1 citations · 1 across the 9 of their papers we have counts for
9 papers
Analysis of the Ill-Conditioning of the Discrete Inverse Laplace transform in Monte Carlo Simulations of Quantum Many-Body Systems
Phil-Alexander Hofmann, Thomas Chuna, Tobias Dornheim +1
Analytic continuation of imaginary-time quantum Monte Carlo data to real-frequency spectra requires the inversion of a severely ill-posed two-sided Laplace transform and arises nat…
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)…
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). However…
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…
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…
Multivariate Newton Interpolation in Downward Closed Spaces Reaches the Optimal Geometric Approximation Rates for Bos--Levenberg--Trefethen Functions
Michael Hecht, Phil-Alexander Hofmann, Damar Wicaksono +5
We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runti…
Learning Partial Differential Equations by Spectral Approximates of General Sobolev Spaces
Juan-Esteban Suarez Cardona, Phil-Alexander Hofmann, Michael Hecht
We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we real…