This course concerns the latest techniques in deep learning and representation learning, focusing on supervised and unsupervised deep learning, embedding methods, metric learning, convolutional and recurrent nets, with applications to computer vision, natural language understanding, and speech recognition.
Home Contribution instructions 1. Week 1 1. Problem Motivation, Linear Algebra, and Visualization 2. Week 2 2. Introduction to Gradient Descent and Backpropagation Algorithm 2.
Artificial neural networks ANNs 3. Week 3 3. Visualization of neural networks parameter transformation and fundamental concepts of convolution 3. Properties of natural signals 4. Week 4 4. Linear Algebra and Convolutions 5. Week 5 5. Optimisation Techniques I 5. Optimisation Techniques II 5. Understanding convolutions and automatic differentiation engine 6.
Week 6 6. Applications of Convolutional Network 6. Week 7 7. Energy-Based Models 7. Introduction to Autoencoders 8. Week 8 8. Contrastive Methods in Energy-Based Models 8. Generative Models - Variational Autoencoders 9. Week 9 9. World Models and Generative Adversarial Networks 9. Generative Adversarial Networks Week 10 Self-Supervised Learning - Pretext Tasks Google DriveNotebooks.
Yann LeCun yann cs. Alfredo Canziani canziani nyu. Mark Goldstein goldstein nyu. Zeming Lin zl nyu.Vortex induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure.
Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not straightforward to solve using standard computational fluid dynamics CFD methods, especially since no information is provided for the pressure. An even greater challenge is to infer the lift and drag forces given some dye or smoke visualizations of the flow field.
In the second case, given scattered data in space-time on a concentration field only, we use five coupled deep neural networks to infer very accurately the vector velocity field and all other quantities of interest as before. This new paradigm of inference in fluid mechanics for coupled multi-physics problems enables velocity and pressure quantification from flow snapshots in small subdomains and can be exploited for flow control applications and also for system identification.
We begin by considering the prototype Vortex induced vibrations VIV problem of flow past a circular cylinder. The fluid motion is governed by the incompressible Navier-Stokes equations while the dynamics of the structure is described in a general form involving displacement, velocity, and acceleration terms. In particular, let us consider the two-dimensional version of flow over a flexible cable, i.
In two dimensions, the physical model of the cable reduces to a mass-spring-damper system. There are two directions of motion for the cylinder: the streamwise i. In this workwe assume that the cylinder can only move in the crossflow i. However, it is a simple extension to study cases where the cylinder is free to move in both streamwise and crossflow directions.
The cylinder displacement is defined by the variable corresponding to the crossflow motion.
The equation of motion for the cylinder is then given by. The fluid lift force on the structure is denoted by.
The mass of the cylinder is usually a known quantity; however, the damping and the stiffness parameters are often unknown in practice. In the current work, we put forth a deep learning approach for estimating these parameters from measurements. We start by assuming that we have access to the input-output data and on the displacement and the lift force functions, respectively. Having access to direct measurements of the forces exerted by the fluid on the structure is obviously a strong assumption.
However, we start with this simpler but pedagogical case and we will relax this assumption later in this section. Inspired by recent developments in physics informed deep learning and deep hidden physics modelswe propose to approximate the unknown function by a deep neural network.
This choice is motivated by modern techniques for solving forward and inverse problems involving partial differential equations, where the unknown solution is approximated either by a neural network or a Gaussian process. Moreover, placing a prior on the solution is fully justified by similar approaches pursued in the past centuries by classical methods of solving partial differential equations such as finite elements, finite differences, or spectral methods, where one would expand the unknown solution in terms of an appropriate set of basis functions.
Approximating the unknown function by a deep neural network and using the above equation allow us to obtain the following physics-informed neural network see the following figure. Pedagogical physics-informed neural network: A plain vanilla densely connected physics uninformed neural network, with 10 hidden layers and 32 neurons per hidden layer per output variable i. As for the activation functions, we use sin x.
For illustration purposes only, the network depicted in this figure comprises of 2 hidden layers and 4 neurons per hidden layers. We employ automatic differentiation to obtain the required derivatives to compute the residual physics informed networks. The total loss function is composed of the regression loss of the displacement on the training data, and the loss imposed by the differential equation.
