Boris Kramer - Lift & Learn: Scientific ML for nonlinear conservative partial differential equations
Recorded 16 April 2026. Boris Kramer of the University of California, San Diego, presents "Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equations" at IPAM's Learning Models from Data for Multi-Fidelity Fusion Plasma Physics Workshop.Abstract: Conservative Hamiltonian systems are models commonly found in high-energy and plasma physics, quantum mechanics, and many engineering domains. These systems exhibit physically interpretable quantities such as momentum, energy, or vorticity; the behavior of these quantities in numerical simulation provides an important measure of accuracy of the model. Yet their simulation can also be expensive.
This talk will first give an overview of a few recently developed approaches for learning structure-preserving (low-dimensional) models and then introduce Hamiltonian Operator Inference, as well as Structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs) with conservation laws. The work leverages a hybrid learning approach based on a recently developed energy-quadratization strategy that uses knowledge of the nonlinearity at the PDE level to derive an equivalent quadratic lifted system with quadratic system energy. Based on the lifting transformations and lifted model form, the proposed method derives quadratic reduced terms analytically and then uses those derived terms to formulate a constrained optimization problem to learn the remaining linear reduced operators in a structure-preserving way.
The proposed hybrid learning approach yields computationally efficient quadratic reduced-order models that respect the underlying physics of the high-dimensional problem. We demonstrate the generalizability of quadratic models learned via the proposed structure-preserving Lift & Learn method through three numerical examples: the one-dimensional wave equation with exponential nonlinearity, the two-dimensional sine-Gordon equation, and the two-dimensional Klein-Gordon-Zakharov equations, used in the study of the dynamics of Langmuir turbulence in plasmas.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-learning-models-from-data-for-multi-fidelity-fusion-plasma-physics/ Receive SMS online on sms24.me
TubeReader video aggregator is a website that collects and organizes online videos from the YouTube source. Video aggregation is done for different purposes, and TubeReader take different approaches to achieve their purpose.
Our try to collect videos of high quality or interest for visitors to view; the collection may be made by editors or may be based on community votes.
Another method is to base the collection on those videos most viewed, either at the aggregator site or at various popular video hosting sites.
TubeReader site exists to allow users to collect their own sets of videos, for personal use as well as for browsing and viewing by others; TubeReader can develop online communities around video sharing.
Our site allow users to create a personalized video playlist, for personal use as well as for browsing and viewing by others.
@YouTubeReaderBot allows you to subscribe to Youtube channels.
By using @YouTubeReaderBot Bot you agree with YouTube Terms of Service.
Use the @YouTubeReaderBot telegram bot to be the first to be notified when new videos are released on your favorite channels.
Look for new videos or channels and share them with your friends.
You can start using our bot from this video, subscribe now to Boris Kramer - Lift & Learn: Scientific ML for nonlinear conservative partial differential equations
What is YouTube?
YouTube is a free video sharing website that makes it easy to watch online videos. You can even create and upload your own videos to share with others. Originally created in 2005, YouTube is now one of the most popular sites on the Web, with visitors watching around 6 billion hours of video every month.
![Sequence Six - Mewali [Pure Trance NEON]](https://img.youtube.com/vi/FphcEH0NoPk/maxresdefault.jpg)
