A special version of Conditional Moment Closure – PCMC – is suggested for modeling reacting flows in porous media. The model involves conditioning on a special tracer scalar, which is introduced to characterize scalar transport in the gaseous phase. (i.e. for the flow in the interparticle space or in the pores). The model accounts for interparticle variations of species concentrations and emula...

In this paper, we present a three-step procedure for the reduction of independent variables u for surrogate modelling. First, the linear material balances are introduced to reduce the number of surrogate models which need to be fit. Second, partial least square (PLS) regression of a sampled space is performed to obtain new variables (components) and third, the new components are used as input v...

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive ‘error indicators’ to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order m...

In continuous optimisation, Surrogate Models (SMs) are often indispensable components of optimisation algorithms aimed at tackling real-world problems whose candidate solutions are very expensive to evaluate. Because of the inherent spatial intuition behind these models, they are naturally suited to continuous problems but they do not seem applicable to combinatorial problems except for the spe...

MGDA stands for Multiple-Gradient Descent Algorithm was introduced in [1]. In a previous report [2], MGDA was tested on several analytical test cases and also compared with a well-known Evolution Strategy algorithm, Pareto Archived Evolution Strategy (PAES) [3]. Using MGDA in a multi-objective optimization problem requires the evaluation of a substantial number of points with regard to criteria...

A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...

With the recent boom in US shale gas production, optimal development of these assets has become a topic of significant interest. In addition to the complex physics typically associated with shale plays, field development optimization can be a challenging problem itself when binary, integer and continuous variables are concurrently present. For complex problems of this nature, it is appropriate ...

The CEA has developed the CERES-MITHRA (C-M) application to model the radionuclide atmospheric dispersion in order to evaluate the consequences on human health of radionuclide releases in the environment. This application is used either for crisis management or to perform assessment calculations for regulatory safety documents relative to nuclear facilities. C-M code is a time consuming complex...

Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from nonspinning binary black hole coalescences with mass ratios in [1,...

In this paper, we have outlined the surrogate management framework for optimization of expensive functions. An initial simple iterative method which we call the “Strawman” method illustrates how surrogates can be incorporated into optimization to stand in for the most expensive function. These ideas are made rigorous by incorporating them into the framework of pattern search methods. The SMF al...