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A new efficient ensemble prediction strategy is developed for a multiscale turbulent model framework with emphasis on the nonlinear interactions between large and small-scale variables. The high computational cost in running large ensemble simulations of high-dimensional equations is effectively avoided by adopting a random batch decomposition of the wide spectrum of the fluctuation states, which is a characteristic feature of the multiscale turbulent systems. The time update of each ensemble sample is then only subject to a small portion of the small-scale fluctuation modes in one batch, while the true model dynamics with multiscale coupling is respected by frequent random resampling of the batches at each time updating step. We investigate both theoretical and numerical properties of the proposed method. First, the convergence of statistical errors in the random batch model approximation is shown rigorously independent of the sample size and full dimension of the system. Next, the forecast skill of the computational algorithm is tested on two representative models of turbulent flows exhibiting many key statistical phenomena with a direct link to realistic turbulent systems. The random batch method displays robust performance in capturing a series of crucial statistical features with general interests, including highly non-Gaussian fat-tailed probability distributions and intermittent bursts of instability, while requires a much lower computational cost than the direct ensemble approach. The efficient random batch method also facilitates the development of new strategies in uncertainty quantification and data assimilation for a wide variety of general complex turbulent systems in science and engineering.
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High-order moment closure models with random batch method for efficient computation of multiscale turbulent systems
We propose a high-order stochastic–statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment equations are closed by a precise calibration of the high-order feedbacks using ensemble solutions of the consistent stochastic equations, suitable for modeling complex phenomena including non-Gaussian statistics and extreme events. To address challenges associated with closely coupled spatiotemporal scales in turbulent states and expensive large ensemble simulation for high-dimensional systems, we introduce efficient computational strategies using the random batch method (RBM). This approach significantly reduces the required ensemble size while accurately capturing essential high-order structures. Only a small batch of small-scale fluctuation modes is used for each time update of the samples, and exact convergence to the full model statistics is ensured through frequent resampling of the batches during time evolution. Furthermore, we develop a reduced-order model to handle systems with really high dimensions by linking the large number of small-scale fluctuation modes to ensemble samples of dominant leading modes. The effectiveness of the proposed models is validated by numerical experiments on the one-layer and two-layer Lorenz ‘96 systems, which exhibit representative chaotic features and various statistical regimes. The full and reduced-order RBM models demonstrate uniformly high skill in capturing the time evolution of crucial leading-order statistics, non-Gaussian probability distributions, while achieving significantly lower computational cost compared to direct Monte-Carlo approaches. The models provide effective tools for a wide range of real-world applications in prediction, uncertainty quantification, and data assimilation.
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- Award ID(s):
- 2106988
- PAR ID:
- 10530682
- Publisher / Repository:
- AIP
- Date Published:
- Journal Name:
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Volume:
- 33
- Issue:
- 10
- ISSN:
- 1054-1500
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0160057
