Deep learning for universal linear embeddings of nonlinear dynamics

Welcome to the DC/NoVA Papers We Love meetup!

Papers We Love is an international organization centered around the appreciation of computer science research papers. There's so much we can learn from the landmark research that shaped the field and the current studies that are shaping our future. Our goal is to create a community of tech professionals passionate about learning and sharing knowledge. Come join us!

New to research papers? Watch The Refreshingly Rewarding Realm of Research Papers (https://www.youtube.com/watch?v=8eRx5Wo3xYA) by Sean Cribbs.

Ideas and suggestions are welcome–fill our our interest survey here (https://docs.google.com/forms/d/e/1FAIpQLSeJwLQhnmzWcuyodPrSmqHgqrvNxRbnNSbiWAuwzHwshhy_Sg/viewform) and let us know what motivates you!

// Tentative Schedule

• 7:00-7:15–Informal paper discussion

• 7:15-7:45–Introduction and announcements

• 7:45-8:40–Deep learning for universal linear embeddings of nonlinear dynamics (https://www.nature.com/articles/s41467-018-07210-0/), presented by Lee Sharma

• 8:40-9:00–Informal paper discussion

// Directions

CustomInk Cafe (3rd Floor)
Mosaic District, 2910 District Ave #300
Fairfax, VA 22031

When you get here you can come in via the patio. Don't be scared by the metal gate and sign. It's accessible via the outside stairs near True Food. There is a parking garage next door for those coming by vehicle. And, there is a walkway to the patio on the 3rd floor of the garage nearest moms organic market.

Metro: The Dunn Loring metro station is about 0.7 miles from our meetup location. It’s very walkable, but if you’d prefer a bus, the 402 Southbound and 1A/1B/1C Westbound leave from Dunn Loring Station about every 5-10 minutes (see a schedule for more detailed timetable).

If you're late, we totally understand–please still come! (via the patio is best) Just be sure to slip in quietly if a speaker is presenting.

// Papers

Deep learning for universal linear embeddings of nonlinear dynamics

HTML: https://www.nature.com/articles/s41467-018-07210-0/
PDF: https://www.nature.com/articles/s41467-018-07210-0.pdf

Abstract:
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear has the potential to enable nonlinear prediction, estimation, and control using linear theory. The Koopman operator is a leading data-driven embedding, and its eigenfunctions provide intrinsic coordinates that globally linearize the dynamics. However, identifying and representing these eigenfunctions has proven challenging. This work leverages deep learning to discover representations of Koopman eigenfunctions from data. Our network is parsimonious and interpretable by construction, embedding the dynamics on a low-dimensional manifold. We identify nonlinear coordinates on which the dynamics are globally linear using a modified auto-encoder. We also generalize Koopman representations to include a ubiquitous class of systems with continuous spectra. Our framework parametrizes the continuous frequency using an auxiliary network, enabling a compact and efficient embedding, while connecting our models to decades of asymptotics. Thus, we benefit from the power of deep learning, while retaining the physical interpretability of Koopman embeddings.