Интеллектуальные системы (семинар, А.В. Грабовой, В.В. Стрижов)/Осень 2021

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Physics-informed machine learning

(seminars by Andriy Graboviy and Vadim Strijov)


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

The talk is based on two-page essay ([template]).

  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


Each student presents two talks. Each talk lasts 25 minutes and concludes with a five-minute written test (discussion is better). A seminar presentation gives 1 point, a formatted seminar text gives 1 point, a test gives 1 point, a reasonable test response gives 0.1 point. Bonus 1 point for a great talk. Highly recommended to present list of references 1 week before (for 1 point bonus reward, of course).

First Theme Second Theme
Student Score Seminars Work T WT PT QT BT T WT PT QT BT
Example 9 1 First example theme 1 1 1 1 Second example theme 1 1 1 1

T - theme; WT - text presented; PT - presentation presented; QT - questions presented; BT - bibliography presented.

All: text, questions and bibliography must be presented here. The presentation should be presented at the seminar and be in the table below.


  1. Spherical harmonics for mechanical motion modelling
  2. Geometric algebra, experior product and quaternions
  3. Tensor representations of the Brain computer interfaces
  4. Multi-view, kernels and metric spaces for the BCI and Brain Imaging
  5. Continuous-Time Representation and Legendre Memory Units for BCI
  6. Riemannian geometry on Shapes and diffeomorphisms for fMRI
  7. The affine connection setting for transformation groups for fMRI
  8. Strain, rotation and stress tensors modelling with examples
  9. Differential forms and fibre bundles with examples
  10. Modelling gravity with machine learning approaches
  11. Geometric manifolds, the Levi-Chivita connection and curvature tensors
  12. Flows and topological spaces
  13. Application for Normalizing flow models (stress on spaces, not statistics)
  14. Alignment in higher dimensions with RNN
  15. Navier-Stokes equations and viscous flow
  16. Newtonian and Non-Newtonian Fluids in Pipe Flows Using Neural Networks [1], [2]
  17. Applications of Geometric Algebra and experior product
  18. High-order splines
  19. Forward and Backward Fourier transform and iPhone lidar imaging analysis
  20. Fourier, cosine and Laplace transform for 2,3,4D and higher dimensions
  21. Spectral analysis on meshes
  22. Graph convolution and continuous Laplace operators


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 Spherical harmonics for mechanical motion modelling Tikhonov Denis
16 Geometric Algebra, exterior product and quaternions Panchenko Sviatoslav GA_slides
October 7 Modelling gravity with machine learning approaches Tikhonov Denis
November 4
December 2
9 Final discussion and grading Andriy Graboviy
Личные инструменты