7 papers
Mitigating Numerical Stiffness in Least-Squares Formulations of Elliptic PDEs for Physics-Informed Neural Networks
Phil-Alexander Hofmann, Michael Hecht
We present theoretical insights into residual loss formulations of physics-informed neural networks (PINNs) for learning solutions of partial differential equations (PDEs)…
Accelerating Multivariate Newton Interpolation in Downward Closed Polynomial Spaces
Phil-Alexander Hofmann, Michael Hecht
We introduce the fast Newton transform (FNT), a multivariate Newton interpolation algorithm for downward closed polynomial spaces in quasi-tensorial grids. The FNT computes the New…
Discovering a well-conditioned analytic continuation problem via dictionary learning
Thomas Chuna, Phil-Alexander Hofmann, Alexander Benedix-Robles +1
Many fields of physics use quantum Monte Carlo (QMC) simulations to simulate quantum systems in imaginary-time and estimate imaginary-time correlation functions (ITCF). Howeve…
Interpolation in Polynomial Spaces of p-Degree
Phil-Alexander Hofmann, Damar Wicaksono, Michael Hecht
We recently introduced the Fast Newton Transform (FNT), an hierarchical algorithm for performing multivariate Newton interpolation in arbitrary downward closed polynomial spaces of…
Second roton feature in the strongly coupled electron liquid
Thomas M. Chuna, Jan Vorberger, Panagiotis Tolias +5
We present extensive \emph{ab initio} path integral Monte Carlo (PIMC) results for the dynamic properties of the finite temperature uniform electron gas (UEG) over a broad range of…
PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods
Alexander Benedix Robles, Phil-Alexander Hofmann, Thomas Chuna +2
Path integral Monte Carlo (PIMC) simulations are a cornerstone for studying quantum many-body systems. The analytic continuation (AC) needed to estimate dynamic quantities from the…