arXiv subjects

Hessam Babaee

Publications and source records attributed to Hessam Babaee.

30 records · Page 2Linked to original sources

arXiv2022

Scalable In Situ Compression of Transient Simulation Data Using Time-Dependent Bases

Large-scale simulations of time-dependent problems generate a massive amount of data and with the explosive increase in computational resources the size of the data generated by these simulations has increased significantly. This has imposed severe limitations on the amount of data that can be stored and has elevated the issue of input/output (I/O) into one of the major bottlenecks of high-performance computing. In this work, we present an in situ compression technique to reduce the size of the data storage by orders of magnitude. This methodology is based on time-dependent subspaces and it extracts low-rank structures from multidimensional streaming data by decomposing the data into a set of time-dependent bases and a core tensor. We derive closed-form evolution equations for the core tensor as well as the time-dependent bases. The presented methodology does not require the data history and the computational cost of its extractions scales linearly with the size of data -- making it suitable for large-scale streaming datasets. To control the compression error, we present an adaptive strategy to add/remove modes to maintain the reconstruction error below a given threshold. We present four demonstration cases: (i) analytical example, (ii) incompressible unsteady reactive flow, (iii) stochastic turbulent reactive flow, and (iv) three-dimensional turbulent channel flow.

cs.CE↗

arXiv2022

Reduced Order Modeling of Turbulence-Chemistry Interactions using Dynamically Bi-Orthonormal Decomposition

The performance of the dynamically bi-orthogonal (DBO) decomposition for the reduced order modeling of turbulence-chemistry interactions is assessed. DBO is an on-the-fly low-rank approximation technique, in which the instantaneous composition matrix of the reactive flow field is decomposed into a set of orthonormal spatial modes, a set of orthonormal vectors in the composition space, and a factorization of the low-rank correlation matrix. Two factors which distinguish between DBO and the reduced order models (ROMs) based on the principal component analysis (PCA) are: (i) DBO does not require any offline data generation; and (ii) in DBO the low-rank composition subspace is time-dependent as opposed to static subspaces in PCA. Because of these features, DBO can adapt on-the-fly to intrinsic and externally excited transient changes in state of the transport variables. For demonstration, simulations are conducted of a non-premixed CO/H2 flame in a temporally evolving jet. The GRI-Mech 3.0 model with 53 species is used for chemical kinetics modeling. The results are appraised via a posteriori comparisons against data generated via full-rank direct numerical simulation (DNS) of the same flame, and the PCA reduction of the DNS data. The DBO also yields excellent predictions of various statistics of the thermo-chemical variables.

physics.flu-dyn↗

arXiv2021

Physics-informed neural networks for improving cerebral hemodynamics predictions

Determining brain hemodynamics plays a critical role in the diagnosis and treatment of various cerebrovascular diseases. In this work, we put forth a physics-informed deep learning framework that augments sparse clinical measurements with fast computational fluid dynamics (CFD) simulations to generate physically consistent and high spatiotemporal resolution of brain hemodynamic parameters. Transcranial Doppler (TCD) ultrasound is one of the most common techniques in the current clinical workflow that enables noninvasive and instantaneous evaluation of blood flow velocity within the cerebral arteries. However, it is spatially limited to only a handful of locations across the cerebrovasculature due to the constrained accessibility through the skull's acoustic windows. Our deep learning framework employs in-vivo real-time TCD velocity measurements at several locations in the brain and the baseline vessel cross-sectional areas acquired from 3D angiography images, and provides high-resolution maps of velocity, area, and pressure in the entire vasculature. We validated the predictions of our model against in-vivo velocity measurements obtained via 4D flow MRI scans. We then showcased the clinical significance of this technique in diagnosing the cerebral vasospasm (CVS) by successfully predicting the changes in vasospastic local vessel diameters based on corresponding sparse velocities measurements. The key finding here is that the combined effects of uncertainties in outlet boundary condition subscription and modeling physics deficiencies render the conventional purely physics-based computational models unsuccessful in recovering accurate brain hemodynamics. Nonetheless, fusing these models with clinical measurements through a data-driven approach ameliorates predictions of brain hemodynamic variables.

