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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…