ujava.org workshop: Tensor Physics for Deep Learning. speaker is Shindong Kang of www.idosi.com

1. Tensor Physics
for Deep Learning
ujava.org Workshop
2015-04-26
www.idosi.com
CEO 강신동
Shindong KANG
(주)지능도시

2. www.idosi.comujava.org

3. www.idosi.comspaceapi.org

4. Differential Equation
F = ma
F = mg (g=9.8m/sec2, 10m/sec2)
ma = mg
a = g
y'' = g
y'' – g = 0

5. Differential Equation

6. www.idosi.comGeometry

7. www.idosi.comEuclidean Geometry

8. www.idosi.comRiemannian Geometry

9. www.idosi.comNumber
Dragon Balls
Pigs

10. www.idosi.comNumber Line
SET
2 = 1 + 1
3 = 1 + 1 + 1
3 = 2 + 1
100 = 1+1+...+1
100 = 99 + 1

11. www.idosi.comPoint Position

12. www.idosi.comVector

13. www.idosi.comLinearity

14. www.idosi.comRelative Coordinates Systems

15. www.idosi.comRelative Coordinates Systems

16. www.idosi.comScalars and Vectors

17. www.idosi.comDimension

18. www.idosi.comCartesian Coordinates

19. www.idosi.comCartesian Coordinates

20. www.idosi.comPolar Coordinates

21. www.idosi.comCylinderical Coordinates

22. www.idosi.comSpherical Coordinates

23. www.idosi.comToroidal Coordinates

24. www.idosi.comSlope

25. www.idosi.comSlope
1

26. www.idosi.comSlope
1
2

27. www.idosi.comSlope
1
2
10

28. www.idosi.comVelocity
mm/picosec
km/hr
m/sec

29. www.idosi.comInertia

30. www.idosi.comGravity & Straight Line

31. www.idosi.comTime & Space
2 cm

32. www.idosi.comFree Axes

33. www.idosi.comField
Field

34. www.idosi.comScalar Field

35. www.idosi.comScalar Field

36. www.idosi.comScalar 3D Field

37. www.idosi.comVector Field

38. www.idosi.comVector Field 3D

39. www.idosi.comStress Tensor Field 3D

40. www.idosi.comTensor Field 3D

41. www.idosi.comVector & Coordinates Transform
Vector &
Coordinates Transform

42. www.idosi.comHeat Transfer

43. www.idosi.comFluid Dynamics

44. www.idosi.comBasis Vectors

45. www.idosi.comBasis Vectors
1. Linear Combination
2. Linear Independent
Vector set = basis
Vector space dimension = basis vector count

46. www.idosi.comCNN

47. www.idosi.comEinstein Summation Convention

48. www.idosi.comMathematical expression LaTex

49. www.idosi.comOblique Coordinates

50. www.idosi.comVector Addition

51. www.idosi.comVector Addition with Parallel Projection
Contravariable
Covariant

52. www.idosi.comCoordinates Transform

53. www.idosi.com3D Coordinates

54. www.idosi.comContravariant & Covariant

55. www.idosi.comCurvilinear coordinate system

56. www.idosi.comDot Product (Inner Product) with basis vector

57. www.idosi.comDot Product (Inner Product)

58. www.idosi.comDot Product (Inner Product)

59. www.idosi.comVector Dot Product Physics

60. www.idosi.comCross Product (Outer Product)

61. www.idosi.comCrocess Product & Physical mean

62. www.idosi.comTorque Cross Product

63. www.idosi.comPrecession with Cross Product

64. www.idosi.comPrecession

65. www.idosi.comTensor
Tensor

66. www.idosi.comRank 0 : Scalar

67. www.idosi.comRank 1 : Vector

68. www.idosi.comDimension & Physical Quantity
n Dimension
1, 2, 3, 4, ...
1
1, 4, 9, 16, ...

69. www.idosi.comRank 2 : Tensor

70. www.idosi.comRank N : Tensor

71. 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

72. www.idosi.comTensor Contraction

73. www.idosi.comTensor Physics
Tensor Physics

74. www.idosi.comNewton's Laws of Motion

75. www.idosi.comDriving Force

76. www.idosi.comForce of Point

77. www.idosi.comForce of Line

78. www.idosi.comForce of Area

79. www.idosi.comHoney

80. www.idosi.comForce of Cubic

81. www.idosi.comStress

82. www.idosi.comNewtonian Fluid

83. www.idosi.comNon-Newtonian Fluid

84. www.idosi.comViscoelasticity

85. Thank you !
(주)지능도시
Intelligent City Ltd.
강신동
Shindong KANG
www.idosi.com
ceo@idosi.com