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{{Main|Численные методы обучения по прецедентам (практика, В.В. Стрижов)}}
{{Main|Численные методы обучения по прецедентам (практика, В.В. Стрижов)}}
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=Machine Learning for Theoretical Physics=
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Physics-informed machine learning<br>
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(seminars by Andriy Hraboviy and Vadim Strijov)
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==Goals==
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The course consists of a series of group discussions devoted to various aspects of data modelling in continuous spaces. It will reduce the gap between the models of theoretical physics and the noisy measurements, performed under complex experimental circumstances. To show the selected neural network is an adequate parametrisation of the modelled phenomenon, we use geometrical axiomatic approach. We discuss the role of manifolds, tensors and differential forms in the neural network-based model selection.
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The basics for the course are the book Geometric Deep Learning: April 2021 by Michael Bronstein et al. and the paper Physics-informed machine learning // Nature: May 2021 by George Em Karniadakis et al.
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==Structure of the talk==
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# Field and goals of a method or a model
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# An overview of the method
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# Notable authors and references
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# Rigorous description, the theoretical part
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# Algorithm and link to the code
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# Application with plots
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Link to the template of the two-page essay.
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==Grading==
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Each student presents two talks. Each talk lasts 25 minutes and concludes with a five-minute written test.
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==Test==
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Todo: how make a test creative, not automised? Here be the test format.
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==Themes==
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*
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*
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*
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*
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==Schedule==
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Thursdays on 12:30 at m1p.org/go_zoom
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* September 2 9 16 23 30
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* October 7 14 21 28
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* November 4 11 18 25 
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* December 2 9
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{|class="wikitable"
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! Date
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! Theme
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! Speaker
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! Links
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|September 2
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|Course introduction and motivation
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|Vadim Strijov
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|[https://geometricdeeplearning.com/ GDL paper], [https://www.researchgate.net/publication/351814752_Physics-informed_machine_learning/link/60ae8f43a6fdcc647ede90f7/download Physics-informed]
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|Final discussion
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* Geometric deep learning
* Geometric deep learning

Версия 08:49, 19 августа 2021

Содержание


Machine Learning for Theoretical Physics

Physics-informed machine learning
(seminars by Andriy Hraboviy and Vadim Strijov)

Goals

The course consists of a series of group discussions devoted to various aspects of data modelling in continuous spaces. It will reduce the gap between the models of theoretical physics and the noisy measurements, performed under complex experimental circumstances. To show the selected neural network is an adequate parametrisation of the modelled phenomenon, we use geometrical axiomatic approach. We discuss the role of manifolds, tensors and differential forms in the neural network-based model selection.

The basics for the course are the book Geometric Deep Learning: April 2021 by Michael Bronstein et al. and the paper Physics-informed machine learning // Nature: May 2021 by George Em Karniadakis et al.

Structure of the talk

  1. Field and goals of a method or a model
  2. An overview of the method
  3. Notable authors and references
  4. Rigorous description, the theoretical part
  5. Algorithm and link to the code
  6. Application with plots

Link to the template of the two-page essay.

Grading

Each student presents two talks. Each talk lasts 25 minutes and concludes with a five-minute written test.

Test

Todo: how make a test creative, not automised? Here be the test format.

Themes

Schedule

Thursdays on 12:30 at m1p.org/go_zoom

  • September 2 9 16 23 30
  • October 7 14 21 28
  • November 4 11 18 25 
  • December 2 9


Date Theme Speaker Links
September 2 Course introduction and motivation Vadim Strijov GDL paper, Physics-informed
9
9
16
16
23
23
30
30
October 7
7
14
14
21
21
28
28
November 4
4
11
11
18
18
25
25
December 2
2
9 Final discussion



  • Geometric deep learning
  • Functional data analysis
  • Applied mathematics for machine learning


General principles

1. The experiment and measurements defines axioms i


Syllabus and goals

Theme 1:

Message

Basics

Application

Code

https://papers.nips.cc/paper/2018/file/69386f6bb1dfed68692a24c8686939b9-Paper.pdf


Theme 1: Manifolds

Code

Surface differential geometry Coursera code video for Image and Video Processing

Theme 1: ODE and flows

Goes to BME

(after RBF)

Theme 1: PDE

Theme 1: Navier-Stokes equations and viscous flow

Fourier for fun and practice 1D

Fourier Code



Fourier for fun and practice nD

See:

  • Fourier analysis on Manifolds 5G page 49
  • Spectral analysis on meshes

Geometric Algebra

experior product and quaternions


Theme 1: High order splines

Theme 1: Topological data analysis

Theme 1: Homology versus homotopy

W: Homology



Fundamental theorems

W: Inverse function theorem and Jacobian

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