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This paper presents a computational method, called Bootstrapped Koopman Direct Encoding (B-KDE) that allows us to approximate the Koopman operator with high accuracy by combining Koopman Direct Encoding (KDE) with a deep neural network. Deep learning has been applied to the Koopman operator method for finding an effective set of observable functions. Training the network, however, inevitably faces difficulties such as local minima, unless enormous computational efforts are made. Incorporating KDE can solve or alleviate this problem, producing an order of magnitude more accurate prediction. KDE converts the state transition function of a nonlinear system to a linear model in the lifted space of observables that are generated by deep learning. The combined KDE-deep model achieves higher accuracy than that of the deep learning alone. In B-KDE, the combined model is further trained until it reaches a plateau, and this computation is alternated between the neural network learning and the KDE computation. The result of the MSE loss implies that the neural network may get rid of local minima or at least find a smaller local minimum, and further improve the prediction accuracy. The KDE computation however, entails an effective algorithm for computing the inner products of observables and the nonlinear functions of the governing dynamics. Here, a computational method based on the Quasi-Monte Carlo integration is presented. The method is applied to a three-cable suspension robot, which exhibits complex switched nonlinear dynamics due to slack in each cable. The prediction accuracy is compared against its traditional counterparts.
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Progress in developing a hybrid deep learning algorithm for identifying and locating primary vertices
The locations of proton-proton collision points in LHC experiments are called primary vertices (PVs). Preliminary results of a hybrid deep learning algorithm for identifying and locating these, targeting the Run 3 incarnation of LHCb, have been described at conferences in 2019 and 2020. In the past year we have made significant progress in a variety of related areas. Using two newer Kernel Density Estimators (KDEs) as input feature sets improves the fidelity of the models, as does using full LHCb simulation rather than the “toy Monte Carlo” originally (and still) used to develop models. We have also built a deep learning model to calculate the KDEs from track information. Connecting a tracks-to-KDE model to a KDE-to-hists model used to find PVs provides a proof-of-concept that a single deep learning model can use track information to find PVs with high efficiency and high fidelity. We have studied a variety of models systematically to understand how variations in their architectures affect performance. While the studies reported here are specific to the LHCb geometry and operating conditions, the results suggest that the same approach could be used by the ATLAS and CMS experiments.
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- PAR ID:
- 10311259
- Editor(s):
- Biscarat, C.; Campana, S.; Hegner, B.; Roiser, S.; Rovelli, C.I.; Stewart, G.A.
- Date Published:
- Journal Name:
- EPJ Web of Conferences
- Volume:
- 251
- ISSN:
- 2100-014X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1051/epjconf/202125104012
