimir Ilievski ◽  
Lorenzo Moneta ◽  
...  
Keyword(s):  
Machine Learning ◽  
Deep Learning ◽  
Cross Validation ◽  
High Energy Physics ◽  
High Energy ◽  
Small Scale ◽  
Training Time ◽  
Learning Module ◽  
Boosted Decision Tree ◽  
High Level

The Toolkit for Multivariate Analysis, TMVA, the machine learning package integrated into the ROOT data analysis framework, has recently seen improvements to its deep learning module, parallelisation of multivariate methods and cross validation. Performance benchmarks on datasets from high-energy physics are presented with a particular focus on the new deep learning module which contains robust fully-connected, convolutional and recurrent deep neural networks implemented on CPU and GPU architectures. Both dense and convo-lutional layers are shown to be competitive on small-scale networks suitable for high-level physics analyses in both training and in single-event evaluation. Par-allelisation efforts show an asymptotical 3-fold reduction in boosted decision tree training time while the cross validation implementation shows significant speed up with parallel fold evaluation.

scholarly journals 4-Class MI-EEG Signal Generation and Recognition with CVAE-GAN

2021 ◽  
Vol 11 (4) ◽  
pp. 1798
Author(s):  
Jun Yang ◽  
Huijuan Yu ◽  
Tao Shen ◽  
Yaolian Song ◽  
Zhuangfei Chen
Keyword(s):  
Deep Learning ◽  
Data Augmentation ◽  
Feature Matching ◽  
Continuous Optimization ◽  
Training Data ◽  
Small Scale ◽  
Eeg Signal ◽  
Generative Adversarial Network ◽  
The Real ◽  
Adversarial Network

As the capability of an electroencephalogram’s (EEG) measurement of the real-time electrodynamics of the human brain is known to all, signal processing techniques, particularly deep learning, could either provide a novel solution for learning but also optimize robust representations from EEG signals. Considering the limited data collection and inadequate concentration of during subjects testing, it becomes essential to obtain sufficient training data and useful features with a potential end-user of a brain–computer interface (BCI) system. In this paper, we combined a conditional variational auto-encoder network (CVAE) with a generative adversarial network (GAN) for learning latent representations from EEG brain signals. By updating the fine-tuned parameter fed into the resulting generative model, we could synthetize the EEG signal under a specific category. We employed an encoder network to obtain the distributed samples of the EEG signal, and applied an adversarial learning mechanism to continuous optimization of the parameters of the generator, discriminator and classifier. The CVAE was adopted to adjust the synthetics more approximately to the real sample class. Finally, we demonstrated our approach take advantages of both statistic and feature matching to make the training process converge faster and more stable and address the problem of small-scale datasets in deep learning applications for motor imagery tasks through data augmentation. The augmented training datasets produced by our proposed CVAE-GAN method significantly enhance the performance of MI-EEG recognition.

scholarly journals Unsupervised Deep Learning for Landslide Detection from Multispectral Sentinel-2 Imagery

2021 ◽  
Vol 13 (22) ◽  
pp. 4698
Author(s):  
Hejar Shahabi ◽  
Maryam Rahimzad ◽  
Sepideh Tavakkoli Piralilou ◽  
Omid Ghorbanzadeh ◽  
Saied Homayouni ◽  
...  
Keyword(s):  
Deep Learning ◽  
Training Data ◽  
New Approach ◽  
Digital Elevation ◽  
Unsupervised Deep Learning ◽  
Elevation Model ◽  
High Level ◽  
The Impact ◽  
Noise Fraction ◽  
Sentinel 2

This paper proposes a new approach based on an unsupervised deep learning (DL) model for landslide detection. Recently, supervised DL models using convolutional neural networks (CNN) have been widely studied for landslide detection. Even though these models provide robust performance and reliable results, they depend highly on a large labeled dataset for their training step. As an alternative, in this paper, we developed an unsupervised learning model by employing a convolutional auto-encoder (CAE) to deal with the problem of limited labeled data for training. The CAE was used to learn and extract the abstract and high-level features without using training data. To assess the performance of the proposed approach, we used Sentinel-2 imagery and a digital elevation model (DEM) to map landslides in three different case studies in India, China, and Taiwan. Using minimum noise fraction (MNF) transformation, we reduced the multispectral dimension to three features containing more than 80% of scene information. Next, these features were stacked with slope data and NDVI as inputs to the CAE model. The Huber reconstruction loss was used to evaluate the inputs. We achieved reconstruction losses ranging from 0.10 to 0.147 for the MNF features, slope, and NDVI stack for all three study areas. The mini-batch K-means clustering method was used to cluster the features into two to five classes. To evaluate the impact of deep features on landslide detection, we first clustered a stack of MNF features, slope, and NDVI, then the same ones plus with the deep features. For all cases, clustering based on deep features provided the highest precision, recall, F1-score, and mean intersection over the union in landslide detection.

scholarly journals Training a Deep Learning Network with an Insignificantly Small Dataset

2020 ◽  
Vol 9 (4) ◽  
pp. 3105-3111
Keyword(s):  
Deep Learning ◽  
Network Model ◽  
Detection System ◽  
Training Data ◽  
Small Scale ◽  
Processing Unit ◽  
Desktop Computer ◽  
Learning Network ◽  
Deep Learning Network ◽  
Small Dataset

In the last few years, Deep Learning is one of the top research areas in academia as well as in industry. Every industry is now looking for a deep learning-based solution to the problems in hand. As a researcher, learning “Deep Learning” through practical experiments will be a very challenging task. Particularly, training a deep learning network with huge amount of training data will make it impractical to do this on a normal desktop computer or laptop. Even a small-scale application in computer vision using deep learning techniques will require several days of training the deep network model on a very higher end Graphical Processing Unit (GPU) clusters or Tensor Processing Unit (TPU) clusters that makes impractical to do that research on a conventional laptop. In this work, we address the possibilities of training a deep learning network with an insignificantly small dataset. Here we mean “significantly small dataset’ as a dataset with only few images (<10) per class. Since we are going to design a prototype drone detection system which is a single class classification problem, we hereby try to train the deep learning network only with few drone images (2 images only). Our research question is: will it be possible to train a YOLO deep learning network model only with two images and achieve a descent detection accurate on a constrained test dataset of drones? This paper addresses that issue and our results prove that it is possible to train a deep learning network only with two images and achieve good performance under constrained application environments.

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