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- Cameron Browne, Edward Jack Powley, +7 authors Simon Colton
- IEEE Transactions on Computational Intelligence…
- 2012

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the… (More)

- T. Wildey, S. Tavener, D. Estep
- 2006

SUMMARY This paper describes the a posteriori estimation of the error in the flux of a finite element approximation on a piece of the boundary of the domain. The estimate is obtained via a generalized Green's function corresponding to the quantity of interest on the boundary. We investigate the effects of smoothing the data corresponding to the quantity of… (More)

- D. Estep, A. Målqvist, S. Tavener
- 2008

SUMMARY In this paper, we develop and apply an efficient adaptive algorithm for computing the propagation of uncertainty into a quantity of interest computed from numerical solutions of an elliptic partial differential equation with a randomly perturbed diffusion coefficient. The algorithm is well-suited for problems for which limited information about the… (More)

We consider inverse problems for a deterministic model in which the dimension of the output quantities of interest computed from the model is smaller than the dimension of the input quantities for the model. In this case, the inverse problem admits set-valued solutions (equivalence classes of solutions). We devise a method for approximating a representation… (More)

- V. Carey, D. Estep, S. Tavener
- 2013

SUMMARY In this paper, we develop an a posteriori error analysis for operator decomposition iteration methods applied to systems of coupled semilinear elliptic problems. The goal is to compute accurate error estimates that account for the combined effects arising from numerical approximation (discretization) and operator decomposition iteration. In an… (More)

- Cameron Browne, Stephen Tavener
- IEEE Transactions on Computational Intelligence…
- 2012

This paper introduces bitwise-parallel reduction (BPR), an efficient method for performing connection tests in hexagonal connection games such as Hex and Y. BPR is based on a known property of Y that games can be reduced to a single value indicating the fully connected player (if any) through a sequence of reduction operations. We adapt this process for… (More)

- B. Sheehan, D. Estep, +6 authors S. Vadlamani
- 2015

We investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. The algorithms considered are based on the widely used approach of iteratively exchanging boundary… (More)

- T. Arbogast, D. Estep, B. Sheehan, S. Tavener
- 2015

We examine two discretization schemes for solving a pair of parabolic problems with significantly different spatial and temporal scales that are coupled through a common interface: a mixed finite element method which uses a rigorous mortar element technique in both space and time for coupling and a finite volume method which employs popular ad hoc… (More)

We derive, implement, and test a posteriori error estimates for numerical methods for a non-autonomous linear system that involve iterative solution of the discrete equations. We consider two iterations: the Picard iteration and the Jacobi iteration for solving the discrete matrix-vector equations. To carry out the analysis, we define an appropriate adjoint… (More)

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