Physics

Using a non-commutative analogue of the isomonodromic problem associated with the discrete first Painlev\'e hierarchy, we construct a non-commutative version of this hierarchy, denoted by $\text{d-PI}_m^{\text{nc}}$. We show that both…

We present a comprehensive benchmarking dataset and empirical scaling law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many body target wavefunctions. The dataset, WF-Bench, spans multiple distinct…

We present MARUT, a scalable multi-GPU computational fluid dynamics (CFD) framework designed for high-fidelity simulations of compressible flows spanning subsonic to hypersonic regimes, including chemically reacting nonequilibrium flows…

This paper presents a deep learning strategy to simultaneously solve Partial Differential Equations (PDEs) and back-calculate their parameters in the context of deep tunnel excavation. A Physics-Informed Neural Network (PINN) model is…

In this paper, we establishes a connection between noncommutative Laurent biorthogonal polynomials (bi-OPs) and matrix discrete Painlev\'e (dP) equations. We first apply nonisospectral deformations to noncommutative Laurent bi-OPs to obtain…

The GW plus Bethe-Salpeter equation (GW-BSE) formalism is a well-established approach for calculating excitation energies and optical spectra of molecules, nanostructures, and crystalline materials. We implement GW-BSE in the CP2K code and…

Given the urgency to reduce fossil fuel energy production to make climate tipping points less likely, we call for resource-aware knowledge gain in the research areas on Universe and Matter with emphasis on the digital transformation. A…

We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN…

High-temperature superconducting (HTS) coated conductors (CCs) can be wound into no-insulation (NI) coils, in which electrical current can partially bypass local normal zones via turn-to-turn contact layers (T2TCLs). Accurate…

In this paper, by considering two non-isospectral problems with matrices chosen on the color Lie algebra $\mathfrak{sp}_{1}(6)$, we construct (1+1)-dimensional and (2+1)-dimensional super integrable systems on $\mathfrak{sp}_{1}(6)$.…

The optimization of energy group structures is integral to ensure the accuracy of multigroup neutron transport calculations. This works introduces the use of reinforcement learning (RL) with surrogate modeling to optimize the group…

We provide necessary and sufficient conditions for maps that satisfy associative-like conditions on families of n-ary magmas to be pentagon maps. We obtain parametric-pentagon maps and we propose a procedure that generates families of…

Coarse graining (CG) is an important task for efficient modeling and simulation of complex multi-scale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general…

In this paper, we investigate two non-isospectral problems on the loop algebra of the Lie superalgebra osp(1,6), and construct two super-integrable systems and their super Hamiltonian structure using the supertrace identity. The resulting…

Proton computed tomography (pCT) aims to facilitate precise dose planning for hadron therapy, a promising and effective method for cancer treatment. Hadron therapy utilizes protons and heavy ions to deliver well focused doses of radiation,…

Two integrable systems are constructed in a 2 + 1-dimensional space. Every of these systems involve two evolutions with negative numbers.

Harmonic vibrational entropy is a key finite-temperature contribution to defect thermodynamics, but direct evaluation by dense Hessian diagonalization scales cubically with atom count and is too costly for supercell convergence,…

Classical Proper Orthogonal Decomposition (POD)-based Galerkin projection models of chaotic flows typically require a large number of modes as well as stabilization or closure terms to achieve adequate accuracy and long-term stability. We…

This paper presents a matrix formulation of the scalar laws of radiative transfer. The method applies to coupled mixed boundary condition problems on general domains. Participating media can range from transparent to absorbing, emitting,…

Spurious numerical mixing is a frequent phenomenon in ocean models. In this paper, we present an efficient and robust methodology that defines the vertical grid motion so that this mixing is reduced. This motion is defined as the solution…