Physics-Informed Dynamic Mode Decomposition (PI-DMD)

In this video, Peter Baddoo from MIT (www.baddoo.co.uk) explains how physical laws can be integrated into the dynamic mode decomposition.
Title: Physics-informed dynamic mode decomposition (piDMD)
Authors: Peter J. Baddoo, Benjamin Herrmann, Beverley J. McKeon, J. Nathan Kutz, and Steven L. Brunton
Paper: arxiv.org/abs/2112.04307
Github: github.com/baddoo/piDMD
Abstract:
In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts low-rank modal structures and dynamics from high-dimensional measurements. However, DMD frequently produces models that are sensitive to noise, fail to generalize outside the training data, and violate basic physical laws. Our physics-informed DMD (piDMD) optimization, which may be formulated as a Procrustes problem, restricts the family of admissible models to a matrix manifold that respects the physical structure of the system. We focus on five fundamental physical principles -- conservation, self-adjointness, localization, causality, and shift-invariance -- and derive several closed-form solutions and efficient algorithms for the corresponding piDMD optimizations. With fewer degrees of freedom, piDMD models are less prone to overfitting, require less training data, and are often less computationally expensive to build than standard DMD models. We demonstrate piDMD on a range of challenging problems in the physical sciences, including energy-preserving fluid flow, travelling-wave systems, the Schrödinger equation, solute advection-diffusion, a system with causal dynamics, and three-dimensional transitional channel flow. In each case, piDMD significantly outperforms standard DMD in metrics such as spectral identification, state prediction, and estimation of optimal forcings and responses.
This video was produced at the University of Washington

[@sergios4214]

Research groups making videos like these to explain their research should become standard procedure!

[@Mutual_Information]

Very interesting. One thing I’m surprised by is that you can model these dynamics with repeated matrix multiplication in the observed space (pixels). Maybe I’m just used to Kalman Filters.. but I’d guess the first step is to assume some to-be-learn function that maps to a lower dimensional latent space.. and then there you apply repeated matrix multiplies.
Very cool. These patterns are beautiful.. it seems repeated matrix multiplication is a lot more flexible than I thought

[@amaningowi1671]

great advancement in data modelling , great presentation brother

[@have_a_nice_day399]

Interesting idea and nice presentation. Thank you!

[@Taka-mn4sw]

R.I.P. Dr. Baddoo

[@the_nuwarrior]

Benjamin fue profesor mio en la FCFM , es impresionante que colabore en investigaciones de prestigio.

[@JousefM]

Very nice presentation!

[@afammadudaniel2982]

Thank you so much. What a wonderful presentation. I learned about PiNN early this year from my mentor and I have been studying it in order to apply it in my research in Quantum sensing and Many body systems. I am Interested in how you applied it to Quantum physics, how did you deal with encoding the underlying physics prior of a system whose state is inherently probabilistic? For example in fermionic systems where measurement destroys the quantum state.

[@oncedidactic]

Very elegant!

[@ashutoshsingh-et7vm]

Nice lecture , @Steve Brunton sir waiting for LCS further lecture

[@amitbhaya384]

Clear and excellent presentation. A little typo on the slide shown at 17:10: you refer to MATLABs backslash, but what appears on the slide is an ordinary (front)slash.

[@peterj.baddoo3813]

Thanks for spotting this! The slide is correct but I should have said "frontslash" (www.mathworks.com/help/matlab/ref/mrdivide.html).

[@moiseszarzuela4673]

Hello, I would like to use this in my thermal project, but it also has a signal q that enters the system. Is it possible to integrate it?

[@Eltro101]

Can you use a convolution instead of a circulant matrix?

[@javeriaayub6203]

How DMD is useful to plot basin of attractor of a chaotic attractor?

[@nimadehghai]

RIP Peter Baddoo

[@ishitasaraswat6450]

Sir can you please make a video on continuous and discrete dynamical systems. How are they related?

[@khawar0o7]

Read any introductory book like Strogatz.

[@SherriMSDRML-qm1pe]

This message is for Steve Burton it is a pleasure to finally be able to leave a message I've been taking your class for The Last 5 Years online on UA-cam Plus my professor Joseph George new physics with Joseph George his wife him and myself plus his son. We have a different Theory on dark matter. Dark hoes. We would like your expertise please? If you could look at what my professor is at in his research with him and his wife and son could you review it and if you could give us 2% more than what we had before yesterday would be fine thank you sir. I'm a theoretical scientist and a sophomore in Applied Mathematics which I enjoy the most is the implied mathematics.! Thank you so much just an old cowboy.:-)

[@chrisw3327]

Was it a snowboarding class?

[@JFrames]

@@chrisw3327 No, it was a dance class