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".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Recentemente, a aprendizagem de sistemas dinâmicos baseada em dados tornou-se uma abordagem promissora porque nenhum conhecimento físico é necessário. Abordagens puras de aprendizado de máquina, como a regressão de processo gaussiana (GPR), aprendem um modelo dinâmico a partir dos dados, com todo o conhecimento físico sobre o sistema descartado. Isto vai de um extremo, nomeadamente métodos baseados na otimização de modelos físicos paramétricos derivados de leis físicas, ao outro. O GPR tem alta flexibilidade e é capaz de modelar qualquer dinâmica, desde que seja localmente suave, mas não pode generalizar bem para áreas inexploradas com poucos ou nenhum dado de treinamento. O modelo físico analítico derivado de suposições é uma aproximação abstrata do verdadeiro sistema, mas possui capacidade de generalização global. Conseqüentemente, a estratégia de aprendizagem ideal é combinar o GPR com o modelo físico analítico. Este artigo propõe um método para aprender sistemas dinâmicos usando GPR com equações diferenciais ordinárias analíticas (EDOs) como informação prévia. A integração única de EDOs analíticas é usada como a função média do processo gaussiano anterior. Os parâmetros totais a serem treinados incluem parâmetros físicos de EDOs analíticas e parâmetros de GPR. Um novo método é proposto para aprender simultaneamente todos os parâmetros, o que é realizado pelo GPR totalmente Bayesiano e mais promissor para aprender um modelo ideal. A regressão do processo gaussiano padrão, o método EDO e o método existente na literatura são escolhidos como linhas de base para verificar o benefício do método proposto. O desempenho preditivo é avaliado tanto pela previsão de uma única etapa quanto pela previsão de longo prazo. Pela simulação do sistema carrinho-pólo, demonstra-se que o método proposto possui melhor desempenho preditivo.
Shengbing TANG
Kyoto University
Kenji FUJIMOTO
Kyoto University
Ichiro MARUTA
Kyoto University
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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
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@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},}
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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 -