169 citations · 837 across the 31 of their papers we have counts for
Showing 2018Show all
3 papers · 1 filter
stat.ML2018★ 1 cited
Importance of the Mathematical Foundations of Machine Learning Methods for Scientific and Engineering Applications
Paul J. Atzberger
There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes a…
math.NA2018★ 3 cited
Stochastic Discontinuous Galerkin Methods (SDGM) Based on Fluctuation-Dissipation Balance
Will Pazner, Nathaniel Trask, Paul J. Atzberger
We introduce a general framework for approximating parabolic Stochastic Partial Differential Equations (SPDEs) based on fluctuation-dissipation balance. Using this approach we form…
cond-mat.soft2018★ 54 cited
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
Ben J. Gross, Paul J. Atzberger
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve nu…