Data-assisted reduced-order modeling of extreme events in complex dynamical systems

Wan, Zhong; Vlachas, Pantelis R.; Koumoutsakos, Petros; Sapsis, Themistoklis P.

doi:10.1371/journal.pone.0197704

Cited by 215 publications

(119 citation statements)

References 57 publications

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“…With the growing interest in data-driven modeling of ROMs using machine learning (ML) architectures, there has been another dimension of research introduced to the community for the improvement in ROM performance, referred as hybrid ROM approach. Generally, the hybridization is done by combining an imperfect physics-based model with a data-driven technique to get a hybrid scheme, and it is observed that the hybrid model shows better predictive performance than the component models [52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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In this study, we present a non-intrusive reduced order modeling (ROM) framework for largescale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the highresolution data snapshots using proper orthogonal decomposition (POD) transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first illustrate that the conventional Galerkin projection based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-GP does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed non-intrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasi-periodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time-window in this paper. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully non-intrusive ROM framework is robust and capable of predicting noisy nonlinear fluid flows in an extremely efficient way compared to the conventional projection based ROM framework.

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Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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“…However, the literature on applications of ML to dynamical instabilities is remarkably scarce. The only related investigation of which we are aware was conducted by Wan et al 31 , who used long-short-term-memory neural networks to predict occurrences of extreme events in chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Learning the tangent space of dynamical instabilities from data

Blanchard

Sapsis

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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For a large class of dynamical systems, the optimally time-dependent (OTD) modes, a set of deformable orthonormal tangent vectors that track directions of instabilities along any trajectory, are known to depend "pointwise" on the state of the system on the attractor, and not on the history of the trajectory. We leverage the power of neural networks to learn this "pointwise" mapping from phase space to OTD space directly from data. The result of the learning process is a cartography of directions associated with strongest instabilities in phase space. Implications for data-driven prediction and control of dynamical instabilities are discussed.The optimally time-dependent (OTD) modes are a set of deformable orthonormal tangent vectors that track directions of instabilities along any trajectory of a dynamical system. Traditionally, these modes are computed by a time-marching approach that involves solving multiple initial-boundary-value problems concurrently with the state equations. However, for a large class of dynamical systems, the OTD modes are known to depend "pointwise" on the state of the system on the attractor, and not on the history of the trajectory. So we propose a neural-network algorithm to learn this "pointwise" mapping from phase space to OTD space directly from data. The neural network produces a cartography of directions of strongest instability in phase space, as well as accurate estimates for the leading Lyapunov exponents.

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“…In practice, for example for large-scale, multi-physics, multi-scale dynamical systems such as weather and climate models, it is likely that a hybrid framework yields the best performance: depending on the application and the spatio-temporal scales of the physical processes involved [18,76], some of the equations could be solved numerically with double precision, some could be solved numerically with lower precisions, and some could be approximated with a surrogate model learned via data-driven approach. Such inexact data-assisted frameworks enable integrating the known physics and PDEs with the AI models, thus overcoming the challenges arising from shortness of datasets, poorly understood physics, and partially known PDEs [77,54], while allowing for automated tuning to make the best use of the computing power and resources. As mentioned before, the data-driven models (e.g., a neural network) can be also designed to benefit from the concepts and philosophy of inexact computing (i.e., reduce precision, save resources, reinvest wisely).…”

Section: Discussionmentioning

confidence: 99%

Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM

Chattopadhyay¹,

Hassanzadeh²,

Subramanian³

2020

Preprint

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Abstract. In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir computing, RC-ESN), deep feed-forward artificial neural network (ANN), and recurrent neural network with long short-term memory (RNN-LSTM). This Lorenz 96 system has three tiers of nonlinearly interacting variables representing slow/large-scale (X), intermediate (Y), and fast/small-scale (Z) processes. For training or testing, only X is available; Y and Z are never known or used. We show that RC-ESN substantially outperforms ANN and RNN-LSTM for short-term prediction, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps, equivalent to several Lyapunov timescales. The RNN-LSTM and ANN show some prediction skills as well; RNN-LSTM bests ANN. Furthermore, even after losing the trajectory, data predicted by RC-ESN and RNN-LSTM have probability density functions (PDFs) that closely match the true PDF, even at the tails. The PDF of the data predicted using ANN, however, deviates from the true PDF. Implications, caveats, and applications to data-driven and data-assisted surrogate modeling of complex nonlinear dynamical systems such as weather/climate are discussed.

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Data-assisted reduced-order modeling of extreme events in complex dynamical systems

Cited by 215 publications

References 57 publications

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Learning the tangent space of dynamical instabilities from data

Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM

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