Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification
C. Offen, (n.d.).
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Abstract
The article introduces a method to learn dynamical systems that
are governed by Euler–Lagrange equations from data. The method is based on
Gaussian process regression and identifies continuous or discrete Lagrangians
and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero
and lower bounds for convergence rates are provided. Next to convergence
guarantees, the method allows for quantification of model uncertainty, which
can provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian,
including of Hamiltonian functions (energy) and symplectic structures, which
is of interest in the context of system identification. The article overcomes
major practical and theoretical difficulties related to the ill-posedness of the
identification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex
minimisation problems in reproducing kernel Hilbert spaces.
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Cite this
Offen C. Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification.
Offen, C. (n.d.). Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification.
@article{Offen, title={Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification}, author={Offen, Christian} }
Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification,” n.d.
C. Offen, “Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification.” .
Offen, Christian. Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.
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Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification
Description
The article introduces a method to learn dynamical systems that
are governed by Euler–Lagrange equations from data. The method is based on
Gaussian process regression and identifies continuous or discrete Lagrangians
and is, therefore, structure preserving by design. A rigorous proof of con-
vergence as the distance between observation data points converges to zero
and lower bounds for convergence rates are provided. Next to convergence
guarantees, the method allows for quantification of model uncertainty, which
can provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian,
including of Hamiltonian functions (energy) and symplectic structures, which
is of interest in the context of system identification. The article overcomes
major practical and theoretical difficulties related to the ill-posedness of the
identification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex
minimisation problems in reproducing kernel Hilbert spaces.
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