Related papers: On the basis-set extrapolation
The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the…
Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their…
This contribution introduces a novel signal extrapolation algorithm and its application to image error concealment. The signal extrapolation is carried out by iteratively generating a model of the signal suffering from distortion. Thereby,…
Stretched exponential relaxation of a quantity n versus time t according to n = n_0 exp[-(lambda* t)^beta] is ubiquitous in many research fields, where lambda* is a characteristic relaxation rate and the stretching exponent beta is in the…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…
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…
We present a method to extrapolate nuclear binding energies from known values for neighbouring nuclei. We select four specific mass relations constructed to eliminate smooth variation of the binding energy as function nucleon numbers. The…
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…
This work presents a general framework for the operationally driven optimal siting and sizing of battery energy storage systems in power transmission networks, aimed at enhancing their resource adequacy. The approach considers multi-period…
Ensembling is commonly used in machine learning on tabular data to boost predictive performance and robustness, but larger ensembles often lead to increased hardware demand. We introduce HAPEns, a post-hoc ensembling method that explicitly…
There has been a veritable explosion of methods and software to perform machine-learned regression on datasets of electronic energies and forces to develop high-dimensional machine learned potential energy surfaces (ML-PESs). A major, but…
A fundamental roadblock to the exact numerical solution of many-fermion problems is the exponential growth of the Hilbert space with system size. It manifests as extreme dynamical memory and computation-time requirements for simulating…
The emergence of abundant electricity time series (ETS) data provides ample opportunities for various applications in the power systems, including demand-side management, grid stability, and consumer behavior analysis. Deep learning models…
A new nine-dimensional potential energy surface (PES) for methane has been generated using state-of-the-art \textit{ab initio} theory. The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete…
Calculating dipole moments with high-order basis sets is generally only possible for the light molecules, such as water. A simple, yet highly effective strategy of obtaining high-order dipoles with small, computationally less expensive…
We propose a novel exemplar selection approach based on Principal Component Analysis (PCA) and median sampling, and a neural network training regime in the setting of class-incremental learning. This approach avoids the pitfalls due to…
In many applications of machine learning, certain categories of examples may be underrepresented in the training data, causing systems to underperform on such "few-shot" cases at test time. A common remedy is to perform data augmentation,…
A simple relaxation function I(t/tauzero; alpha, beta) unifying the stretched exponential with the compressed hyperbola is obtained, and its properties studied. The scaling parameter tauzero has dimensions of time, whereas the…
Attaining a reliable complete basis set (CBS) limit remains a significant challenge in ab initio correlated electronic-structure calculations. Building on our previous work for atoms and diatomic molecules, we present a finite-element (FE)…