### Abstract

In this paper, a semiparametric modeling approach is introduced as a paradigm for addressing model error arising from unresolved physical phenomena. Our approach compensates for model error by learning an auxiliary dynamical model for the unknown parameters. Practically, the proposed approach consists of the following steps. Given a physics-based model and a noisy data set of historical observations, a Bayesian filtering algorithm is used to extract a time-series of the parameter values. Subsequently, the diffusion forecast algorithm is applied to the retrieved time-series in order to construct the auxiliary model for the time evolving parameters. The semiparametric forecasting algorithm consists of integrating the existing physics-based model with an ensemble of parameters sampled from the probability density function of the diffusion forecast. To specify initial conditions for the diffusion forecast, a Bayesian semiparametric filtering method that extends the Kalman-based filtering framework is introduced. In difficult test examples, which introduce chaotically and stochastically evolving hidden parameters into the Lorenz-96 model, we show that our approach can effectively compensate for model error, with forecasting skill comparable to that of the perfect model.

Original language | English (US) |
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Pages (from-to) | 305-321 |

Number of pages | 17 |

Journal | Journal of Computational Physics |

Volume | 308 |

DOIs | |

State | Published - Mar 1 2016 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

### Cite this

}

*Journal of Computational Physics*, vol. 308, pp. 305-321. https://doi.org/10.1016/j.jcp.2015.12.043

**Semiparametric modeling : Correcting low-dimensional model error in parametric models.** / Berry, Tyrus; Harlim, John.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Semiparametric modeling

T2 - Correcting low-dimensional model error in parametric models

AU - Berry, Tyrus

AU - Harlim, John

PY - 2016/3/1

Y1 - 2016/3/1

N2 - In this paper, a semiparametric modeling approach is introduced as a paradigm for addressing model error arising from unresolved physical phenomena. Our approach compensates for model error by learning an auxiliary dynamical model for the unknown parameters. Practically, the proposed approach consists of the following steps. Given a physics-based model and a noisy data set of historical observations, a Bayesian filtering algorithm is used to extract a time-series of the parameter values. Subsequently, the diffusion forecast algorithm is applied to the retrieved time-series in order to construct the auxiliary model for the time evolving parameters. The semiparametric forecasting algorithm consists of integrating the existing physics-based model with an ensemble of parameters sampled from the probability density function of the diffusion forecast. To specify initial conditions for the diffusion forecast, a Bayesian semiparametric filtering method that extends the Kalman-based filtering framework is introduced. In difficult test examples, which introduce chaotically and stochastically evolving hidden parameters into the Lorenz-96 model, we show that our approach can effectively compensate for model error, with forecasting skill comparable to that of the perfect model.

AB - In this paper, a semiparametric modeling approach is introduced as a paradigm for addressing model error arising from unresolved physical phenomena. Our approach compensates for model error by learning an auxiliary dynamical model for the unknown parameters. Practically, the proposed approach consists of the following steps. Given a physics-based model and a noisy data set of historical observations, a Bayesian filtering algorithm is used to extract a time-series of the parameter values. Subsequently, the diffusion forecast algorithm is applied to the retrieved time-series in order to construct the auxiliary model for the time evolving parameters. The semiparametric forecasting algorithm consists of integrating the existing physics-based model with an ensemble of parameters sampled from the probability density function of the diffusion forecast. To specify initial conditions for the diffusion forecast, a Bayesian semiparametric filtering method that extends the Kalman-based filtering framework is introduced. In difficult test examples, which introduce chaotically and stochastically evolving hidden parameters into the Lorenz-96 model, we show that our approach can effectively compensate for model error, with forecasting skill comparable to that of the perfect model.

UR - http://www.scopus.com/inward/record.url?scp=84952878819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952878819&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2015.12.043

DO - 10.1016/j.jcp.2015.12.043

M3 - Article

VL - 308

SP - 305

EP - 321

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -