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The interpolation of high-dimensional potential energy surfaces (PESs) is commonly done with physically-inspired deep-neural network models. In this work, we illustrate that Gaussian Processes (GPs) are also capable of interpolating…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Potential Energy Surfaces (PESs) are an indispensable tool to investigate, characterise and understand chemical and biological systems in the gas and condensed phases. Advances in Machine Learning (ML) methodologies have led to the…
Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the…
We investigate the endofullerene system Ne@C$_{70}$, by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. We compare a plethora of electronic structure methods including:…
Physics-based Ising machines (IM) have been developed as dedicated processors for solving hard combinatorial optimization problems with higher speed and better energy efficiency. Generally, such systems employ local search heuristics to…
Impedance controllers are popularly used in the field of lower limb prostheses and exoskeleton development. Such controllers assume the joint to be a spring-damper system described by a discrete set of equilibria and impedance parameters.…
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
Perfect Electric Conductors (PECs) are imaged integrating the subspace-based optimizationmethod (SOM) within the iterative multi-scaling scheme (IMSA). Without a-priori information on the number or/and the locations of the scatterers and…
Classical intermolecular potentials typically require an extensive parametrization procedure for any new compound considered. To do away with prior parametrization, we propose a combination of physics-based potentials with machine learning…
Using machine learning (ML) to construct interatomic interactions and thus potential energy surface (PES) has become a common strategy for materials design and simulations. However, those current models of machine learning interatomic…
Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual…
For robust visual-inertial SLAM in perceptually-challenging indoor environments,recent studies exploit line features to extract descriptive information about scene structure to deal with the degeneracy of point features. But existing…
The accurate and efficient evaluation of potentials is of great importance for the numerical solution of partial differential equations. When the integration domain of the potential is irregular and is discretized by an unstructured mesh,…
The combination of a recently proposed linear interpolation method (LIM) [Senjean et al., Phys. Rev. A 92, 012518 (2015)], which enables the calculation of weight-independent excitation energies in range-separated ensemble…
This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half $\mathbb{R}^n$ plane, where fundamental solutions satisfy Laplace's equation, and the…
In this paper, we conduct a systematic numerical analysis of the spectral properties of the collocation and mass matrices in the isogeometric least-squares collocation method (IGA-L), for the approximation of the Poisson problem with…
The past decade has witnessed a spectacular development of machine-learned interatomic potentials (MLIPs), to the extent that they are already the approach of choice for most atomistic simulation studies not requiring an explicit treatment…