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Neural Networks as Surrogates of Nonlinear High-Dimensional Parameter-to-Prediction Maps

Jakeman, John D.; Perego, Mauro P.; Severa, William M.

We present a preliminary investigation of the use of Multi-Layer Perceptrons (MLP) and Recurrent Neural Networks (RNNs) as surrogates of parameter-to-prediction maps of com- putational expensive dynamical models. In particular, we target the approximation of Quan- tities of Interest (QoIs) derived from the solution of a Partial Differential Equations (PDEs) at different time instants. In order to limit the scope of our study while targeting a rele- vant application, we focus on the problem of computing variations in the ice sheets mass (our QoI), which is a proxy for global mean sea-level changes. We present a number of neural network formulations and compare their performance with that of Polynomial Chaos Expansions (PCE) constructed on the same data.

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TYPE SAND Report YEAR 2018
OSTIDOI

Towards a scalable multifidelity simulation approach for electrokinetic problems at the mesoscale

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Hong, Brian D.; Perego, Mauro P.; Bochev, Pavel B.; Frischknecht, Amalie F.; Phillips, Edward G.

In this work we present a computational capability featuring a hierarchy of models with different fidelities for the solution of electrokinetics problems at the micro-/nano-scale. A multifidelity approach allows the selection of the most appropriate model, in terms of accuracy and computational cost, for the particular application at hand. We demonstrate the proposed multifidelity approach by studying the mobility of a colloid in a micro-channel as a function of the colloid charge and of the size of the ions dissolved in the fluid.

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TYPE Conference Poster YEAR 2018
ScopusOSTIDOI

A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale

Journal of Computational Physics

Cheung, James C.; Frischknecht, Amalie F.; Perego, Mauro P.; Bochev, Pavel B.

We develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson–Nernst–Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independently on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.

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TYPE Journal Article YEAR 2017
ScopusOSTIDOI
Results 51–75 of 147
Results 51–75 of 147