7 papers
CATAPULT: A CUDA-Accelerated Timestepper for Alpha Particles Using Local Tricubics
Michael Czekanski, Alexey R. Knyazev, David Bindel +1
We introduce a CUDA-Accelerated Timestepper for Alpha Particles Using Local Tricubics (CATAPULT) for use in Monte Carlo calculations of alpha particle confinement in stellarators.…
Stochastic Poisson Surface Reconstruction with One Solve using Geometric Gaussian Processes
Sidhanth Holalkere, David S. Bindel, Silvia Sellán +1
Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface informati…
The High-Order Magnetic Near-Axis Expansion: Ill-Posedness and Regularization
Maximilian Ruth, Rogerio Jorge, David Bindel
When analyzing stellarator configurations, it is common to perform an asymptotic expansion about the magnetic axis. This so-called near-axis expansion is convenient for the same re…
Differentiating Policies for Non-Myopic Bayesian Optimization
Darian Nwankwo, David Bindel
Bayesian optimization (BO) methods choose sample points by optimizing an acquisition function derived from a statistical model of the objective. These acquisition functions are cho…
Walking on Spheres and Talking to Neighbors: Variance Reduction for Laplace's Equation
Michael Czekanski, Benjamin Faber, Margaret Fairborn +2
Walk on Spheres algorithms leverage properties of Brownian Motion to create Monte Carlo estimates of solutions to a class of elliptic partial differential equations. We propose a n…
Finding Birkhoff Averages via Adaptive Filtering
Maximilian Ruth, David Bindel
In many applications, one is interested in classifying trajectories of Hamiltonian systems as invariant tori, islands, or chaos. The convergence rate of ergodic Birkhoff averages c…
Level Set Learning for Poincaré Plots of Symplectic Maps
Maximilian Ruth, David Bindel
Many important qualities of plasma confinement devices can be determined via the Poincaré plot of a symplectic return map. These qualities include the locations of periodic orbits,…