GPU-Accelerated Solution of Activated Sludge Model's System of ODEs with a High Degree of Stiffness

Alikhania, Jamal; Massoudiehb, Arash; Bhowmika, Ujjal K.

doi:10.1109/csci.2016.0111

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…The most expensive part of the ensemble method is the construction of the 3.4 million solutions of, for example, a system of nonlinear ordinary differential equations (ODEs). Parallelization may be accomplished in several ways either by: (i) changing the method for solving ODEs [53]- [55]; (ii) using GPUs to carry the burden in solving the ODEs [10], [56], [57] in the Monte Carlo Experiment; (iii) using multiple agents in carrying out a search for good solutions [58]. All three approaches potentially allow ensemble methods to scale to networks involving thousands of genes and their products [59] (referred to as genetic networks hereafter) to understand the regulation of metabolism.…”

Section: B Ensemble Methods For Large Networkmentioning

confidence: 99%

Ensemble Methods for Identifying RNA Operons and Regulons in the Clock Network of Neurospora Crassa

et al. 2022

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With both light entrainment data (L/D) and free running data in the dark (D/D), Variable Topology Ensemble Methods (VTENS) were used to reconstruct the entire genome-scale clock network involving 3380 genes and their products under the hypothesis that clock-controlled genes are both transcriptionally regulated and post-transcriptionally regulated through RNA operons. The clock network has 12 hubs with target genes surrounding twelve regulators, and 694 putative clock-controlled genes provide linkage between hubs in their joint regulation. There were 71 significant feedforward loops within this clock network, the majority of which involved genes lhp-1 and NCU06108 targeting genes connected with the ribosome and ribosome biogenesis. All 12 regulators target amino acid biosynthesis. The largest hub (768 genes) surrounded the post-transcriptional regulator lhp-1defining an RNA operon. There appears to be no partitioning of light-regulated genes and circadian genes between the 12 hubs. The regulators lhp-1, has-1, and rrp-3 appear to target putative clock-controlled genes in ribosome biogenesis. The combined hypothesis of 6 RNA operons and 5 transcriptional regulons was successful in describing the dynamics of the clock network with 3380 genes and their products with a χ 2 = 2.133 per data point for 60,759 mRNA time points. With little known about allosteric regulation of metabolism, the clock network provided a major link between gene regulation and metabolism.

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Section: B Ensemble Methods For Large Networkmentioning

confidence: 99%

Ensemble Methods for Identifying RNA Operons and Regulons in the Clock Network of Neurospora Crassa

et al. 2022

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“…This system consists of several reactions that operate on significantly different time scales, and as a result is characterized by a large degree of stiffness . In practice, exact kinetics may depend on the exact bacterial ecology of the process unit.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Global optimization of stiff dynamical systems

Wilhelm

Stuber

2019

AIChE Journal

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We present a deterministic global optimization method for nonlinear programming formulations constrained by stiff systems of ordinary differential equation (ODE) initial value problems (IVPs). The examples arise from dynamic optimization problems exhibiting both fast and slow transient phenomena commonly encountered in model-based systems engineering applications. The proposed approach utilizes unconditionally stable implicit integration methods to reformulate the ODEconstrained problem into a nonconvex nonlinear program (NLP) with implicit functions embedded. This problem is then solved to global optimality in finite time using a spatial branch-and-bound framework utilizing convex/concave relaxations of implicit functions constructed by a method which fully exploits problem sparsity. The algorithms were implemented in the Julia programming language within the EAGO.jl package and demonstrated on five illustrative examples with varying complexity relevant in process systems engineering. The developed methods enable the guaranteed global solution of dynamic optimization problems with stiff ODE-IVPs embedded. K E Y W O R D S dynamic simulation, global optimization, implicit functions, stiff systems

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“…High-performance computing can largely enhance the performance of MCMC sampling methods to deal with uncertainties. For example, Alikhani et al [8] [9] showed an application of adaptive ODE solution algorithm in parallel-based GPU to accelerate the solution of mass balance rate equations in the kinetic models. They showed that applying these improvements can reduce the overall computation time by up to 50%.…”

Section: Introductionmentioning

confidence: 99%

Reaction Rate Constant Evaluation of Thermal Isomerization of α-Pinene

Zhang¹,

Li²,

Zhang³

et al. 2017

MSCE

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Bayesian inference is applied in this study to evaluate the posterior distribution of rate consents for a thermal isomerization of α-pinene by considering the uncertainty associated with rate constant parameters and kinetic model structural error. The kinetic model of the thermal isomerization of α-pinene is shown to have a mathematically ill-conditioned system that makes it difficult to apply gradient-based optimization methods for rate constant evaluation. The Bayesian inference relates the posterior probability distribution of the rate constants to the likelihood probability of modeled concentration of reaction products meeting the experimentally measured concentration and the prior probability distribution of the parameters. A Markov chain Monte Carlo (MCMC) is used to draw samples from posterior distribution while the Bayesian inference relationship is considered. Multinomial random walk Metropolis-Hastings is applied in this study to construct the histograms of rate constants as well as the confidence intervals and the correlation coefficient matrix. Results showed that the Bayesian approach can successfully apply to estimate the confidence interval of rate constants of reaction model by taking into consideration the uncertainty.

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GPU-Accelerated Solution of Activated Sludge Model's System of ODEs with a High Degree of Stiffness

Cited by 4 publications

References 13 publications

Ensemble Methods for Identifying RNA Operons and Regulons in the Clock Network of Neurospora Crassa

Ensemble Methods for Identifying RNA Operons and Regulons in the Clock Network of Neurospora Crassa

Global optimization of stiff dynamical systems

Reaction Rate Constant Evaluation of Thermal Isomerization of α-Pinene

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