Physics-enhanced Gaussian Process Variational Autoencoder

Thomas Beckers, Qirui Wu, George J. Pappas
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:521-533, 2023.

Abstract

Variational autoencoders allow to learn a lower-dimensional latent space based on high-dimensional input/output data. Using video clips as input data, the encoder may be used to describe the movement of an object in the video without ground truth data (unsupervised learning). Even though the object’s dynamics is typically based on first principles, this prior knowledge is mostly ignored in the existing literature. Thus, we propose a physics-enhanced variational autoencoder that places a physical-enhanced Gaussian process prior on the latent dynamics to improve the efficiency of the variational autoencoder and to allow physically correct predictions. The physical prior knowledge expressed as linear dynamical system is here reflected by the Green’s function and included in the kernel function of the Gaussian process. The benefits of the proposed approach are highlighted in a simulation with an oscillating particle.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-beckers23a, title = {Physics-enhanced Gaussian Process Variational Autoencoder}, author = {Beckers, Thomas and Wu, Qirui and Pappas, George J.}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {521--533}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/beckers23a/beckers23a.pdf}, url = {https://proceedings.mlr.press/v211/beckers23a.html}, abstract = {Variational autoencoders allow to learn a lower-dimensional latent space based on high-dimensional input/output data. Using video clips as input data, the encoder may be used to describe the movement of an object in the video without ground truth data (unsupervised learning). Even though the object’s dynamics is typically based on first principles, this prior knowledge is mostly ignored in the existing literature. Thus, we propose a physics-enhanced variational autoencoder that places a physical-enhanced Gaussian process prior on the latent dynamics to improve the efficiency of the variational autoencoder and to allow physically correct predictions. The physical prior knowledge expressed as linear dynamical system is here reflected by the Green’s function and included in the kernel function of the Gaussian process. The benefits of the proposed approach are highlighted in a simulation with an oscillating particle.} }
Endnote
%0 Conference Paper %T Physics-enhanced Gaussian Process Variational Autoencoder %A Thomas Beckers %A Qirui Wu %A George J. Pappas %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-beckers23a %I PMLR %P 521--533 %U https://proceedings.mlr.press/v211/beckers23a.html %V 211 %X Variational autoencoders allow to learn a lower-dimensional latent space based on high-dimensional input/output data. Using video clips as input data, the encoder may be used to describe the movement of an object in the video without ground truth data (unsupervised learning). Even though the object’s dynamics is typically based on first principles, this prior knowledge is mostly ignored in the existing literature. Thus, we propose a physics-enhanced variational autoencoder that places a physical-enhanced Gaussian process prior on the latent dynamics to improve the efficiency of the variational autoencoder and to allow physically correct predictions. The physical prior knowledge expressed as linear dynamical system is here reflected by the Green’s function and included in the kernel function of the Gaussian process. The benefits of the proposed approach are highlighted in a simulation with an oscillating particle.
APA
Beckers, T., Wu, Q. & Pappas, G.J.. (2023). Physics-enhanced Gaussian Process Variational Autoencoder. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:521-533 Available from https://proceedings.mlr.press/v211/beckers23a.html.

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