Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session L30: Modeling Methods V: Reconstruction, Estimation, and Data Assimilation |
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Chair: Petros Koumoutsakos, Harvard University Room: 154AB |
Monday, November 20, 2023 8:00AM - 8:13AM |
L30.00001: Data-Induced Interactions of Sparse Sensors Andrei A Klishin, J. Nathan Kutz, Krithika Manohar Large-dimensional empirical data in science and engineering frequently has low-rank structure and can be represented as a combination of just a few eigenmodes. Because of this structure, we can use just a few spatially localized sensor measurements to reconstruct the full state of a complex system. The quality of this reconstruction, especially in the presence of sensor noise, depends significantly on the spatial configuration of the sensors. Multiple algorithms based on gappy interpolation and QR factorization have been proposed to optimize sensor placement. Here, instead of an algorithm that outputs a singular "optimal" sensor configuration, we take a thermodynamic view to compute the full landscape of sensor interactions induced by the training data. The landscape takes the form of the Ising model in statistical physics, and accounts for both the data variance captured at each sensor location and the crosstalk between sensors. Mapping out these data-induced sensor interactions allows combining them with external selection criteria and anticipating sensor replacement impacts. |
Monday, November 20, 2023 8:13AM - 8:26AM |
L30.00002: Scientific Machine Learning Workflows for Phase-Change Heat Transfer Applications Akash V Dhruv, Shakeel Hasan, Arthur Feeney, Aparna Chandramowlishwaran, Anshu Dubey Scientific Machine Learning (SciML) models show promise in various fields, including phase-change heat transfer. However, obtaining diverse and accurately labeled datasets for training remains a significant challenge, particularly in this domain where evaporation and bubble dynamics play a critical role in determining heat transfer efficiency. Specialized experimental setups, including instrumentation, sensors, and high-speed visualization techniques, incur substantial costs and challenges. This greatly limits the availability of high-fidelity datasets that encompass a wide range of operating conditions necessary to train generalizable SciML models. Numerical simulations can offer high-fidelity multiscale data to complement and enhance experimental measurements. However, training SciML models with large spatio-temporal simulation datasets requires scalable workflows for distributed memory systems with efficient cache and memory management. In this talk, we will present an approach to address these challenges using Flash-X, an open-source simulation software, and BoxKit, a Python interface for managing simulation data. Our computational pipeline integrates numerical simulations, experimental data, and SciML models, enabling learning predictive models capable of handling large 4D spatio-temporal datasets for thermal science applications. |
Monday, November 20, 2023 8:26AM - 8:39AM |
L30.00003: Data-Driven Diffusion Coefficient Estimation in Marine Lakes Alex Ho, Francois Blanchette Marine lakes, located near the sea, allow limited exchanges between the lake and the nearby sea. We provide an efficient method to estimate, as a function of depth, the diffusion coefficient, D, within the lake using easily available measurements for quantities such as temperature, salinity, or both. Our method solves for the spatially varying D by minimizing the misfit to data subject to a regularization condition. We model the system with a Helmholtz-type partial differential equation (PDE) that encapsulates specific characteristics of marine lakes, including the exchanges between the lake and the nearby sea and the absorption of solar heat by algae sheets beneath the lake's surface. Our empirical investigation unveils mathematical requirements of the model that underscore the previously unsuspected importance of the role played by algae sheets as a heat source in this ecosystem. By offering a versatile and insightful tool, our method not only contributes to a better understanding of marine ecosystems but also holds promise for broader applications. |
Monday, November 20, 2023 8:39AM - 8:52AM |
L30.00004: Adjoint-accelerated Bayesian Inference Matthew P Juniper Bayesian Inference provides a probabilistic framework that is well suited to Machine Learning of model parameters from data. We specify any number of candidate models, their parameters, and their prior probability distributions. When data arrives, we calculate (i) the most likely parameter values, (ii) their posterior probability distributions, (iii) the marginal likelihood of each model. This combines how well each model fits the data with how much each parameter space collapses when the data arrive. This penalizes (i) models that do not fit the data and (ii) models that fit the data but whose parameters require excessively delicate tuning to do so. |
Monday, November 20, 2023 8:52AM - 9:05AM |
L30.00005: Data assimilation for compressible flows by optimizing a discrete loss (ODIL) with automatic differentiation Petr Karnakov, Deniz Bezgin, Aaron Buhendwa, Nikolaus Adams, Petros Koumoutsakos We solve data assimilation and other inverse problems for compressible fluid flows including flow reconstruction from sparse measurements, inference of body shape from supersonic flow past the body, and inference of material parameters for two-phase flows. Our method is a combination of the ODIL (Optimizing a DIscrete Loss) framework to formulate the inverse problem through optimization and the fully-differentiable JAX-Fluids CFD package to obtain gradients of the residuals of the governing equations. The loss function includes residuals of the Euler equations, terms to impose known flow measurements, and regularization terms. The ODIL framework employs multiresolution techniques in the loss function and representation of unknown discrete fields to speed up the convergence of standard gradient-based optimizers. We identify combinations of boundary conditions and measurements necessary to infer the flow field, and study the effects of regularization terms on the convergence speed and reconstruction accuracy. Our results suggest that our framework can incorporate noisy and incomplete data into flow simulations and therefore complement experimental measurements. In addition, we provide a comparative study with the popular Physics-Informed Neural Networks (PINNs) method. |
Monday, November 20, 2023 9:05AM - 9:18AM |
