An exploratory study of discrete time state-space models using kriging

Hernandez, Andres F.; Gallivan, Martha Grover

doi:10.1109/acc.2008.4587117

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…Hernandez and Gallivan [73] presented an early work using dynamic surrogates studying the use of kriging surrogates for modeling a second-order elementary reaction with a single reactant. Hernandez and Grover [74] later expanded this work to the practical problem of optimally producing platinum nanoparticles.…”

Section: Surrogates For Dynamic Processesmentioning

confidence: 99%

Overview of Surrogate Modeling in Chemical Process Engineering

McBride

Sundmacher

2019

Chemie Ingenieur Technik

198

108

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The ability to accurately model and simulate chemical processes has been paramount to the growing success and efficiency in process design and operation. These improvements usually come with increasing complexity of the underlying models leading to substantial computational effort in their use. It may also occur that the structure of the model is sometimes unknown making optimization and study difficult. To circumvent these issues, mathematically simpler models, commonly known as surrogate models, have been designed and used to successfully replace these complex, underlying models with much success. This technique has seen increasing use within the chemical process engineering field and this article summarizes some popular surrogates and their recent use in this area.

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Section: Surrogates For Dynamic Processesmentioning

confidence: 99%

Overview of Surrogate Modeling in Chemical Process Engineering

McBride

Sundmacher

2019

Chemie Ingenieur Technik

198

108

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“…It is especially meaningful when the main purpose is to learn an optimal of the system. To many real world optimization problems, typically in cases that require expensive and time-consuming experiments and/or simulations to evaluate design objective and constraint functions, surrogate modeling approach becomes reasonable [16], and has been successfully applied in many real world problems [17][18]. The real robot based gait pattern learning is right one of this kind of tasks, and hence provides an ideal bed for the utilizing of the surrogate model.…”

Section: Surrogate Modelmentioning

confidence: 99%

A Surrogate Model Based Gait Learning for Biped Robot

Luo

Wang

2013

AMM

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Gait learning is usually under a so-called simulation based framework, where a simulation platform is firstly setup, and then based on which the gait pattern is learned via some learning algorithm. For the reason that there exist big differences between simulation platform and real circumstances, an additional adapting procedure is always required when learned gait pattern is applied to a real robot. This case turns out to be more critical for a biped robot, because its control appears more difficult than others, such as a quadruped robot. This leads the new scheme that the gait is directly learned on real robot to be attractive. However, under this real robot based learning scheme, most of those learning algorithms that commonly used under simulation based framework appear to be trivial, since they always needs too many learning trials which may wear out the robot hardware. Faced to this situation, in this paper, a surrogate model based gait learning approach for biped robot is proposed. And the experimental results on a real humanoid robot PKU-HR3 show the effectiveness of the proposed approach.

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“…Dynamic mapping Kriging (DMK, see Hernandez and Gallivan 22 ) is an extension to the time‐dependent case of Kriging 23 or Gaussian process (GP) regression. 24 , 25 Kriging is a regression method that uses a GP, with a covariance function dependent on hyper‐parameters to be tuned from data, as prior for the outcome of a function.…”

Section: Introductionmentioning

confidence: 99%

Combining data assimilation and machine learning to build data‐driven models for unknown long time dynamics—Applications in cardiovascular modeling

Regazzoni

Chapelle

Moireau

2021

Numer Methods Biomed Eng

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We propose a method to discover differential equations describing the long-term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast-scale. Our methodology is based on a synergetic combination of Data Assimilation (DA), used to estimate the parameters associated with the known fast-scale dynamics, and Machine Learning (ML), used to infer the laws underlying the slow-scale dynamics. Specifically, by exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden. Then, we propose a ML algorithm that learns a parametric mathematical model from a collection of time series coming from the phenomenon to be modeled. Moreover, we study the interpretability of the data-driven models obtained within the black-box learning framework proposed in this paper. In particular, we show that every model can be rewritten in infinitely many different equivalent ways, thus making intrinsically illposed the problem of learning a parametric differential equation starting from time series. Hence, we propose a strategy that allows to select a unique representative model in each equivalence class, thus enhancing the interpretability of the results. We demonstrate the effectiveness and noise-robustness of the proposed methods through several test cases, in which we reconstruct several differential models starting from time series generated through the models themselves. Finally, we show the results obtained for a test case in the cardiovascular modeling context, which sheds light on a promising field of application of the proposed methods.

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An exploratory study of discrete time state-space models using kriging

Cited by 9 publications

References 21 publications

Overview of Surrogate Modeling in Chemical Process Engineering

Overview of Surrogate Modeling in Chemical Process Engineering

A Surrogate Model Based Gait Learning for Biped Robot

Combining data assimilation and machine learning to build data‐driven models for unknown long time dynamics—Applications in cardiovascular modeling

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