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The many-body Green's function provides access to electronic properties beyond density functional theory level in ab inito calculations. In this manuscript, we propose a deep learning framework for predicting the finite-temperature Green's…

Chemical Physics · Physics 2024-02-20 Xinyang Dong , Emanuel Gull , Lei Wang

Neural operators are a popular technique in scientific machine learning to learn a mathematical model of the behavior of unknown physical systems from data. Neural operators are especially useful to learn solution operators associated with…

Numerical Analysis · Mathematics 2022-08-05 Nicolas Boullé , Seick Kim , Tianyi Shi , Alex Townsend

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning…

Numerical Analysis · Mathematics 2025-11-21 Wenrui Hao , Rui Peng Li , Yuanzhe Xi , Tianshi Xu , Yahong Yang

We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from…

Machine Learning · Computer Science 2018-06-20 Subham S. Sahoo , Christoph H. Lampert , Georg Martius

Learning the Green's function using deep learning models enables to solve different classes of partial differential equations. A practical limitation of using deep learning for the Green's function is the repeated computationally expensive…

Machine Learning · Computer Science 2023-08-02 Kishan Wimalawarne , Taiji Suzuki , Sophie Langer

Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in physics. The prior knowledge for specific physical systems routinely offers essential regularization schemes for solving the ill-posed…

Computational Physics · Physics 2021-12-14 Lingxiao Wang , Shuzhe Shi , Kai Zhou

We seek to improve the data efficiency of neural networks and present novel implementations of parameterized piece-wise polynomial activation functions. The parameters are the y-coordinates of n+1 Chebyshev nodes per hidden unit and…

Machine Learning · Computer Science 2019-06-25 Yuchen Li , Frank Rudzicz , Jekaterina Novikova

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

Classical Analysis and ODEs · Mathematics 2012-05-11 Yu. A. Konyaev

We propose a highly efficient numerical method to describe inhomogeneous superconductivity by using the kernel polynomial method in order to calculate the Green's functions of a superconductor. Broken translational invariance of any type…

Superconductivity · Physics 2010-10-13 L. Covaci , F. M. Peeters , M. Berciu

A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…

Materials Science · Physics 2007-05-23 R. Takayama , T. Hoshi , T. Sogabe , S. -L. Zhang , T. Fujiwara

In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural…

Machine Learning · Computer Science 2016-10-11 Georg Martius , Christoph H. Lampert

Causal learning from data has received much attention recently. Bayesian networks can be used to capture causal relationships. There, one recovers a weighted directed acyclic graph in which random variables are represented by vertices, and…

Machine Learning · Computer Science 2026-01-06 Pavel Rytir , Ales Wodecki , Georgios Korpas , Jakub Marecek

The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…

Mesoscale and Nanoscale Physics · Physics 2016-10-14 Mariana M. Odashima , Beatriz G. Prado , E. Vernek

In this paper, we propose symbolic decision trees as surrogate models for approximating model predictive control laws. The proposed approach learns simultaneously the partition of the input domain (splitting logic) as well as local…

Systems and Control · Electrical Eng. & Systems 2025-10-14 Ilias Mitrai

Integral equation methods provide an effective framework for solving partial differential equations, but their applicability typically relies on the availability of explicit free-space Green's functions. For coupled systems arising in…

Analysis of PDEs · Mathematics 2026-04-14 Fredrik Fryklund

I review the application of self-consistent Green's functions methods to study the properties of infinite nuclear systems. Improvements over the last decade, including the consistent treatment of three-nucleon forces and the development of…

Nuclear Theory · Physics 2020-06-19 A. Rios

The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…

Chemical Physics · Physics 2016-11-15 Alexei A. Kananenka , Alicia Rae Welden , Tran Nguyen Lan , Emanuel Gull , Dominika Zgid

A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…

Machine Learning · Statistics 2023-02-10 Tapas Tripura , Souvik Chakraborty

We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems…

Rings and Algebras · Mathematics 2023-08-11 Markus Rosenkranz , Nitin Serwa

The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on…

Strongly Correlated Electrons · Physics 2024-09-24 Dominik Kiese , Anxiang Ge , Nepomuk Ritz , Jan von Delft , Nils Wentzell