L30.00006: Optimizing the Discrete Loss for the Solution for Inverse problems in fluid mechanics: multiresolution and automatic differentiation Petros Koumoutsakos, Petr Karnakov, Sergey Litvinov We present a potent method, Optimizing the DIscrete Loss (ODIL) for the solution of inverse problems in fluid mechanics .In ODIL inverse problems are formulated in terms of a deterministic loss function, based on a discete version of the governing equations, that can accommodate data and regularization terms. ODIL is based on similar ideas as the popular Physics Informed Neural Networks (PINNS) but does not deploy neural networks. A multigrid decomposition accelerates the convergence of gradient-based methods for optimization problems with parameters on a grid. The multiresolution ODIL (mODIL) improves the avoidance of local minima while automatic differentiation used for calculating the gradients of the loss function facilitates implementation of the framework. We demonstrate the capabilities of ODIL and mODIL on a variety of inverse and flow reconstruction problems: solution reconstruction for the Burgers equation, inferring conductivity from temperature measurements, and inferring the body shape from wake velocity measurements in three dimensions. A comparative study demonstrates that mODIL is 1000x to 100'000X faster than PINNs in a number of benchmark problems ranging from simple PDEs to lid-driven cavity problems. We discuss the advantages and defficiencies of the method. Our results suggest that mODIL is a very potent, fast and consistent method for solving inverse problems in fluid mechanics. |
Monday, November 20, 2023 9:18AM - 9:31AM |
L30.00007: Elucidating the 3D topology of a cantilevered square cylinder wake using multi-time-delay estimation with FIR-based SPOD Chris Morton, Ali Mohammadi, Robert J Martinuzzi FIR-based spectral proper orthogonal decomposition (SPOD) (Sieber et al., 2016) is used for remote-sensor based estimation of a highly modulated bluff body wakes. The estimator is trained on individual stereoscopic particle image velocimetry (PIV) planes synchronized with surface pressure measurements. Estimation is then used to reconstruct time-resolved 3D coherent motions with the aim of investigating cycle-to-cycle variations in vortex interactions. The candidate flow is the near turbulent, quasi-periodic near-wake of a cantilevered square cylinder with a height-to-width ratio 4, protruding a thin laminar boundary layer at a Reynolds number of 10600. In a phase-averaged sense, the wake is described as a half-loop shedding pattern, consisting of inter-connected Kármán vortex structures. |
Monday, November 20, 2023 9:31AM - 9:44AM |
L30.00008: Real-time digital twins of thermoacoustic instabilities in hydrogen-fuelled annular combustors Andrea Nóvoa, Nicolas Noiray, James R Dawson, Luca Magri The dynamics of azimuthal thermoacoustic instabilities in annular combustors are intricate and changeable with respect to the operating conditions. To control thermoacoustic instabilities, we need quantitatively accurate low-order models that can infer the dynamics in real-time from sensor's data. In this work, we propose real-time digital twins of thermoacoustic instabilities by combining data from laboratory experiments and nonlinear low-order models. We employ the recently proposed regularized bias-aware ensemble Kalman filter to infer on the fly the thermoacoustic state, model parameters, and model errors from pressure measurements only. We validate the real-time digital twin by comparing the prediction with the state-of-the-art methods based on offline calibration. This research introduces new possibilities for safe operation of hydrogen-based aeroengines through real-time digital twinning. |
Monday, November 20, 2023 9:44AM - 9:57AM |
L30.00009: A Schwarz-type domain decomposition method for physics-constrained neural networks Inanc Senocak, shamsulhaq basir We present a Schwarz-type, non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). We adopt a generalized Robin-type interface condition, which is a convex combination of Dirichlet and Neumann conditions with a unique Robin parameter assigned to each subdomain. These subdomain-specific Robin parameters are learned to minimize the mismatch at the subdomain interfaces, facilitating efficient information exchange during training. Our method is applicable to both the Laplace's and Helmholtz equations. Our overall meshless solution method represents local solutions by an independent neural network model which is trained to minimize the loss on the governing PDE while strictly enforcing boundary and interface conditions through an augmented Lagrangian formalism. Our results show that the learned Robin parameters adapt to the local behavior of the solution, domain partitioning and subdomain location relative to the overall domain. Extensive experiments on forward and inverse problems, including one-way and two-way decompositions with crosspoints, demonstrate the versatility and performance of our proposed approach. |
Monday, November 20, 2023 9:57AM - 10:10AM |
L30.00010: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting Chuanqi Chen, Nan Chen, Jinlong Wu Online nonlinear system identification with sequential data has recently become important in many applications, e.g., extreme weather events, climate change, and autonomous systems. In this work, we developed a causation entropy boosting (CEBoosting) framework for online nonlinear system identification. For each sequential data batch, this framework calculates the causation entropy that evaluates the contribution of each function in a large set of candidate functions to the system dynamics. The causation entropies based on multiple data batches are then aggregated to identify a few candidate functions that have significant impacts on the system dynamics. With the identified sparse set of functions, the framework further fits a model of the system dynamics. The results show that the CEBoosting method can capture the regime switching and then fit models of system dynamics for various types of complex dynamical based on a limited amount of sequential data. |
Monday, November 20, 2023 10:10AM - 10:23AM |
L30.00011: Data Assimilation of the Minimal Flow Unit Isabel Scherl, Eviatar Bach, Tim Colonius State-estimation and prediction are central challenges in turbulent flows. Data-driven approaches can provide accurate representations of these systems thus improving modeling and control. Techniques in data assimilation, a sequential time-stepping strategy which seeks to optimally combine a model forecast and system observations, provide an opportunity for improved state estimation using limited measurements. Reconstruction using sparse measurements is advantageous due to limited availability of sensors. We utilize a high-dimensional model efficiently using ensemble Kalman methods. These methods are demonstrated on a turbulent channel simulation of the minimal flow unit. The measurements and model outputs are assimilated following short episodes of simulation advancement. Using a perfect model or assimilation with synthetic observations, where the simulation provides data for both the model and measurement, we assimilate these data streams for improved state estimation. |
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