Moreover, the gradients of the loss function are back-propagated through the entire network to train the parameters of the neural network as well as the damping and the stiffness parameters using the Adam optimizer. It is worth noting that the damping and the stiffness parameters turn into parameters of the resulting physics informed neural network. We obtain the required derivatives to compute the residual network by applying the chain rule for differentiating compositions of functions using automatic differentiation.
Automatic differentiation is different from, and in several respects superior to, numerical or symbolic differentiation — two commonly encountered techniques of computing derivatives. In its most basic description, automatic differentiation relies on the fact that all numerical computations are ultimately compositions of a finite set of elementary operations for which derivatives are known.
Combining the derivatives of the constituent operations through the chain rule gives the derivative of the overall composition.Our discussion of fluid pressure began in the previous chapter. As a reminder, Pressure is the force applied perpendicular to a surface per unit area. When we speak of pressure we are typically dealing with a gas or a liquid that is confined to a container.
For the remainder of this course we will use psi as the standard unit of pressure when working in the USCS of units.Real-Time User-Guided Image Colorization with Learned Deep Priors
The pressure when measured relative to an absolute vacuum is called the absolute pressure. In practice a near absolute vacuum is difficult to obtain.
Therefore most pressure-measuring devices record pressure relative to the local atmospheric pressure. In this design the pressure gauge is calibrated to read zero when it is at atmospheric pressure and the pressure indicated is actually the difference between the absolute pressure and local atmospheric pressure. This difference is called the gauge pressure and can be expressed as.
An automobile tire is inflated to a pressure of 30 psi gauge. Determine the absolute pressure in the tire. The absolute pressure inside the tire is. The pressure in a fluid increases with depth simply because more fluid sits above the deeper layers of fluid. In order for the deeper layers of fluid to support the increasing weight resting above it, the pressure of the fluid must increase accordingly.
For a static, homogenous, incompressible fluid the relationship between pressure and depth is. The minus sign indicates that a decrease in elevation causes an increase in pressure.
In practice I just calculate the magnitude of the change in pressure ignore the minus sign and afterwards determine whether the pressure decreased increase in elevation or the pressure increased decrease in elevation. Just remember that as you increase the amount of fluid above you, the fluid pressure will also increase.
As one descends to the bottom of the pool the pressure increases by about 3. Atmospheric pressure is Was the hiker climbing or descending? The pressure was larger at the start of the trip. In order for the pressure to decrease the hiker must have been ascending.Export Loading.
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Sign up for. Web Translator without limits. Try free for 30 days or. Learn more. Tech giants Google, Microsoft and Facebook are all applying the lessons of machine learning to translation, but a small company called DeepL has outdone them all and raised the bar for the field. TechCrunch USA. DeepL has also outperformed other services, thanks to more "French-sounding" expressions.
Le Monde France. Even though the translations from English by Google and Microsoft are quite good, DeepL still surpasses them. We have translated a report from a French daily newspaper - the DeepL result was perfect. A quick test carried out for the combination English-Italian and vice versa, even without any statistical pretensions, allowed us to confirm that the quality of the translation is really good.
Especially from Italian into English. La Stampa Italy.
Hidden Fluid Mechanics
The system recognizes the language quickly and automatically, converting the words into the language you want and trying to add the particular linguistic nuances and expressions.
ABC Spain. Indeed, a few tests show that DeepL Translator offers better translations than Google Translate when it comes to Dutch to English and vice versa.We present hidden fluid mechanics HFMa physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations.
In particular, we seek to leverage the underlying conservation laws i. Our approach towards solving the aforementioned data assimilation problem is unique as we design an algorithm that is agnostic to the geometry or the initial and boundary conditions.
This makes HFM highly flexible in choosing the spatio-temporal domain of interest for data acquisition as well as subsequent training and predictions. Consequently, the predictions made by HFM are among those cases where a pure machine learning strategy or a mere scientific computing approach simply cannot reproduce.
The proposed algorithm achieves accurate predictions of the pressure and velocity fields in both two and three dimensional flows for several benchmark problems motivated by real-world applications. Our results demonstrate that this relatively simple methodology can be used in physical and biomedical problems to extract valuable quantitative information e. Let us consider the transport of a passive scalar field by a velocity field. Such a problem arises, for example, while studying the spreading of smoke or dye advected by a given velocity field and subject to molecular diffusion.
We expect the dynamics of to be governed by an effective transport equation written in the form of. Transport of scalar fields in fluid flow has been studied in numerous applications such as aerodynamicsbiofluid mechanicsand non-reactive flow mixing to name a few.
The use of smoke in wind tunnels or dye in water tunnels for flow visualization and quantification has long been practiced in experimental fluid mechanics. The use of scalar transport in conjunction with advanced imaging modalities to quantify blood flow in the vascular networks is now a common practice. For example, coronary computed tomography CT angiography is typically performed on multidetector CT systems after the injection of non-diffusible iodine contrast agent, which allows coronary artery visualization and the detection of coronary stenoses.
Another example is the quantification of cerebral blood flowwhich is detrimental in the prognostic assessments in stroke patients using a contrast agent and perfusion CT, and in cognitive neuroscience with the use of functional magnetic resonance imaging that only relies on the blood-oxygen-level dependent contrast to measure brain activity.
Inspired by recent developments in physics-informed deep learning and deep hidden physics modelswe propose to leverage the hidden physics of fluid mechanics i. This choice is motivated by modern techniques for solving forward and inverse problems associated with partial differential equations, where the unknown solution is approximated either by a neural network or a Gaussian process.
Moreover, placing a prior on the solution itself is fully justified by the similar approach pursued in the past century using classical methods of solving partial differential equations such as finite elements and spectral methodswhere one would expand the unknown solution in terms of an appropriate set of basis functions.
Our focus here is the transport of a passive scalar by incompressible Newtonian flows in both unbounded geometries i. We demonstrate the success of our Navier-Stokes informed deep learning algorithm by recovering the flow velocity and pressure fields solely from time series data collected on the passive scalar in arbitrary domains. In the above equations, and are the, and components of the velocity fieldrespectively, and denotes the pressure.
A passive scalar is a diffusive field in the fluid flow that has no dynamical effect such as the effect of temperature in a buoyancy-driven flow on the fluid motion itself. Smoke and dye are two typical examples of passive scalars. In this work, we assume that the only observables are noisy data on the concentration of the passive scalar.
Given such data, scattered in space and time, we are interested in inferring the latent hidden quantities,and. To solve the aforementioned data assimilation problem, we would like to design an algorithm that is agnostic to the geometry as well as the initial and boundary conditions.
This is enabling as it will give us the flexibility to work with data acquired in arbitrarily complex domains such as human arteries or brain aneurysms. One question that would naturally arise is whether the information on the passive scalar in the training domain and near its boundaries is sufficient to result in a unique velocity field.
The answer is that normally there are no guarantees for unique solutions unless some form of boundary conditions are explicitly imposed on the domain boundaries.
Deep Learning of Vortex Induced Vibrations
However, as shown later for the benchmark problems studied in the current work, an informed selection of the training boundaries in the regions where there are sufficient gradients in the concentration of the passive scalar would eliminate the requirement of imposing velocity and pressure boundary conditions.
In addition to the proper design of the training domain and the use of the passive scalarwe can improve the model predictions further by introducing an auxiliary variable essentially the complement of that satisfies the transport equation. This can be clearly seen by a change of variable from to and using equation scalar transport equation. The complementary nature of the auxiliary variable helps the algorithm better detect the geometry and the corresponding boundary conditions.
This makes the training algorithm agnostic to the physical geometry of the problem, hence, keeping the implementation and training significantly simpler. In addition, the region of interest becomes very flexible to be chosen with its boundaries no longer required to be the physical boundaries.GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together.
If nothing happens, download GitHub Desktop and try again. If nothing happens, download Xcode and try again. If nothing happens, download the GitHub extension for Visual Studio and try again. Note that numpy cmake option should be set to enable support for numpy arrays. The left image shows the middle slice of xy domain, and the right image is the middle slice view of zy domain.
In each image, the top three rows are velocity profiles, and the rest rows are vorticity profiles. Skip to content. Dismiss Join GitHub today GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together.
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Deep Learning of Vortex Induced Vibrations
Find file. Sign in Sign up. Go back. Launching Xcode If nothing happens, download Xcode and try again. Latest commit Fetching latest commit…. Result 3D Reconstruction from each parameter after epochs. You signed in with another tab or window. Reload to refresh your session. You signed out in another tab or window.
Feb 14, Update run. Dec 18,