Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session A31: Nonlinear Dynamics: General & Chaos |
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Chair: Wenbo Tang, Arizona State University Room: North 232 ABC |
Sunday, November 21, 2021 8:00AM - 8:13AM |
A31.00001: Data-driven discovery of model error in chaotic systems by integrating Bayesian sparse regression and data assimilation Rambod Mojgani, Pedram Hassanzadeh, Ashesh K Chattopadhyay We propose the application of a Bayesian machine learning technique to discover a closed-form representation of the model error, i.e. the symbolic representation of the difference between the true dynamics of a system and its corresponding model. The technique incorporates a data assimilation step and therefore is capable of handling noisy observations. The models of complex physical phenomena such as fluid flows, climate, and weather often contain missing representations of certain hard-to-model processes, which leads to prediction inaccuracies. An increasing abundance of data from observations provides the opportunity to discover these missing physics, and therefore to improve the predictive capabilities of numerical, purely data-driven, or hybrid models with minimal changes. Accordingly, we propose the use of relevant vector machines (RVM), an inherently sparsity promoting Bayesian model, in conjunction with a stochastic ensemble Kalman filter (EnKF) to discover the closed form of model error from noisy observations. We demonstrate the robustness of our technique in the presence of different magnitudes of noise in a well-known challenging task in system identification, i.e. Kuramoto–Sivashinsky (KS) equation in a chaotic regime. |
Sunday, November 21, 2021 8:13AM - 8:26AM |
A31.00002: Reconstructing various regimes of the complex Ginzburg--Landau model from data Sijie Huang, Poorbayan Das, Jeonglae Kim The complex Ginzburg--Landau equation (CGLE) is widely used in fluid mechanics, superconductivity, liquid crystal and string theory. CGLE also models the amplitude variation of traveling wave solution occurring at low frequencies, which often results in modulational instability. Relative significance of linear and nonlinear dispersion is described by the Benjamin--Feir criterion with which various regimes of CGLE are characterized. Those regimes exhibit stark qualitative differences, rendering the data-based eduction of CGLE less straightforward. This study applies a sparse regression method (PDE-FIND) to discover CGLE out of high-fidelity simulation data and show the robustness of the algorithm. The one-dimensional cubic CGLE is solved using a non-dissipative high-order compact finite difference scheme. Several distinct regimes of CGLE characterized by regular plane wave, spatio-temporal chaos, intermittency and coherent structures, respectively, are simulated by altering the linear and nonlinear dispersion parameters. The numerical data are exploited to discover CGLE. Excellent reconstruction accuracy is obtained regardless of the regimes of CGLE. |
Sunday, November 21, 2021 8:26AM - 8:39AM |
A31.00003: Unsupervised Learning of Dimensionless Groups and Minimally Parametrized Equations Joseph Bakarji, Steven L Brunton, Nathan Kutz, Jared Callaham We address the fundamental problem of developing algorithms that learn interpretable physical models from measurement data. In particular, we focus on the data-driven discovery of non-dimensional numbers. An encoder layer constrained by the Buckingham Pi theorem (BuckiNet) and embedded in a deep network that fits input-output measurements, is designed to discover the set of dimensionless numbers that best collapses the data to a low dimensional parameter space and reveals dominant bifurcation parameters. In addition, we develop a SINDy-based algorithm that constrains the dimensionless numbers to be part of a sparse parametric differential equation, thus directly relating the Pi groups to the underlying dynamics that describe the system. We test our methods on nonlinear systems, including the rotating hoop, the boundary layer flow, and Rayleigh-Benard problems. |
Sunday, November 21, 2021 8:39AM - 8:52AM |
A31.00004: Robust machine learning of turbulence through generalized Buckingham Pi-inspired pre-processing of training data Kai Fukami, Kunihiko Taira Applications of machine learning to unseen situations are challenging for turbulent flows. With turbulence resulting from strong nonlinear dynamics, categorizing seen and unseen events and structures are generally not clear-cut, especially for modern machine learning methods that can accommodate some stretching and rotational invariances. In such circumstances encountered in machine learning approaches, we develop a technique for pre-processing the training data by generalizing the Buckingham Pi theorem and combining it with sparse regression. Identifying the appropriate non-dimensional scaling functions, we show that machine learning can be performed with enhanced accuracy and robustness. We also note that the concept of interpolation and extrapolation becomes clearer through such scaling procedure, providing guidance on when users of machine learning techniques should be mindful of possible high-risk extrapolations. Two and three-dimensional decaying isotropic turbulence are selected to demonstrate the robustness of the proposed approach and highlight its potential to enhance the training process for learning complex turbulent flow dynamics. |
