Related papers: A framework for large-scale relativistic simulatio…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
The analytic characterization of the high-dimensional behavior of optimization for Generalized Linear Models (GLMs) with Gaussian data has been a central focus in statistics and probability in recent years. While convex cases, such as the…
Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows a standard…
Sample efficiency in Reinforcement Learning (RL) has traditionally been driven by algorithmic enhancements. In this work, we demonstrate that scaling can also lead to substantial improvements. We conduct a thorough investigation into the…
Einstein's field equation of General Relativity (GR) has been known for over 100 years, yet it remains challenging to solve analytically in strongly relativistic regimes, particularly where there is a lack of a priori symmetry. Numerical…
Equation discovery is aimed at directly extracting physical laws from data and has emerged as a pivotal research domain. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require the design of…
The modified Langevin noise formalism has been proposed for the correct charaterization of quantum electromagnetic fields in the presence of finite-sized lossy dielectric objects in free space. The main modification to the original one…
We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type…
Quantizing large language models has become a standard way to reduce their memory and computational costs. Typically, existing methods focus on breaking down the problem into individual layer-wise sub-problems, and minimizing per-layer…
We perform a canonical analysis of the Holst model for General Relativity, within the framework laid out in arXiv:2401.07307 and arXiv:2010.07725, distinguishing our approach by setting the Barbero parameter to $\beta=0$ and leaving the…
All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the model formulations, both nonlinear eigenvalue problem and…
Although exploratory landscape analysis (ELA) has shown its effectiveness in various applications, most previous studies focused only on low- and moderate-dimensional problems. Thus, little is known about the scalability of the ELA approach…
Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…
In the Entropic Dynamics (ED) framework quantum theory is derived as an application of entropic methods of inference. The physics is introduced through appropriate choices of variables and of constraints that codify the relevant physical…
The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
We describe a numerical framework that uses random sampling to efficiently capture low-rank local solution spaces of multiscale PDE problems arising in domain decomposition. In contrast to existing techniques, our method does not rely on…
We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
We derive a formalism of numerical relativity for higher-dimensional spacetimes and develop numerical codes for simulating a wide variety of five-dimensional (5D) spacetimes for the first time. First, the Baumgarte-Shapiro-Shibata-Nakamura…