The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Baru-baru ini pembelajaran berasaskan data sistem dinamik telah menjadi pendekatan yang menjanjikan kerana tiada pengetahuan fizikal diperlukan. Pendekatan pembelajaran mesin tulen seperti regresi proses Gaussian (GPR) mempelajari model dinamik daripada data, dengan semua pengetahuan fizikal tentang sistem dibuang. Ini berlaku dari satu ekstrem, iaitu kaedah berdasarkan pengoptimuman model fizikal parametrik yang diperoleh daripada undang-undang fizikal, kepada yang lain. GPR mempunyai fleksibiliti yang tinggi dan mampu memodelkan mana-mana dinamik asalkan ia lancar secara tempatan, tetapi tidak boleh menyamaratakan dengan baik ke kawasan yang belum diterokai dengan sedikit atau tiada data latihan. Model fizik analitik yang diperoleh di bawah andaian adalah anggaran abstrak bagi sistem sebenar, tetapi mempunyai keupayaan generalisasi global. Oleh itu, strategi pembelajaran yang optimum adalah untuk menggabungkan GPR dengan model fizikal analitik. Kertas kerja ini mencadangkan kaedah untuk mempelajari sistem dinamik menggunakan GPR dengan persamaan pembezaan biasa analitik (ODEs) sebagai maklumat terdahulu. Penyepaduan satu langkah bagi ODE analitik digunakan sebagai fungsi min proses Gaussian sebelumnya. Jumlah parameter yang akan dilatih termasuk parameter fizikal ODE analitik dan parameter GPR. Kaedah baru dicadangkan untuk mempelajari semua parameter secara serentak, yang direalisasikan oleh GPR Bayesian sepenuhnya dan lebih menjanjikan untuk mempelajari model yang optimum. Regresi proses Gaussian standard, kaedah ODE dan kaedah sedia ada dalam literatur dipilih sebagai garis dasar untuk mengesahkan faedah kaedah yang dicadangkan. Prestasi ramalan dinilai oleh ramalan satu langkah dan ramalan jangka panjang. Dengan simulasi sistem kutub kereta, ditunjukkan bahawa kaedah yang dicadangkan mempunyai prestasi ramalan yang lebih baik.
Shengbing TANG
Kyoto University
Kenji FUJIMOTO
Kyoto University
Ichiro MARUTA
Kyoto University
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Salinan
Shengbing TANG, Kenji FUJIMOTO, Ichiro MARUTA, "Learning Dynamic Systems Using Gaussian Process Regression with Analytic Ordinary Differential Equations as Prior Information" in IEICE TRANSACTIONS on Information,
vol. E104-D, no. 9, pp. 1440-1449, September 2021, doi: 10.1587/transinf.2020EDP7186.
Abstract: Recently the data-driven learning of dynamic systems has become a promising approach because no physical knowledge is needed. Pure machine learning approaches such as Gaussian process regression (GPR) learns a dynamic model from data, with all physical knowledge about the system discarded. This goes from one extreme, namely methods based on optimizing parametric physical models derived from physical laws, to the other. GPR has high flexibility and is able to model any dynamics as long as they are locally smooth, but can not generalize well to unexplored areas with little or no training data. The analytic physical model derived under assumptions is an abstract approximation of the true system, but has global generalization ability. Hence the optimal learning strategy is to combine GPR with the analytic physical model. This paper proposes a method to learn dynamic systems using GPR with analytic ordinary differential equations (ODEs) as prior information. The one-time-step integration of analytic ODEs is used as the mean function of the Gaussian process prior. The total parameters to be trained include physical parameters of analytic ODEs and parameters of GPR. A novel method is proposed to simultaneously learn all parameters, which is realized by the fully Bayesian GPR and more promising to learn an optimal model. The standard Gaussian process regression, the ODE method and the existing method in the literature are chosen as baselines to verify the benefit of the proposed method. The predictive performance is evaluated by both one-time-step prediction and long-term prediction. By simulation of the cart-pole system, it is demonstrated that the proposed method has better predictive performances.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2020EDP7186/_p
Salinan
@ARTICLE{e104-d_9_1440,
author={Shengbing TANG, Kenji FUJIMOTO, Ichiro MARUTA, },
journal={IEICE TRANSACTIONS on Information},
title={Learning Dynamic Systems Using Gaussian Process Regression with Analytic Ordinary Differential Equations as Prior Information},
year={2021},
volume={E104-D},
number={9},
pages={1440-1449},
abstract={Recently the data-driven learning of dynamic systems has become a promising approach because no physical knowledge is needed. Pure machine learning approaches such as Gaussian process regression (GPR) learns a dynamic model from data, with all physical knowledge about the system discarded. This goes from one extreme, namely methods based on optimizing parametric physical models derived from physical laws, to the other. GPR has high flexibility and is able to model any dynamics as long as they are locally smooth, but can not generalize well to unexplored areas with little or no training data. The analytic physical model derived under assumptions is an abstract approximation of the true system, but has global generalization ability. Hence the optimal learning strategy is to combine GPR with the analytic physical model. This paper proposes a method to learn dynamic systems using GPR with analytic ordinary differential equations (ODEs) as prior information. The one-time-step integration of analytic ODEs is used as the mean function of the Gaussian process prior. The total parameters to be trained include physical parameters of analytic ODEs and parameters of GPR. A novel method is proposed to simultaneously learn all parameters, which is realized by the fully Bayesian GPR and more promising to learn an optimal model. The standard Gaussian process regression, the ODE method and the existing method in the literature are chosen as baselines to verify the benefit of the proposed method. The predictive performance is evaluated by both one-time-step prediction and long-term prediction. By simulation of the cart-pole system, it is demonstrated that the proposed method has better predictive performances.},
keywords={},
doi={10.1587/transinf.2020EDP7186},
ISSN={1745-1361},
month={September},}
Salinan
TY - JOUR
TI - Learning Dynamic Systems Using Gaussian Process Regression with Analytic Ordinary Differential Equations as Prior Information
T2 - IEICE TRANSACTIONS on Information
SP - 1440
EP - 1449
AU - Shengbing TANG
AU - Kenji FUJIMOTO
AU - Ichiro MARUTA
PY - 2021
DO - 10.1587/transinf.2020EDP7186
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E104-D
IS - 9
JA - IEICE TRANSACTIONS on Information
Y1 - September 2021
AB - Recently the data-driven learning of dynamic systems has become a promising approach because no physical knowledge is needed. Pure machine learning approaches such as Gaussian process regression (GPR) learns a dynamic model from data, with all physical knowledge about the system discarded. This goes from one extreme, namely methods based on optimizing parametric physical models derived from physical laws, to the other. GPR has high flexibility and is able to model any dynamics as long as they are locally smooth, but can not generalize well to unexplored areas with little or no training data. The analytic physical model derived under assumptions is an abstract approximation of the true system, but has global generalization ability. Hence the optimal learning strategy is to combine GPR with the analytic physical model. This paper proposes a method to learn dynamic systems using GPR with analytic ordinary differential equations (ODEs) as prior information. The one-time-step integration of analytic ODEs is used as the mean function of the Gaussian process prior. The total parameters to be trained include physical parameters of analytic ODEs and parameters of GPR. A novel method is proposed to simultaneously learn all parameters, which is realized by the fully Bayesian GPR and more promising to learn an optimal model. The standard Gaussian process regression, the ODE method and the existing method in the literature are chosen as baselines to verify the benefit of the proposed method. The predictive performance is evaluated by both one-time-step prediction and long-term prediction. By simulation of the cart-pole system, it is demonstrated that the proposed method has better predictive performances.
ER -