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Atlas Simulation: A Numerical Scheme for Approximating Multiscale Diffusions Embedded in High Dimensions

dc.contributor.advisor Maggioni, Mauro
dc.contributor.author Crosskey, Miles Martin
dc.date.accessioned 2014-05-14T19:18:11Z
dc.date.available 2014-05-14T19:18:11Z
dc.date.issued 2014
dc.identifier.uri https://hdl.handle.net/10161/8718
dc.description.abstract <p>When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales and high-dimensionality can make simulations expensive. The computational cost is dictated by microscale properties and interactions of many variables, while interesting behavior often occurs on the macroscale with few important degrees of freedom. For many problems bridging the gap between the microscale and macroscale by direct simulation is computationally infeasible, and one would like to learn a fast macroscale simulator. In this paper we present an unsupervised learning algorithm that uses short parallelizable microscale simulations to learn provably accurate macroscale SDE models. The learning algorithm takes as input: the microscale simulator, a local distance function, and a homogenization scale. The learned macroscale model can then be used for fast computation and storage of long simulations. I will discuss various examples, both low- and high-dimensional, as well as results about the accuracy of the fast simulators we construct, and its dependency on the number of short paths requested from the microscale simulator.</p>
dc.subject Mathematics
dc.subject Dynamical Systems
dc.subject Machine Learning
dc.subject Multiscale
dc.subject Stochastic
dc.title Atlas Simulation: A Numerical Scheme for Approximating Multiscale Diffusions Embedded in High Dimensions
dc.type Dissertation
dc.department Mathematics


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