Related papers: GridSPT: Grid-based calculation for perturbation t…
Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…
In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact…
A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
Part I of this paper discusses the problem of learning the operational structure of the grid from nodal voltage measurements. In this work (Part II), the learning of the operational radial structure is coupled with the problem of estimating…
We present a simple and intuitive approximation for solving perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
The Laplacian appears in several partial differential equations used to model wave propagation. Summation-by-parts--simultaneous approximation term (SBP-SAT) finite difference methods are often used for such equations, as they combine…
We present a novel and flexible data-driven framework for estimating the response of higher-order moments of nonlinear stochastic systems to small external perturbations. The classical Generalized Fluctuation--Dissipation Theorem (GFDT)…
The thermal physics of a massless scalar field with a phi^4 interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the lagrangian.…
We introduce an algorithm that can be used to perform stochastic perturbation theory (sPT) to correct any non-linearly parametrized wavefunction that can be optimized using orbital space Variational Monte Carlo (VMC). Although the…
The reliable operation of modern power grids requires probabilistic load forecasts with well-calibrated uncertainty estimates. However, existing deep learning models produce overconfident point predictions that fail catastrophically under…
This article investigates the performance of grid computing systems whose interconnections are given by random and scale-free complex network models. Regular networks, which are common in parallel computing architectures, are also used as a…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize…
Graph generation is an important area in network science. Traditional approaches focus on replicating specific properties of real-world graphs, such as small diameters or power-law degree distributions. Recent advancements in deep learning,…
Many important problems require modelling large-scale spatio-temporal datasets, with one prevalent example being weather forecasting. Recently, transformer-based approaches have shown great promise in a range of weather forecasting…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
The consistency relations in large scale structure relate the lower-order correlation functions with their higher-order counterparts. They are direct outcome of the underlying symmetries of a dynamical system and can be tested using data…
Stochastic resonance (SR) - a counter-intuitive phenomenon in which the signal due to a weak periodic force in a nonlinear system can be {\it enhanced} by the addition of external noise - is reviewed. A theoretical approach based on linear…