Related papers: Importance truncation in non-perturbative many-bod…
Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method…
The Security-Constrained Unit Commitment (SCUC) problem presents formidable computational challenges due to its combinatorial complexity, large-scale network dimensions, and numerous security constraints. While conventional temporal…
One of the premier utilities of present day noisy quantum computers is simulation of many-body quantum systems. We study how long in time is such a discrete-time simulation representative of a continuous time Hamiltonian evolution, namely,…
In the nonequilibrium Green's function approach, the approximation of the correlation self-energy at the second-Born level is of particular interest, since it allows for a maximal speed-up in computational scaling when used together with…
We consider large scale empirical risk minimization (ERM) problems, where both the problem dimension and variable size is large. In these cases, most second order methods are infeasible due to the high cost in both computing the Hessian…
The present thesis aims at studying the properties of symmetric nuclear and pure neutron matter from a Green's functions point of view, including two-body and three-body chiral forces. An extended self-consistent Green's function formalism…
High-precision predictions of nuclear properties are a central objective of ab initio nuclear structure theory. However, state-of-the-art many-body methods rely on truncated model spaces to render the nuclear many-body problem tractable,…
We establish rigorous error bounds for prime counting using a truncated Gaussian (TG) kernel in the explicit formula framework. Our main theorem proves that the approximation error remains globally below 1/2 for all sufficiently large…
The numerical computation of equilibrium reward gradients for Markov chains appears in many applications for example within the policy improvement step arising in connection with average reward stochastic dynamic programming. When the state…
We introduce Perturbative Gradient Training (PGT), a novel training paradigm that overcomes a critical limitation of physical reservoir computing: the inability to perform backpropagation due to the black-box nature of physical reservoirs.…
We review the theoretical foundations and most important physical applications of the Pinch Technique (PT). This method allows the construction of off-shell Green's functions in non-Abelian gauge theories that are independent of the…
Deep neural networks (DNNs) offer significant flexibility and robust performance. This makes them ideal for building not only system models but also advanced neural network controllers (NNCs). However, their high complexity and…
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
Classical simulation is essential in quantum algorithm development and quantum device verification. With the increasing complexity and diversity of quantum circuit structures, existing classical simulation algorithms need to be improved and…
We present the fundamental techniques and working equations of many-body Green's function theory for calculating ground state properties and the spectral strength. Green's function methods closely relate to other polynomial scaling…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
The GW approximation of many-body perturbation theory is an accurate method for computing electron addition and removal energies of molecules and solids. In a canonical implementation, however, its computational cost is $O(N^4)$ in the…
The recent trend toward increasingly deep convolutional neural networks (CNNs) leads to a higher demand of computational power and memory storage. Consequently, the deployment of CNNs in hardware has become more challenging. In this paper,…
Spiking Neural Networks (SNNs) are bio-plausible models that hold great potential for realizing energy-efficient implementations of sequential tasks on resource-constrained edge devices. However, commercial edge platforms based on standard…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…