Youssef Marzouk | Massachusetts Institute of Technology (MIT) (original) (raw)

Papers by Youssef Marzouk

Nuclear Fusion, 2015

ABSTRACT The need to fit smooth temperature and density profiles to discrete observations is ubiq... more ABSTRACT The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, but the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We show that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. We also discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts.

This paper presents recent progress on the use of Computational Singular Perturbation (CSP) techn... more This paper presents recent progress on the use of Computational Singular Perturbation (CSP) techniques for time integration of stiff chemical systems. The CSP integration approach removes fast time scales from the reaction system, thereby enabling integration with explicit time stepping algorithms. For further efficiency improvements, a tabulation strategy was developed to allow reuse of the relevant CSP quantities. This paper

International Journal for Numerical Methods in Engineering, 2014

One of the major challenges in the Bayesian solution of inverse problems governed by partial diff... more One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. This paper proposes a data-driven projection-based model reduction technique to reduce this computational cost. The proposed technique has two distinctive features. First, the model reduction strategy is tailored to inverse problems: the snapshots used to construct the reduced-order model are computed adaptively from the posterior distribution. Posterior exploration and model reduction are thus pursued simultaneously. Second, to avoid repeated evaluations of the full-scale numerical model as in a standard MCMC method, we couple the full-scale model and the reduced-order model together in the MCMC algorithm. This maintains accurate inference while reducing its overall computational cost. In numerical experiments considering steady-state flow in a porous medium, the data-driven reduced-order model achieves better accuracy than a reduced-order model constructed using the classical approach. It also improves posterior sampling efficiency by several orders of magnitude compared to a standard MCMC method.

ABSTRACT We describe a method for accelerating a 3D Monte Carlo forward radiative transfer model ... more ABSTRACT We describe a method for accelerating a 3D Monte Carlo forward radiative transfer model to the point where it can be used in a new kind of Bayesian retrieval framework. The remote sensing challenge is to detect and quantify a chemical effluent of a known absorbing gas produced by an industrial facility in a deep valley. The available data is a single low-resolution noisy image of the scene in the near IR at an absorbing wavelength for the gas of interest. The detected sunlight has been multiply reflected by the variable terrain and/or scattered by an aerosol that is assumed partially known and partially unknown. We thus introduce a new class of remote sensing algorithms best described as “multi-pixel” techniques that call necessarily for a 3D radiative transfer model (but demonstrated here in 2D); they can be added to conventional ones that exploit typically multi-or hyper-spectral data, sometimes with multi-angle capability, with or without information about polarization. The novel Bayesian inference methodology uses adaptively, with efficiency in mind, the fact that a Monte Carlo forward model has a known and controllable uncertainty depending on the number of sun-to-detector paths used.

SIAM Journal on Scientific Computing, 2014

The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such... more The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or forward model. When these evaluations are computationally intensive, approximations of the forward model are essential to accelerating sample-based inference. Yet the construction of globally accurate approximations for nonlinear forward models can be computationally prohibitive and in fact unnecessary, as the posterior distribution typically concentrates on a small fraction of the support of the prior distribution. We present a new approach that uses stochastic optimization to construct polynomial approximations over a sequence of measures adaptively determined from the data, eventually concentrating on the posterior distribution. The approach yields substantial gains in efficiency and accuracy over prior-based surrogates, as demonstrated via application to inverse problems in partial differential equations.

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2011

Experimental diagnostics play an essential role in the development and refinement of chemical kin... more Experimental diagnostics play an essential role in the development and refinement of chemical kinetic models, whether for the combustion of common complex hydrocarbons or of emerging alternative fuels. Questions of experimental design-e.g., which variables or species to interrogate, at what resolution and under what conditions-are extremely important in this context, particularly when experimental resources are limited. This paper attempts to answer such questions in a rigorous and systematic way. We propose a Bayesian framework for optimal experimental design with nonlinear simulation-based models. While the framework is broadly applicable, we use it to infer rate parameters in a combustion system with detailed kinetics. The framework introduces a utility function that reflects the expected information gain from a particular experiment. Straightforward evaluation (and maximization) of this utility function requires Monte Carlo sampling, which is infeasible with computationally intensive models. Instead, we construct a polynomial surrogate for the dependence of experimental observables on model parameters and design conditions, with the help of dimension-adaptive sparse quadrature. Results demonstrate the efficiency and accuracy of the surrogate, as well as the considerable effectiveness of the experimental design framework in choosing informative experimental conditions.

International Journal for Uncertainty Quantification, 2014

Optimal experimental design (OED) seeks experiments expected to yield the most useful data for so... more Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue OED for nonlinear systems from a Bayesian perspective, with the goal of choosing experiments that are optimal for parameter inference. Our objective in this context is the expected information gain in model parameters, which in general can only be estimated using Monte Carlo methods. Maximizing this objective thus becomes a stochastic optimization problem. This paper develops gradient-based stochastic optimization methods for the design of experiments on a continuous parameter space. Given a Monte Carlo estimator of expected information gain, we use infinitesimal perturbation analysis to derive gradients of this estimator. We are then able to formulate two gradient-based stochastic optimization approaches: (i) Robbins-Monro stochastic approximation, and (ii) sample average approximation combined with a deterministic quasi-Newton method. A polynomial chaos approximation of the forward model accelerates objective and gradient evaluations in both cases. We discuss the implementation of these optimization methods, then conduct an empirical comparison of their performance. To demonstrate design in a nonlinear setting with partial differential equation forward models, we use the problem of sensor placement for source inversion. Numerical results yield useful guidelines on the choice of algorithm and sample sizes, assess the impact of estimator bias, and quantify tradeoffs of computational cost versus solution quality and robustness.

