Symplectic Gaussian Process Dynamics
- URL: http://arxiv.org/abs/2102.01606v1
- Date: Tue, 2 Feb 2021 17:02:55 GMT
- Title: Symplectic Gaussian Process Dynamics
- Authors: Katharina Ensinger, Friedrich Solowjow, Michael Tiemann, Sebastian
Trimpe
- Abstract summary: We introduce a sparse process based variational inference scheme that is able to discretize the underlying system with any explicit implicit single or multistep integrator.
In particular we discuss Hamiltonian problems coupled with symplectic producing volume preserving predictions.
- Score: 5.171909600633905
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Dynamics model learning is challenging and at the same time an active field
of research. Due to potential safety critical downstream applications, such as
control tasks, there is a need for theoretical guarantees. While GPs induce
rich theoretical guarantees as function approximators in space, they do not
explicitly cope with the time aspect of dynamical systems. However, propagating
system properties through time is exactly what classical numerical integrators
were designed for. We introduce a recurrent sparse Gaussian process based
variational inference scheme that is able to discretize the underlying system
with any explicit or implicit single or multistep integrator, thus leveraging
properties of numerical integrators. In particular we discuss Hamiltonian
problems coupled with symplectic integrators producing volume preserving
predictions.
Related papers
- Exact Inference for Continuous-Time Gaussian Process Dynamics [6.941863788146731]
In practice, the true system is often unknown and has to be learned from measurement data.
Most methods in Gaussian process (GP) dynamics model learning are trained on one-step ahead predictions.
We show how to derive flexible inference schemes for these types of evaluations.
arXiv Detail & Related papers (2023-09-05T16:07:00Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - Structure-Preserving Learning Using Gaussian Processes and Variational
Integrators [62.31425348954686]
We propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression.
We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty.
arXiv Detail & Related papers (2021-12-10T11:09:29Z) - Optimization on manifolds: A symplectic approach [127.54402681305629]
We propose a dissipative extension of Dirac's theory of constrained Hamiltonian systems as a general framework for solving optimization problems.
Our class of (accelerated) algorithms are not only simple and efficient but also applicable to a broad range of contexts.
arXiv Detail & Related papers (2021-07-23T13:43:34Z) - The Connection between Discrete- and Continuous-Time Descriptions of
Gaussian Continuous Processes [60.35125735474386]
We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining'
This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
arXiv Detail & Related papers (2021-01-16T17:11:02Z) - Moment dynamics and observer design for a class of quasilinear quantum
stochastic systems [2.0508733018954843]
This paper is concerned with a class of open quantum systems whose dynamic variables have an algebraic structure.
The system interacts with external bosonic fields, and its Hamiltonian and coupling operators depend linearly on the system variables.
The tractability of the moment dynamics is also used for mean square optimal Luenberger observer design in a measurement-based filtering problem for a quasilinear quantum plant.
arXiv Detail & Related papers (2020-12-15T11:01:53Z) - Stochastically forced ensemble dynamic mode decomposition for
forecasting and analysis of near-periodic systems [65.44033635330604]
We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system.
We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony.
Results are presented for a test case using load data from an electrical grid.
arXiv Detail & Related papers (2020-10-08T20:25:52Z) - On dissipative symplectic integration with applications to
gradient-based optimization [77.34726150561087]
We propose a geometric framework in which discretizations can be realized systematically.
We show that a generalization of symplectic to nonconservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error.
arXiv Detail & Related papers (2020-04-15T00:36:49Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.