Sunday, November 21, 2021 8:52AM - 9:05AM |
A31.00005: Multi-point penalty-based optimization for optimal control of chaotic turbulent flow Seung Whan Chung, Jonathan B Freund Gradient-based optimization can augment the utility of a simulation for both scientific and engineering applications, but obtaining useful gradient for a chaotic turbulent flow is challenging because any quantity-of-interest $\mathcal{J}$ to become significantly non-convex over time. As such, even an exact gradient is restricted in finding a useful optimum. We introduce an optimization framework to circumvent this challenge for optimal control of turbulent flow. It splits the simulation time into intervals with discontinuities that are increasingly penalized. The challenge and method are illustrated with a logistics map and the Lorenz system before being successfully applied to a three-dimensional turbulent Kolmogorov flow. For the turbulence case, the method suppresses large-scale pressure fluctuations without laminarization, effectively targeting a controllable component of the flow amidst the more chaotic turbulence. The utility of such an optimization, which might be questioned because of the restricted controllability of chaotic systems, is discussed. |
Sunday, November 21, 2021 9:05AM - 9:18AM |
A31.00006: Reservoir Computing as a Tool for Climate Predictability Studies Balu Nadiga Reduced-order dynamical models continue to play a central role in developing our understanding of predictability of climate. In this context, the Linear Inverse Modeling (LIM) approach (closely related to Dynamic Mode Decomposition DMD), by helping capture a few essential interactions between dynamical components of the full system, has proven valuable in being able to give insights into the dynamical behavior of the full system. While nonlinear extensions of the LIM approach have been attempted none have gained widespread acceptance. |
Sunday, November 21, 2021 9:18AM - 9:31AM |
A31.00007: Autoencoded Reservoir Computing for the Spatio-Temporal Prediction of a Turbulent Flow Nguyen Anh Khoa Doan, Luca Magri The recent development and success in deep learning have demonstrated the ability of neural networks to learn the dynamics of chaotic systems. However, this has mostly been applied to low dimensional systems. The applicability of these deep learning tools to turbulence remains a challenge because of high dimensionality and chaotic dynamics that span multiple spatiotemporal scales. |
Sunday, November 21, 2021 9:31AM - 9:44AM |
A31.00008: Gradient-free optimization of chaotic acoustics with echo state networks Francisco Huhn, Luca Magri Gradient-based optimisation of chaotic acoustics is challenging due to: (i) the exponential divergence of first-order perturbations (butterfly effect), (ii) the slow convergence rate of statistics and gradients, and (iii) the possibility that the gradient may not be defined for some design parameters. We propose a gradient-free methodology based on Bayesian optimization that overcomes all these issues. To bypass the high cost of time integration (due to slow convergence of statistics), we propose the use of echo state networks, which have been shown to predict chaotic systems with good performance. We analyze their short- and long-time predictive capabilities in thermoacoustics, finding that the network is capable of predicting the dynamics both time-accurately and statistically. Importantly, incorporating physical knowledge via a reduced-order model significantly improves the accuracy and robustness of the prediction. Finally, using the model-informed architecture, we find the set of heat source parameters that minimizes the time-averaged acoustic energy, a measure of the size of the chaotic acoustic oscillations. This optimal set is found with the same accuracy as brute-force grid search, but with a convergence rate that is more than one order of magnitude faster. |
Sunday, November 21, 2021 9:44AM - 9:57AM |
A31.00009: The Lorenz 63 model by quantum machine learning Philipp Pfeffer, Florian Heyder, Joerg Schumacher Complex fluid flows often require extensive analysis which can be avoided with easier and faster machine learning models for various tasks. These models tend to utilize high dimensional linear algebra that can be realized effectively on quantum computers. In this talk, we present a quantum reservoir computing model for the Lorenz 63 model which describes two-dimensional thermal convection between two free-slip walls right above the onset of thermal convection. It is taken to show the usability of the approach for chaotic fluid flow problems where known data can be used to predict or reproduce single or multiple states of a nonlinear model or system. We summarize some critical steps of the implementation on real quantum computers. |
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