Exploiting network topology for large-scale inference of nonlinear reaction models

The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to estimate unknown parameters, but also to learn model structure. Bayesian inference provides a natural approach to this data-driven construction of models. Yet traditional Bayesian model inference methodologies that numerically evaluate the evidence for each model are often infeasible for nonlinear reaction network inference, as the number of plausible models can be combinatorially large. Alternative approaches based on model-space sampling can enable large-scale network inference, but their realization presents many challenges. In this paper, we present new computational methods that make large-scale nonlinear network inference tractable. First, we exploit the topology of networks describing potential interactions among chemical species to design improved "between-model" proposals for reversible-jump Markov chain Monte Carlo. Second, we introduce a sensitivity-based determination of move types which, when combined with network-aware proposals, yields significant additional gains in sampling performance. These algorithms are demonstrated on inference problems drawn from systems biology, with nonlinear differential equation models of species interactions

Bayesian inference of chemical kinetic models from proposed reactions

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

Algorithms for particle remeshing applied to smoothed particle hydrodynamics

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 57-59).This thesis outlines adaptivity schemes for particle-based methods for the simulation of nearly incompressible fluid flows. As with the remeshing schemes used in mesh and grid-based methods, there is a need to use localized refinement in particle methods to reduce computational costs. Various forms of particle refinement have been proposed for particle-based methods such as Smoothed Particle Hydrodynamics (SPH). However, none of the techniques that exist currently are able to retain the original degree of randomness among particles. Existing methods reinitialize particle positions on a regular grid. Using such a method for region localized refinement can lead to discontinuities at the interfaces between refined and unrefined particle domains. In turn, this can produce inaccurate results or solution divergence. This thesis outlines the development of new localized refinement algorithms that are capable of retaining the initial randomness of the particles, thus eliminating transition zone discontinuities. The algorithms were tested through SPH simulations of Couette Flow and Poiseuille Flow with spatially varying particle spacing. The determined velocity profiles agree well with theoretical results. In addition, the algorithms were also tested on a flow past a cylinder problem, but with a complete domain remeshing. The original and the remeshed particle distributions showed similar velocity profiles. The algorithms can be extended to 3-D flows with few changes, and allow the simulation of multi-scale flows at reduced computational costs.by Nikhil Galagali.S.M

Bayesian inference of chemical kinetic models from proposed reactions

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 structuresuch 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

Bayesian inference of chemical reaction networks

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 189-198).The development of chemical reaction models aids system design and optimization, along with fundamental understanding, in areas including combustion, catalysis, electrochemistry, and biology. A systematic approach to building reaction network models uses available data not only to estimate unknown parameters, but to also learn the model structure. Bayesian inference provides a natural approach for this data-driven construction of models. Traditional Bayesian model inference methodology is based on evaluating a multidimensional integral for each model. This approach is often infeasible for reaction network inference, as the number of plausible models can be very large. An alternative approach based on model-space sampling can enable large-scale network inference, but its efficient implementation presents many challenges. In this thesis, we present new computational methods that make large-scale nonlinear network inference tractable. Firstly, we exploit the network-based interactions of species to design improved "between-model" proposals for Markov chain Monte Carlo (MCMC). We then introduce a sensitivity-based determination of move types which, when combined with the network-aware proposals, yields further sampling efficiency. These algorithms are tested on example problems with up to 1000 plausible models. We find that our new algorithms yield significant gains in sampling performance, with almost two orders of magnitude reduction in the variance of posterior estimates. We also show that by casting network inference as a fixed-dimensional problem with point-mass priors, we can adapt existing adaptive MCMC methods for network inference. We apply this novel framework to the inference of reaction models for catalytic reforming of methane from a set of ~/~ 32000 possible models and real experimental data. We find that the use of adaptive MCMC makes large-scale inference of reaction networks feasible without the often extensive manual tuning that is required with conventional approaches. Finally, we present an approximation-based method that allows sampling over very large model spaces whose exploration remains prohibitively expensive with ex-act sampling methods. We run an MCMC algorithm over model indicators and for each visited model approximate the model evidence via Laplace's method. Limited and sparse available data tend to produce multi-modal posteriors over the model indicators. To perform inference in this setting, we develop a population-based approximate model inference MCMC algorithm. Numerical tests on problems with around 109 models demonstrate the superiority of our population-based algorithm over single-chain MCMC approaches.by Nikhil Galagali.Ph. D