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Found 9 papers, 6 papers with code
PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator
PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system.
On the lifting and reconstruction of nonlinear systems with multiple invariant sets
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace.
Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data
High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace.
Discretization-independent surrogate modeling over complex geometries using hypernetworks and implicit representations
Test cases include a vehicle-aerodynamics problem with complex geometry and limited training data, with a design-variable hypernetwork performing best, with a competitive time-to-best-model despite a much greater parameter count.
Sparsity-promoting algorithms for the discovery of informative Koopman invariant subspaces
Despite being endowed with a richer dictionary of nonlinear observables, nonlinear variants of the DMD, such as extended/kernel dynamic mode decomposition (EDMD/KDMD) are seldom applied to large-scale problems primarily due to the difficulty of discerning the Koopman invariant subspace from thousands of resulting Koopman eigenmodes.
Particle reconstruction of volumetric particle image velocimetry with strategy of machine learning
Three-dimensional particle reconstruction with limited two-dimensional projections is an under-determined inverse problem that the exact solution is often difficult to be obtained.
Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
In this work, we formalize the problem of learning the continuous-time Koopman operator with deep neural networks in a measure-theoretic framework.
Long-time predictive modeling of nonlinear dynamical systems using neural networks
We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data.
Data-driven Discovery of Closure Models
In this work, we present a framework of operator inference to extract the governing dynamics of closure from data in a compact, non-Markovian form.
