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Koopman Regularization
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Koopman Regularization is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field. Koopman Regularization extracts a functionally independent set of Koopman Eigenfunctions from the samples. This set implements the principle of parsimony, since, even though its cardinality is finite, it restores the dynamics precisely.Koopman Regularization formulates the Koopman Partial Differential Equation as the objective function and the condition of functional independence as the feasible region. Then, this work suggests a barrier method-based algorithm to solve this constrained optimization problem that yields promising results in denoising, generalization, and dimensionality reduction.
Title: Koopman Regularization
Description:
Koopman Regularization is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field.
Koopman Regularization extracts a functionally independent set of Koopman Eigenfunctions from the samples.
This set implements the principle of parsimony, since, even though its cardinality is finite, it restores the dynamics precisely.
Koopman Regularization formulates the Koopman Partial Differential Equation as the objective function and the condition of functional independence as the feasible region.
Then, this work suggests a barrier method-based algorithm to solve this constrained optimization problem that yields promising results in denoising, generalization, and dimensionality reduction.
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