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Using adaptive sparse grids to solve high-dimensional dynamic models


Brumm, Johannes; Scheidegger, Simon (2013). Using adaptive sparse grids to solve high-dimensional dynamic models. SSRN 2349281, University of Zurich.

Abstract

We present a flexible and scalable method to compute global solutions of high-dimensional non-smooth dynamic models. Within a time-iteration setup, we interpolate policy functions using an adaptive sparse grid algorithm with piecewise multi-linear (hierarchical) basis functions. As the dimensionality increases, sparse grids grow considerably slower than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients or even non-differentiabilities. To further increase the maximal problem size we can handle, our implementation is fully hybrid parallel, i.e. using a combination of MPI and OpenMP. This parallelization enables us to efficiently use modern high-performance computing architectures. Our time iteration algorithm scales up nicely to more than one thousand parallel processes. To demonstrate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.

Abstract

We present a flexible and scalable method to compute global solutions of high-dimensional non-smooth dynamic models. Within a time-iteration setup, we interpolate policy functions using an adaptive sparse grid algorithm with piecewise multi-linear (hierarchical) basis functions. As the dimensionality increases, sparse grids grow considerably slower than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients or even non-differentiabilities. To further increase the maximal problem size we can handle, our implementation is fully hybrid parallel, i.e. using a combination of MPI and OpenMP. This parallelization enables us to efficiently use modern high-performance computing architectures. Our time iteration algorithm scales up nicely to more than one thousand parallel processes. To demonstrate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.

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13 citations in Microsoft Academic

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
JEL Classification:C63, C68, F41
Language:English
Date:2013
Deposited On:23 Dec 2013 14:47
Last Modified:16 Feb 2018 18:41
Series Name:SSRN
Number of Pages:36
OA Status:Green
Official URL:http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2349281
Other Identification Number:merlin-id:8587

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