physics.med-ph↗

arXiv2021

On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds

One of the principal barriers in developing accurate and tractable predictive models in turbulent flows with a large number of species is to track every species by solving a separate transport equation, which can be computationally impracticable. In this paper, we present an on-the-fly reduced order modeling of reactive as well as passive transport equations to reduce the computational cost. The presented approach seeks a low-rank decomposition of the species to three time-dependent components: (i) a set of orthonormal spatial modes, (ii) a low-rank factorization of the instantaneous species correlation matrix, and (iii) a set of orthonormal species modes, which represent a low-dimensional time-dependent manifold. Our approach bypasses the need to solve the full-dimensional species to generate high-fidelity data - as it is commonly performed in data-driven dimension reduction techniques such as the principle component analysis. Instead, the low-rank components are directly extracted from the species transport equation. The evolution equations for the three components are obtained from optimality conditions of a variational principle. The time-dependence of the three components enables an on-the-fly adaptation of the low-rank decomposition to transient changes in the species. Several demonstration cases of reduced order modeling of passive and reactive transport equations are presented.

cs.CE↗

arXiv2020

Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy

We present a new methodology for computing sensitivities in evolutionary systems using a model-driven low-rank approximation. To this end, we formulate a variational principle that seeks to minimize the distance between the time derivative of the reduced approximation and sensitivity dynamics. The first-order optimality condition of the variational principle leads to a system of closed-form evolution equations for an orthonormal basis and corresponding sensitivity coefficients. This approach allows for the computation of sensitivities with respect to a large number of parameters in an accurate and tractable manner by extracting correlations between different sensitivities on the fly. The presented method requires solving forward evolution equations, sidestepping the restrictions imposed by forward/backward workflow of adjoint sensitivities. For example, the presented method, unlike the adjoint equation, does not impose any I/O load and can be used in applications in which real time sensitivities are of interest. We demonstrate the utility of the method for three test cases: (1) computing sensitivity with respect to model parameters in the Rossler system (2) computing sensitivity with respect to an infinite-dimensional forcing parameter in the chaotic Kuramoto-Sivashinsky equation and (3) computing sensitivity with respect to reaction parameters for species transport in a turbulent reacting flow.

math.OC↗

arXiv2020

Multi-fidelity Bayesian Neural Networks: Algorithms and Applications

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we use the Hamiltonian Monte Carlo method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fideilty data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

cs.LG↗

arXiv2020

Low-rank representation of head impact kinematics: A data-driven emulator

Head motion induced by impacts has been deemed as one of the most important measures in brain injury prediction, given that the majority of brain injury metrics use head kinematics as input. Recently, researchers have focused on using fast approaches, such as machine learning, to approximate brain deformation in real-time for early brain injury diagnosis. However, those requires large number of kinematic measurements, and therefore data augmentation is required given the limited on-field measured data available. In this study we present a principal component analysis-based method that emulates an empirical low-rank substitution for head impact kinematics, while requiring low computational cost. In characterizing our existing data set of 537 head impacts, consisting of 6 degrees of freedom measurements, we found that only a few modes, e.g. 15 in the case of angular velocity, is sufficient for accurate reconstruction of the entire data set. Furthermore, these modes are predominantly low frequency since over 70% to 90% of the angular velocity response can be captured by modes that have frequencies under 40Hz. We compared our proposed method against existing impact parametrization methods and showed significantly better performance in injury prediction using a range of kinematic-based metrics -- such as head injury criterion and rotational injury criterion (RIC) -- and brain tissue deformation-metrics -- such as brain angle metric, maximum principal strain (MPS) and axonal fiber strains (FS). In all cases, our approach reproduced injury metrics similar to the ground truth measurements with no significant difference, whereas the existing methods obtained significantly different (p<0.01) values as well as poor injury classification sensitivity and specificity. This emulator will enable us to provide the necessary data augmentation to build a head impact kinematic data set of any size.

q-bio.QM↗

arXiv2019

Real-Time Reduced-Order Modeling of Stochastic Partial Differential Equations via Time-Dependent Subspaces

We present a new methodology for the real-time reduced-order modeling of stochastic partial differential equations called the dynamically/bi-orthonormal (DBO) decomposition. In this method, the stochastic fields are approximated by a low-rank decomposition to spatial and stochastic subspaces. Each of these subspaces is represented by a set of orthonormal time-dependent modes. We derive exact evolution equations of these time-dependent modes and the evolution of the factorization of the reduced covariance matrix. We show that DBO is equivalent to the dynamically orthogonal (DO) and bi-orthogonal (BO) decompositions via linear and invertible transformation matrices that connect DBO to DO and BO. However, DBO shows several improvements compared to DO and BO: (i) DBO performs better than DO and BO for cases with ill-conditioned covariance matrix; (ii) In contrast to BO, the issue of eigenvalue crossing is not present in the DBO formulation; (iii) In contrast to DO, the stochastic modes are orthonormal, which leads to more accurate representation of the stochastic subspace. We study the convergence properties of the method and compare it to the DO and BO methods. For demonstration, we consider three cases: (i) stochastic linear advection equation, (ii) stochastic Burgers' equation, and (iii) stochastic incompressible flow over a bump in a channel. Overall we observe improvements in the numerical accuracy of DBO compared against DO and BO.

physics.comp-ph↗

arXiv2019

A Scalable Observation-Driven Time-Dependent Basis for a Reduced Description of Transient Systems

We present a variational principle for the extraction of a time-dependent orthonormal basis from random realizations of transient systems. The optimality condition of the variational principle leads to a closed-form evolution equation for the orthonormal basis and its coefficients. The extracted modes are associated with the most transient subspace of the system, and they provide a reduced description of the transient dynamics that may be used for reduced-order modeling, filtering and prediction. The presented method is matrix-free and relies only on the observables of the system and ignores any information about the underlying system. In that sense, the presented reduction is purely observation-driven and may be applied to systems whose models are not known. The presented method has linear computational complexity and memory storage requirement with respect to the number of observables and the number of random realizations. Therefore, it may be used for a large number of observations and samples. The effectiveness of the proposed method is tested on three examples: (i) stochastic advection equation, (ii) a reduced description of transient instability of Kuramoto-Sivashinsky, and (iii) a transient vertical jet governed by incompressible Navier-Stokes equation. In these examples, we contrast the performance of the time-dependent basis versus static basis such as proper orthogonal decomposition, dynamic mode decomposition and polynomial chaos expansion.

math.NA↗

arXiv2018

Deep Learning of Turbulent Scalar Mixing

Based on recent developments in physics-informed deep learning and deep hidden physics models, we put forth a framework for discovering turbulence models from scattered and potentially noisy spatio-temporal measurements of the probability density function (PDF). The models are for the conditional expected diffusion and the conditional expected dissipation of a Fickian scalar described by its transported single-point PDF equation. The discovered model are appraised against exact solution derived by the amplitude mapping closure (AMC)/ Johnsohn-Edgeworth translation (JET) model of binary scalar mixing in homogeneous turbulence.

physics.flu-dyn↗

arXiv2017

Reduced-order Description of Transient Instabilities and Computation of Finite-Time Lyapunov Exponents

High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g. long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy--Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples.

math.DS↗

arXiv2015

A minimization principle for the description of time-dependent modes associated with transient instabilities

We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have finite lifetime they can play a crucial role by either altering the system dynamics through the activation of other instabilities, or by creating sudden nonlinear energy transfers that lead to extreme responses. However, their essentially transient character makes their description a particularly challenging task. We develop a minimization framework that focuses on the optimal approximation of the system dynamics in the neighborhood of the system state. This minimization formulation results in differential equations that evolve a time-dependent basis so that it optimally approximates the most unstable directions. We demonstrate the capability of the method for two families of problems: i) linear systems including the advection-diffusion operator in a strongly non-normal regime as well as the Orr-Sommerfeld/Squire operator, and ii) nonlinear problems including a low-dimensional system with transient instabilities and the vertical jet in crossflow. We demonstrate that the time-dependent subspace captures the strongly transient non-normal energy growth (in the short time regime), while for longer times the modes capture the expected asymptotic behavior.

physics.comp-ph↗