Uncertainty Quantification in MD Simulations. Part I: Forward Propagation

Rizzi, Francesco; Najm, Habib N.; Debusschere, Bert; Sargsyan, Khachik; Salloum, Maher; Adalsteinsson, Helgi; Knio, Omar M.

doi:10.1137/110853169

Cited by 61 publications

(66 citation statements)

References 41 publications

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“…To some extent, these limitations can be remedied considering high-order and mixed derivatives, a global-derivative-based approach 30 or more advanced representations of the parametric dependencies of the moments. [31][32][33] We advocate for the simplicity and generality of the global variance decomposition method, as other sensitivity approaches may miss the characterization of the variance incurred due to the stochasticity of the channels, which is essential for a complete understanding of the stochastic dynamics. The advantages afforded by global sensitivity approach are thus regarded as highly beneficial in a range of applications.…”

Section: Discussionmentioning

confidence: 99%

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Jimenez

Maître

Knio

2016

The Journal of Chemical Physics

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Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

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Section: Discussionmentioning

confidence: 99%

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Jimenez

Maître

Knio

2016

The Journal of Chemical Physics

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“…On the fundamental side, interesting generalizations include the potential of leveraging the present approach for the purpose of model reduction, [33][34][35][36] and for quantifying the impact of uncertainties that may affect system parameters. 22,[37][38][39][40][41][42][43] In particular, such extensions would offer the promise of accounting for and distinguishing between the impacts of parametric sensitivity and irreducible noise, 43 as well as providing estimates where reduced model approximations are valid. These topics are the subject of ongoing work.…”

Section: Discussionmentioning

confidence: 99%

Variance decomposition in stochastic simulators

2015

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Articles you may be interested inThis work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models. C 2015 AIP Publishing LLC. [http://dx

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“…Various approaches have been developed in order to overcome this issue. [42][43][44][45]48 In the present work, application of specific techniques to filter out noise proved unnecessary, because of (i) our ability to perform a very large number of MC samples and (ii) to consider multiple replica. As a result, the obtained estimates exhibit sufficient smoothness, which justifies the application of direct projection technique.…”

Section: Introductionmentioning

confidence: 97%

“…In fact, those studies have worked with Molecular Dynamics (MD) instead of MC molecular simulations. For instance, Rizzi et al have demonstrated a successful coupling between PC and MD in studying force field parameters of water molecules 42,43 in addition to concentration driven ionic flow in nano-pores. 44,45 Later on, similar coupling is adopted in order to investigate flow at nanoscale 46 and quantify parametric uncertainty in multi-scale simulations.…”

Section: Introductionmentioning

confidence: 99%

Single-site Lennard-Jones models via polynomial chaos surrogates of Monte Carlo molecular simulation

Kadoura

Siripatana

Sun

et al. 2016

The Journal of Chemical Physics

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In this work, two Polynomial Chaos (PC) surrogates were generated to reproduce Monte Carlo (MC) molecular simulation results of the canonical (single-phase) and the NVT-Gibbs (two-phase) ensembles for a system of normalized structureless Lennard-Jones (LJ) particles. The main advantage of such surrogates, once generated, is the capability of accurately computing the needed thermodynamic quantities in a few seconds, thus efficiently replacing the computationally expensive MC molecular simulations. Benefiting from the tremendous computational time reduction, the PC surrogates were used to conduct large-scale optimization in order to propose single-site LJ models for several simple molecules. Experimental data, a set of supercritical isotherms, and part of the two-phase envelope, of several pure components were used for tuning the LJ parameters (ε, σ). Based on the conducted optimization, excellent fit was obtained for different noble gases (Ar, Kr, and Xe) and other small molecules (CH4, N2, and CO). On the other hand, due to the simplicity of the LJ model used, dramatic deviations between simulation and experimental data were observed, especially in the two-phase region, for more complex molecules such as CO2 and C2 H6.

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Uncertainty Quantification in MD Simulations. Part I: Forward Propagation

Cited by 61 publications

References 41 publications

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Variance decomposition in stochastic simulators

Single-site Lennard-Jones models via polynomial chaos surrogates of Monte Carlo molecular simulation

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