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Found 8 papers, 3 papers with code
Operator learning without the adjoint
There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint?
A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning
In this paper, we provide a unifying theoretical and methodological framework for incorporating symmetry into machine learning models in three ways: 1. enforcing known symmetry when training a model; 2. discovering unknown symmetries of a given model or data set; and 3. promoting symmetry during training by learning a model that breaks symmetries within a user-specified group of candidates when there is sufficient evidence in the data.
Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders
To begin to address these issues, we introduce a parametric class of nonlinear projections described by constrained autoencoder neural networks in which both the manifold and the projection fibers are learned from data.
Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories
Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control.
Model Reduction for Nonlinear Systems by Balanced Truncation of State and Gradient Covariance
We provide an efficient snapshot-based computational method analogous to balanced proper orthogonal decomposition.
Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems; a New Approach Using Secants
In order to remedy these problems, we introduce a novel data-driven approach for sensor placement and feature selection for a general type of nonlinear inverse problem based on the information contained in secant vectors between data points.
A Discrete Empirical Interpolation Method for Interpretable Immersion and Embedding of Nonlinear Manifolds
Instead, we propose to identify a small collection of the original variables which are capable of uniquely determining all others either locally via immersion or globally via embedding of the underlying manifold.
Linearly-Recurrent Autoencoder Networks for Learning Dynamics
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator.