Communications in Computational Physics, 2009

We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochas... more We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. This approximation then defines a surrogate posterior probability density that can be evaluated repeatedly at minimal computational cost. The ability to simulate a large number of samples from the posterior distribution results in very accurate estimates of the inverse solution and its associated uncertainty. Combined with high accuracy of the gPC-based forward solver, the new algorithm can provide great efficiency in practical applications. A rigorous error analysis of the algorithm is conducted, where we establish convergence of the approximate posterior to the true posterior and obtain an estimate of the convergence rate. It is proved that fast (exponential) convergence of the gPC forward solution yields similarly fast (exponential) convergence of the posterior. The numerical strategy and the predicted convergence rates are then demonstrated on nonlinear inverse problems of varying smoothness and dimension.

Chemical Engineering Science, 2015

ABSTRACT Bayesian inference provides a natural framework for combining experimental data with pri... more ABSTRACT Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure—such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.

IEICE Proceeding Series, 2014

Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national... more Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national security concern since the anthrax attacks of 2001. The ability to characterize the parameters of such attacks, i.e., to estimate the number of people infected, the time of infection, the average dose received, and the rate of disease spread in contemporary American society (for contagious diseases), is important when planning a medical response. For non-contagious diseases, we address the characterization problem by formulating a Bayesian inverse problem predicated on a short time-series of diagnosed patients exhibiting symptoms. To keep the approach relevant for response planning, we limit ourselves to 3-5 days of data. In computational tests performed for anthrax, we usually find these observation windows sufficient, especially if the outbreak model employed in the inverse problem is accurate. For contagious diseases, we formulated a Bayesian inversion technique to infer both pathogenic transmissibility and the social network from outbreak observations, ensuring that the two determinants of spreading are identified separately. We tested this technique on data collected from a 1967 smallpox epidemic in Abakaliki, Nigeria. We inferred, probabilistically, different transmissibilities in the structured Abakaliki population, the social network, and the chain of transmission. Finally, we developed an individual-based epidemic ¡ § ¦ 2¨25¡ 10 2 ¤. In both cases, PDFs are reported after 3-, 4-and 5-day observational periods (dotted, dashed, and solid lines respectively).. .. .. .. 9 Posterior PDFs for N (top), τ (middle), and log D (bottom) based on the time series for Case C (left) and Case D (right), as tabulated in Table 2.

43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005

44th AIAA Aerospace Sciences Meeting and Exhibit, 2006

Inverse Problems and Imaging, 2013

The full application of Bayesian inference to inverse problems requires exploration of a posterio... more The full application of Bayesian inference to inverse problems requires exploration of a posterior distribution that typically does not possess a standard form. In this context, Markov chain Monte Carlo (MCMC) methods are often used. These methods require many evaluations of a computationally intensive forward model to produce the equivalent of one independent sample from the posterior. We consider applications in which approximate forward models at multiple resolution levels are available, each endowed with a probabilistic error estimate. These situations occur, for example, when the forward model involves Monte Carlo integration. We present a novel MCMC method called M C 3 that uses low-resolution forward models to approximate draws from a posterior distribution built with the high-resolution forward model. The acceptance ratio is estimated with some statistical error; then a confidence interval for the true acceptance ratio is found, and acceptance is performed correctly with some confidence. The high-resolution models are rarely run and a significant speed up is achieved.

Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitm... more Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback.

Data assimilation is an essential tool for predicting the behavior of real physical systems given... more Data assimilation is an essential tool for predicting the behavior of real physical systems given approximate simulation models and limited observations. For many complex systems, there may exist several models, each with different properties and predictive capabilities. It is desirable to incorporate multiple models into the assimilation procedure in order to obtain a more accurate prediction of the physics than any model alone can provide. In this paper, we propose a framework for conducting sequential data assimilation with multiple models and sources of data. The assimilated solution is a linear combination of all model predictions and data. One notable feature is that the combination takes the most general form with matrix weights. By doing so the method can readily utilize different weights in different sections of the solution state vectors, allow the models and data to have different dimensions, and deal with the case of a singular state covariance. We prove that the proposed assimilation method, termed direct assimilation, minimizes a variational functional, a generalized version of the one used in the classical Kalman filter. We also propose an efficient iterative assimilation method that assimilates two models at a time until all models and data are assimilated. The mathematical equivalence of the iterative method and the direct method is established. Numerical examples are presented to demonstrate the effectiveness of the new method.

Page 1. IW013 3rd IWMRRF CSP simplification of chemical kinetic systems under uncertainty Thomas ... more Page 1. IW013 3rd IWMRRF CSP simplification of chemical kinetic systems under uncertainty Thomas MK Coles∗, Habib N. Najm, and Youssef M. Marzouk∗ ∗Massachusetts Institute of Technology; Cambridge, MA USA Sandia National Laboratories; Livermore, CA USA ...

A cantilevered ramp fuel-injection strategy is considered as a means of delivering rapid mixing f... more A cantilevered ramp fuel-injection strategy is considered as a means of delivering rapid mixing for use in scramjets and shock-induced combustion ramjets (shcramjets). The primary objective is to perform parametric studies of the injector array spacing, injection angle, and sweeping angle at a convective Mach number of 1.5. Analysis of the 3D steady-state hypersonic flowfields is accomplished through the WARP code, using the Yee-Roe flux-limiting scheme and the Wilcox k-omega turbulence model, along with the Wilcox ...