Title:
Data-driven estimation of inertial manifold dimension for chaotic Kolmogorov flow and time evolution on the manifold
Part 3: Data-driven dimension reduction, dynamic modeling, and control of complex chaotic systems
Data-driven estimation of inertial manifold dimension for chaotic Kolmogorov flow and time evolution on the manifold
Part 3: Data-driven dimension reduction, dynamic modeling, and control of complex chaotic systems
| dc.contributor.author | Pérez De Jesús, Carlos | |
| dc.contributor.corporatename | Georgia Institute of Technology. School of Physics | en_US |
| dc.contributor.corporatename | University of Wisconsin-Madison. Dept. of Chemical and Biological Engineering | en_US |
| dc.date.accessioned | 2021-11-07T21:14:06Z | |
| dc.date.available | 2021-11-07T21:14:06Z | |
| dc.date.issued | 2021-11-03 | |
| dc.description | This is part three of the Nonlinear Science Webinar, titled "Data-driven dimension reduction, dynamic modeling, and control of complex chaotic systems", which was presented online via Bluejeans Meetings on November 3, 2021 at 3:00 p.m. | en_US |
| dc.description | Carlos Pérez De Jesús is a PhD student at the University of Wisconsin - Madison and is a member of the Complex Flows and Fluids Research Group. | en_US |
| dc.description | Runtime: 57:49 minutes | en_US |
| dc.description.abstract | Model reduction techniques have previously been applied to evolve the Navier-Stokes equations in time, however finding the minimal dimension needed to correctly capture the key dynamics is not a trivial task. To estimate this dimension we trained an undercomplete autoencoder on weakly chaotic vorticity data (32x32 grid) from Kolmogorov flow simulations, tracking the reconstruction error as a function of dimension. We also trained a discrete time stepper that evolves the reduced order model with a nonlinear dense neural network. The trajectory travels in the vicinity of relative periodic orbits (RPOs) followed by sporadic bursting events. At a dimension of five (as opposed to the full state dimension of 1024), power input-dissipation probability density function is well-approximated; Fourier coefficient evolution shows that the trajectory correctly captures the heteroclinic connections (bursts) between the different RPOs, and the prediction and true data track each other for approximately a Lyapunov time. | en_US |
| dc.format.extent | 57:49 minutes | |
| dc.identifier.uri | http://hdl.handle.net/1853/65418 | |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | Nonlinear Science Seminar | |
| dc.subject | Inertial manifold | en_US |
| dc.subject | Kolmogorov flow | en_US |
| dc.subject | Neural networks | en_US |
| dc.title | Data-driven estimation of inertial manifold dimension for chaotic Kolmogorov flow and time evolution on the manifold | en_US |
| dc.title | Part 3: Data-driven dimension reduction, dynamic modeling, and control of complex chaotic systems | |
| dc.type | Moving Image | |
| dc.type.genre | Lecture | |
| dspace.entity.type | Publication | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Physics | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 2ba39017-11f1-40f4-9bc5-66f17b8f1539 |
Files
Original bundle
1 - 4 of 4
No Thumbnail Available
- Name:
- dejesus.mp4
- Size:
- 301.58 MB
- Format:
- MP4 Video file
- Description:
- Download video
No Thumbnail Available
- Name:
- dejesus_videostream.html
- Size:
- 1.32 KB
- Format:
- Hypertext Markup Language
- Description:
- Streaming video
No Thumbnail Available
- Name:
- transcript.txt
- Size:
- 39.87 KB
- Format:
- Plain Text
- Description:
- Transcription
- Name:
- thumbnail.jpg
- Size:
- 51.28 KB
- Format:
- Joint Photographic Experts Group/JPEG File Interchange Format (JFIF)
- Description:
- Thumbnail
License bundle
1 - 1 of 1
No Thumbnail Available
- Name:
- license.txt
- Size:
- 3.13 KB
- Format:
- Item-specific license agreed upon to submission
- Description: