arXiv subjects

Di Qi

Publications and source records attributed to Di Qi.

32 records · Page 2Linked to original sources

arXiv2023

Effective Statistical Control Strategies for Complex Turbulent Dynamical Systems

Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling the statistical features of a turbulent system offers a more robust and efficient approach. Crude first-order linear response approximations were typically employed in previous works for statistical control with small initial perturbations. This paper aims to develop two new statistical control strategies for scenarios with more significant initial perturbations and stronger nonlinear responses, allowing the statistical control framework to be applied to a much wider range of problems. First, higher-order methods, incorporating the second-order terms, are developed to resolve the full control-forcing relation. The corresponding changes to recovering the forcing perturbation effectively improve the performance of the statistical control strategy. Second, a mean closure model for the mean response is developed, which is based on the explicit mean dynamics given by the underlying turbulent dynamical system. The dependence of the mean dynamics on higher-order moments is closed using linear response theory but for the response of the second-order moments to the forcing perturbation rather than the mean response directly. The performance of these methods is evaluated extensively on prototype nonlinear test models, which exhibit crucial turbulent features, including non-Gaussian statistics and regime switching with large initial perturbations. The numerical results illustrate the feasibility of different approaches due to their physical and statistical structures and provide detailed guidelines for choosing the most suitable method based on the model properties.

math.DS↗

arXiv2023

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 spatio-temporal 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 dimension 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.

math.NA↗

arXiv2023

A Data-Driven Statistical-Stochastic Surrogate Modeling Strategy for Complex Nonlinear Non-stationary Dynamics

We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the purely statistical modeling approach that is practically limited to the homogeneous statistical regime for high-dimensional state variables. The new closure system allows one to overcome several practical issues that emerge in the non-homogeneous statistical regimes. First, the proposed ensemble modeling that couples the mean statistics and stochastic fluctuations naturally produces positive-definite covariance matrix estimation, which is a challenging issue that hampers the purely statistical modeling approaches. Second, the proposed closure model, which embeds a non-Markovian neural-network model for the unresolved fluxes such that the variance of the dynamics is consistent, overcomes the inherent instability of the stochastic fluctuation dynamics. Effectively, the proposed framework extends the classical stochastic parametric modeling paradigm for the unresolved dynamics to a semi-parametric parameterization with a residual Long-Short-Term-Memory neural network architecture. Third, based on empirical information metric, we provide an efficient and effective training procedure by fitting a loss function that measures the differences between response statistics. Supporting numerical examples are provided with the Lorenz-96 model, a system of ODEs that admits the characteristic of chaotic dynamics with both homogeneous and inhomogeneous statistical regimes. In the latter case, we will see the effectiveness of the statistical prediction even though the resolved Fourier modes corresponding to the leading mean energy and variance spectra do not coincide.

physics.data-an↗

arXiv2022

A Random Batch Method for Efficient Ensemble Forecasts of Multiscale Turbulent Systems

A new efficient ensemble prediction strategy is developed for a general 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. Then, the forecast skill of the computational algorithm is tested on two representative models of turbulent flows exhibiting many key statistical phenomena with direct link to realistic turbulent systems. The random batch method displays robust performance in capturing a series of crucial statistical features of 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 complex turbulent systems in science and engineering.

physics.flu-dyn↗

arXiv2022

Machine Learning-Based Statistical Closure Models for Turbulent Dynamical Systems

We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure problem is the lack of training data, which is a configuration that is not desirable in supervised learning with neural network models. In this study with the 40-dimensional Lorenz-96 model, the shortage of data (in temporal) is due to the stationarity of the statistics beyond the decorrelation time, thus, the only informative content in the training data is on short-time transient statistics. We adopted a unified closure framework on various truncation regimes, including and excluding the detailed dynamical equations for the variances. The closure frameworks employ a Long-Short-Term-Memory architecture to represent the higher-order unresolved statistical feedbacks with careful consideration to account for the intrinsic instability yet producing stable long-time predictions. We found that this unified agnostic ML approach performs well under various truncation scenarios. Numerically, the ML closure model can accurately predict the long-time statistical responses subjected to various time-dependent external forces that are not (and maximum forcing amplitudes that are relatively larger than those) in the training dataset.

physics.comp-ph↗

arXiv2022

A Physics-Informed Data-Driven Algorithm for Ensemble Forecast of Complex Turbulent Systems

A new ensemble forecast algorithm, named as the physics-informed data-driven algorithm with conditional Gaussian statistics (PIDD-CG), is developed to predict the time evolution of the probability density functions (PDFs) of complex turbulent systems with partial observations. The PIDD-CG algorithm integrates a unique multiscale statistical closure model with an extremely efficient nonlinear data assimilation scheme to represent the PDF as a mixture of conditional statistics, which overcomes the curse of dimensionality for high-dimensional systems. The multiscale features in the time evolution of each conditional statistics ensemble member effectively captured by an appropriate combination of physics-informed analytic formulae and recurrent neural networks. An information metric is adopted as the loss function for the latter to more accurately calibrate the key turbulent signals with strong fluctuations. The proposed algorithm succeeds in forecasting both the transient and statistical equilibrium non-Gaussian PDFs of strongly turbulent systems with intermittency, regime switching and extreme events.

physics.flu-dyn↗

arXiv2021

Anomalous Statistics and Large Deviations of Turbulent Water Waves past a Step

A computational strategy based on large deviation theory (LDT) is used to study the anomalous statistical features of turbulent surface waves propagating past an abrupt depth change created via a step in the bottom topography. The dynamics of the outgoing waves past the step are modeled using the truncated Korteweg-de Vries (TKdV) equation with random initial conditions at the step drawn from the system's Gibbs invariant measure of the incoming waves. Within the LDT framework, the probability distributions of the wave height can be obtained via the solution of a deterministic optimization problem. Detailed numerical tests show that this approach accurately captures the non-Gaussian features of the wave height distributions, in particular their asymmetric tails leading to high skewness. These calculations also give the spatio-temporal pattern of the anomalous waves most responsible for these non-Gaussian features. The strategy shows potential for a general class of nonlinear Hamiltonian systems with highly non-Gaussian statistics.

physics.flu-dyn↗

arXiv2020

Dimits shift, avalanche-like bursts, and Solitary propagating structures in the two-field Flux-Balanced Hasegawa-Wakatani model for plasma edge turbulence

We show that the recently introduced two-field flux-balanced Hasegawa-Wakatani (BHW) model captures the key features of drift-wave turbulent transport mediated by zonal flows observed in more complete and accurate gyrokinetic simulations, such as the existence of a nonlinear upshift of the threshold for drift wave turbulence driven transport, often called the Dimits shift, as well as non-local transport with avalanche bursts and solitary propagating structures. Because of the approximations made in the BHW model, these observations are made for the particle flux instead of the heat flux more commonly studied in ion temperature gradient (ITG) driven turbulence in fluid or gyrokinetic codes. Many of these features are not seen in other Hasegawa-Wakatani models, which confirms the critical role of the electron dynamics parallel to the magnetic field lines. To address questions regarding the role of boundary conditions on the drift-wave zonal flow dynamics, we apply our model to both a channel domain geometry and the more typical doubly periodic geometry. We only observe strong soliton-like solutions in the particle flux for the channel geometry, in the vicinity of the boundaries, where strong velocity shear and density gradients are generated which are absent in the doubly periodic simulations. Changing the aspect ratio of the simulation domain also has a significant effect. In domains which are elongated in the radial direction, more complex multiscale dynamics takes place, with multiple zonal jets interacting with each other, and large scale avalanches.

physics.plasm-ph↗

arXiv2020

ImageBERT: Cross-modal Pre-training with Large-scale Weak-supervised Image-Text Data

In this paper, we introduce a new vision-language pre-trained model -- ImageBERT -- for image-text joint embedding. Our model is a Transformer-based model, which takes different modalities as input and models the relationship between them. The model is pre-trained on four tasks simultaneously: Masked Language Modeling (MLM), Masked Object Classification (MOC), Masked Region Feature Regression (MRFR), and Image Text Matching (ITM). To further enhance the pre-training quality, we have collected a Large-scale weAk-supervised Image-Text (LAIT) dataset from Web. We first pre-train the model on this dataset, then conduct a second stage pre-training on Conceptual Captions and SBU Captions. Our experiments show that multi-stage pre-training strategy outperforms single-stage pre-training. We also fine-tune and evaluate our pre-trained ImageBERT model on image retrieval and text retrieval tasks, and achieve new state-of-the-art results on both MSCOCO and Flickr30k datasets.

cs.CV↗

arXiv2020

Anomalous waves triggered by abrupt depth changes: laboratory experiments and truncated KdV statistical mechanics

Recent laboratory experiments of Bolles et al. (2019) demonstrate that an abrupt change in bottom topography can trigger anomalous statistics in randomized surface waves. Motivated by these observations, Majda et al. (2019) developed a theoretical framework, based on deterministic and statistical analysis of the truncated Korteweg-de Vries (TKdV) system, that successfully captures key qualitative features of the experiments, including the robust emergence of anomalous statistics and heightened skewness in the outgoing wavefield. Here, we extend these parallel experimental and modeling efforts with several new findings that have resulted from a synergetic interaction between the two. By precisely relating model parameters to physical ones, we calibrate the model inverse temperature to the specific conditions present in the experiments, thereby permitting a quantitative comparison. We find theoretically predicted distributions of surface displacement to match the experimental measurements with surprising detail. Prompted by the presence of surface slope in the TKdV Hamiltonian, we present new experimental measurements on surface slope statistics and compare them to model predictions. Analysis of some deterministic trajectories of TKdV elucidates the experimental length and time scales required for the statistical transition to a skewed state. Finally, the theory predicts a peculiar relationship between the outgoing displacement skewness and the change in slope variance, specifically how their ratio depends on the wave amplitude and depth ratio. New experimental measurements confirm this prediction in spectacular fashion.

physics.flu-dyn↗

arXiv2019

Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence

A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence. The core physics in the edge regime of the magnetic-fusion tokamaks can be described qualitatively by the one-state modified Hasegawa-Mima (MHM) model, which creates enhanced zonal flows and more physically relevant features in comparison with the familiar Charney-Hasegawa-Mima (CHM) model for both plasma and geophysical flows. The generation mechanism of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a background base state. Strong exponential growth in the zonal modes is induced due to a non-zonal drift wave base state in the MHM model, while stabilizing damping effect is shown with a zonal flow base state. Together with the selective decay effect from the dissipation, the secondary instability offers a complete characterization of the convergence process to the purely zonal structure. Direct numerical simulations with and without dissipation are carried out to confirm the instability theory. It shows clearly the emergence of a dominant zonal flow from pure non-zonal drift waves with small perturbation in the initial configuration. In comparison, the CHM model does not create instability in the zonal modes and usually converges to homogeneous turbulence.

physics.plasm-ph↗

arXiv2018

A Flux-Balanced Fluid Model for Collisional Plasma Edge Turbulence: Numerical Simulations with Different Aspect Ratios

We investigate the drift wave -- zonal flow dynamics in a shearless slab geometry with the new flux-balanced Hasegawa-Wakatani model. As in previous Hasegawa-Wakatani models, we observe a sharp transition from a turbulence dominated regime to a zonal jet dominated regime as we decrease the plasma resistivity. However, unlike previous models, zonal structures are always present in the flux-balanced model, even for high resistivity, and strongly reduce the level of particle and vorticity flux. The more robust zonal jets also have a higher variability than in previous models, which is further enhanced when the computational domain is chosen to be elongated in the radial direction. In these cases, we observe complex multi-scale dynamics, with multiple jets interacting with one another, and intermittent bursts. We present a detailed statistical analysis which highlights how the changes in the aspect ratio of the computational domain affect the third-order statistical moments, and thus modify the turbulent dynamics.

physics.plasm-ph↗

arXiv2018

A Flux-Balanced Fluid Model for Collisional Plasma Edge Turbulence: Model Derivation and Basic Physical Features

We propose a new reduced fluid model for the study of the drift wave -- zonal flow dynamics in magnetically confined plasmas. Our model can be viewed as an extension of the classic Hasegawa-Wakatani (HW) model, and is based on an improved treatment of the electron dynamics parallel to the field lines, to guarantee a balanced electron flux on the magnetic surfaces. Our flux-balanced HW (bHW) model contains the same drift-wave instability as previous HW models, but unlike these models, it converges exactly to the modified Hasegawa-Mima model in the collisionless limit. We rely on direct numerical simulations to illustrate some of the key features of the bHW model, such as the enhanced variability in the turbulent fluctuations, and the existence of stronger and more turbulent zonal jets than the jets observed in other HW models, especially for high plasma resistivity. Our simulations also highlight the crucial role of the feedback of the third-order statistical moments in achieving a statistical equilibrium with strong zonal structures. Finally, we investigate the changes in the observed dynamics when more general dissipation effects are included, and in particular when we include the reduced model for ion Landau damping originally proposed by Wakatani and Hasegawa.

physics.plasm-ph↗

arXiv2018

Strategies for Reduced-Order Models for Predicting the Statistical Responses and Uncertainty Quantification in Complex Turbulent Dynamical Systems

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent systems containing a large number of positive Lyapunov exponents results in a rapid growth of small uncertainties, requiring naturally a probabilistic characterization for the evolution of the turbulent system. Uncertainty quantification in turbulent dynamical systems is a grand challenge where the goal is to obtain statistical estimates such as the change in mean and variance for key physical quantities in their nonlinear responses to changes in external forcing parameters or uncertain initial data. One central issue in contemporary research is the development of a systematic methodology that can recover the crucial features of the natural system in statistical equilibrium (model fidelity) and improve the imperfect model prediction skill in response to various external perturbations (model sensitivity). A general mathematical framework to construct statistically accurate reduced-order models that have skill in capturing the statistical variability in the principal directions with largest energy of a general class of damped and forced complex turbulent dynamical systems is discussed here. The methods are developed under a universal class of turbulent dynamical systems with quadratic nonlinearity that is representative in many applications in applied mathematics and engineering. The validity of general framework of reduced-order models is demonstrated on instructive stochastic triad models. Recent applications to two-layer baroclinic turbulence in the atmosphere and ocean with combinations of turbulent jets and vortices are also surveyed.

physics.flu-dyn↗