Embed Size (px)
Citation preview
Tensor Physics for Deep Learning
ujava.org Workshop
2015-04-26
www.idosi.com
CEO 강신동
Shindong KANG
(주)지능도시
www.idosi.comujava.org
www.idosi.comspaceapi.org
Differential Equation
F = maF = mg (g=9.8m/sec2, 10m/sec2)
ma = mg a = g y'' = g
y'' – g = 0
Differential Equation
www.idosi.comGeometry
www.idosi.comEuclidean Geometry
www.idosi.comNumber
Dragon Balls Pigs
www.idosi.comNumber Line
SET
2 = 1 + 1 3 = 1 + 1 + 1 3 = 2 + 1
100 = 1+1+...+1 100 = 99 + 1
www.idosi.comPoint Position
www.idosi.comVector
www.idosi.comLinearity
www.idosi.comRelative Coordinates Systems
www.idosi.comRelative Coordinates Systems
www.idosi.comScalars and Vectors
www.idosi.comDimension
www.idosi.comCartesian Coordinates
www.idosi.comCartesian Coordinates
www.idosi.comPolar Coordinates
www.idosi.comCylinderical Coordinates
www.idosi.comSpherical Coordinates
www.idosi.comToroidal Coordinates
www.idosi.comSlope
www.idosi.comSlope
1
www.idosi.comSlope
1
2
www.idosi.comSlope
1
2
10
www.idosi.comVelocity
mm/picosec
km/hr
m/sec
www.idosi.comInertia
www.idosi.comGravity & Straight Line
www.idosi.comTime & Space
2 cm
www.idosi.comFree Axes
www.idosi.comField
Field
www.idosi.comScalar Field
www.idosi.comScalar Field
www.idosi.comScalar 3D Field
www.idosi.comVector Field
www.idosi.comStress Tensor Field 3D
www.idosi.comTensor Field 3D
www.idosi.comVector & Coordinates Transform
Vector & Coordinates Transform
www.idosi.comHeat Transfer
www.idosi.comFluid Dynamics
www.idosi.comBasis Vectors
www.idosi.comBasis Vectors
1. Linear Combination
2. Linear Independent
Vector set = basis
Vector space dimension = basis vector count
www.idosi.comCNN
www.idosi.comEinstein Summation Convention
www.idosi.comMathematical expression LaTex
www.idosi.comOblique Coordinates
www.idosi.comVector Addition
www.idosi.comVector Addition with Parallel Projection
Contravariable
Covariant
www.idosi.comCoordinates Transform
www.idosi.com3D Coordinates
www.idosi.comContravariant & Covariant
www.idosi.comDot Product (Inner Product) with basis vector
www.idosi.comDot Product (Inner Product)
www.idosi.comDot Product (Inner Product)
www.idosi.comVector Dot Product Physics
www.idosi.comCrocess Product & Physical mean
www.idosi.comPrecession with Cross Product
www.idosi.comTensor
Tensor
www.idosi.comRank 0 : Scalar
www.idosi.comRank 1 : Vector
www.idosi.comDimension & Physical Quantity
n Dimension
1, 2, 3, 4, ...
1
1, 4, 9, 16, ...
www.idosi.comRank 2 : Tensor
www.idosi.comRank N : Tensor
www.idosi.comHigh Dimension Vector & Low Dimension Tensor
10 Dimension Vector Rank 1 Tensor(1,2,3,4,5,6,7,8,9,10)
3 Dimension Stress Rank 2 Tensor
www.idosi.comTensor Contraction
www.idosi.comTensor Physics
Tensor Physics
www.idosi.comNewton's Laws of Motion
www.idosi.comDriving Force
www.idosi.comForce of Point
www.idosi.comForce of Line
www.idosi.comForce of Area
www.idosi.comHoney
www.idosi.comForce of Cubic
www.idosi.comStress
www.idosi.comNewtonian Fluid
www.idosi.comNon-Newtonian Fluid
Thank you !
(주)지능도시
Intelligent City Ltd.
강신동
Shindong KANG
![Deep learning con TensorFloPor ejemplo, podr amos tener un tensor de tipo oat32 con rank 2 y con shape [3, 4]. Gabriel Munoz~ R os Deep learning con TensorFlow Variables Las variables](https://img.pdfslide.tips/doc/110x75/5e9964acb9507e4a325d4764/deep-learning-con-por-ejemplo-podr-amos-tener-un-tensor-de-tipo-oat32-con-rank.jpg){kind=icon}
