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Numerical Analysis Seminar

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Numerical Analysis Seminar
Zoom Meeting ID: 97661035379
• Host: Deep Ray
• Meeting Start: 12/03/2024 @ 3:26 PM
• Recording Start: 12/03/2024 @ 3:37 PM
• Duration: 1 hr 8 mins
• Participants: Ratna Khatri (NRL), deepray seminar, Deep Ray, Wuchen Li, Zezheng Song, Bryan Gorman, Mansur Shakipov, Ke Chen
person_outlineDeep Ray
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    Transport information geometric computations
    0:09
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    Collaborating group
    1:09
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    AlphaGo
    1:54
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    Samples from image distributions
    3:30
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    Generative probability models
    6:09
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    Information Geometry
    12:24
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    Learning: Objective function
    14:54
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    Learning: Gradient direction
    17:57
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    Optimal transport
    23:42
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    Optimal transport density manifold
    28:21
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    Learning Wasserstein type gradient directions
    31:06
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    TIG computations of complex systems
    33:15
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    Main question
    34:36
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    Background: Natural gradient methods
    35:18
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    Wasserstein natural gradient flows
    35:30
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    "Least square" in fluid dynamics
    36:03
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    Wasserstein gradient flow (Eulerian formulation)
    36:24
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    Famous example from Jordan-Kinderleherer-Otto
    37:21
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    Examples in Eulerian and Lagrangian coordinates
    41:48
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    Formulation
    42:12
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    Neural network functions
    43:18
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    Models
    45:18
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    Energies
    45:57
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    = E EZpr
    46:18
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    Neural information matrix
    46:42
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    Neural network projected gradient flows
    48:03
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    Example I: Linear energy
    50:39
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    Example II: Interaction energy
    51:12
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    Example III: Internal energy
    51:24
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    Algorithm
    52:57
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    Numerical analysis
    53:45
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    Analytic formula for
    54:03
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    Consistency via analytic formula
    55:33
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    Well-posedness for projected heat flow
    59:57
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    Consistency analysis for general cases
    1:03:39
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    Linear transport equation
    1:04:30
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    Fokker-Planck equation
    1:05:27
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    Porous medium equation
    1:06:18
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    Discussions
    1:06:39
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