TY - JOUR
T1 - Conditional Gaussian systems for multiscale nonlinear stochastic systems
T2 - Prediction, state estimation and uncertainty quantification
AU - Chen, Nan
AU - Majda, Andrew J.
N1 - Funding Information:
The research of A.J.M. is partially supported by the Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) Grant N0001416-1-2161 and the New York University Abu Dhabi Research Institute. N.C. is supported as a postdoctoral fellow through A.J.M.'s ONR MURI Grant. The authors thank Yoonsang Lee, Di Qi and Sulian Thual for useful discussion
Publisher Copyright:
© 2018 by the author.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - A conditional Gaussian framework for understanding and predicting complex multiscale nonlinear stochastic systems is developed. Despite the conditional Gaussianity, such systems are nevertheless highly nonlinear and are able to capture the non-Gaussian features of nature. The special structure of the system allows closed analytical formulae for solving the conditional statistics and is thus computationally efficient. A rich gallery of examples of conditional Gaussian systems are illustrated here, which includes data-driven physics-constrained nonlinear stochastic models, stochastically coupled reaction-diffusion models in neuroscience and ecology, and large-scale dynamical models in turbulence, fluids and geophysical flows. Making use of the conditional Gaussian structure, efficient statistically accurate algorithms involving a novel hybrid strategy for different subspaces, a judicious block decomposition and statistical symmetry are developed for solving the Fokker-Planck equation in large dimensions. The conditional Gaussian framework is also applied to develop extremely cheap multiscale data assimilation schemes, such as the stochastic superparameterization, which use particle filters to capture the non-Gaussian statistics on the large-scale part whose dimension is small whereas the statistics of the small-scale part are conditional Gaussian given the large-scale part. Other topics of the conditional Gaussian systems studied here include designing new parameter estimation schemes and understanding model errors.
AB - A conditional Gaussian framework for understanding and predicting complex multiscale nonlinear stochastic systems is developed. Despite the conditional Gaussianity, such systems are nevertheless highly nonlinear and are able to capture the non-Gaussian features of nature. The special structure of the system allows closed analytical formulae for solving the conditional statistics and is thus computationally efficient. A rich gallery of examples of conditional Gaussian systems are illustrated here, which includes data-driven physics-constrained nonlinear stochastic models, stochastically coupled reaction-diffusion models in neuroscience and ecology, and large-scale dynamical models in turbulence, fluids and geophysical flows. Making use of the conditional Gaussian structure, efficient statistically accurate algorithms involving a novel hybrid strategy for different subspaces, a judicious block decomposition and statistical symmetry are developed for solving the Fokker-Planck equation in large dimensions. The conditional Gaussian framework is also applied to develop extremely cheap multiscale data assimilation schemes, such as the stochastic superparameterization, which use particle filters to capture the non-Gaussian statistics on the large-scale part whose dimension is small whereas the statistics of the small-scale part are conditional Gaussian given the large-scale part. Other topics of the conditional Gaussian systems studied here include designing new parameter estimation schemes and understanding model errors.
KW - Conditional Gaussian mixture
KW - Conditional Gaussian systems
KW - Conformation theory;model error
KW - Hybrid strategy
KW - Multiscale nonlinear stochastic systems
KW - Parameter estimation
KW - Physics-constrained nonlinear stochastic models
KW - Stochastically coupled reaction-diffusion models
KW - Superparameterization
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U2 - 10.3390/e20070509
DO - 10.3390/e20070509
M3 - Article
AN - SCOPUS:85050302934
SN - 1099-4300
VL - 20
JO - Entropy
JF - Entropy
IS - 7
ER -