Fluid Dynamics

Navier-Stokes Equation

\rho [kg/m^3] : fluid density

\mu  [Pa\cdot s] : dynamic viscosity

\nu [N/\rho=m^2/s] : kinematic viscosity

\vec{V}=(u,v,w) [m/s] : velocity

\forall : volume

Conservation of mass

  1. For a system:

        \[ \frac{d}{dt}M_{SYS}=0 \]

  2. For a C.V. (Reynolds transport theorem):\]

    \[\frac{\partial}{\partial t}\int_{CV}{\rho d\forall}+\int_{CS}{\rho \vec{V}\cdot \hat{n} dA}=0 \]

Differential form (\delta x\delta y\delta z):

    \[ \frac{\partial}{\partial t}\int_{CV}{\rho d\forall}=\frac{\rho}{\partial t} \delta x\delta y\delta z \]

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CPU vs GPU | Neural Network

GPU vs CPU neural network

I have done two libraries for AI,

  • CPU with Eigen 1 2
  • GPU with CUDA 1 2

They are optimized and work properly. However, there are significant differences in performance.

The GPU library can adapt to other Nvidia graphic card and furthermore improve the time that I obtain within my circumstances. In addition, the graphics card industry is constantly improving their models and we have recently seen the clusters of the graphics card in the business.

The CPU library is stable and can work on any computer because it does not rely on Nvidia hardware, it is a completely cross-platform library that only needs Eigen library which is compatible with every OS.

I have used for the test: i7-7700k vs Nvidia GeForce GTX 1070

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Deep Neural Network in GPU

I have been developing a neural network API for GPUs. It is based on CUDA technology and I tried to exploit the full potential of the computer.

Most of us, do not know the real potential of GPUs in AI. This kind of hardware is specialized in logical operations and it was used by the industry of engines and videogames. Some years ago, we have experienced a ‘boom’ in graphics cards, the improvement in speed, price and the ease of programming had triggered a new mother-lode.

GPUs provide a bunch of parallelism algorithms to improve performance.

As we know, neural networks use matrix-to-matrix and matrix-to-vector operations. We can take advance in the optimization of them. Unfortunately, feed-forward and backpropagation are linear functions, they can neither be optimized nor parallelized.


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LiDAR: Autonomous Car

LiDAR implementation in self-driving cars

LiDAR (Light Imaging, Direction And Ranging) is a method that measures the distance to a target by illuminating the target with pulsed laser light and measuring the reflected pulses with a sensor. Autonomous cars take advantage of this new technology.

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