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In this study, we explore the potential of machine learning for modeling molecular electronic spectral intensities as a continuous function in a given wavelength range. Since presently available chemical space datasets provide excitation…

This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…

Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier…

Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the…

The role of numerical accuracy in training and evaluating neural network-based potential energy surfaces is examined for different experimental observables. For observables that require third- and fourth-order derivatives of the total…

From a structural point of view, plasmonic nanoparticles are always at least two-layer structures with a dielectric layer of stabilizing, targeting, fluorescent, Raman, or other functional molecules. To optimize the optical properties of…

We introduce Sprecher Networks (SNs), a family of trainable architectures derived from David Sprecher's 1965 constructive form of the Kolmogorov-Arnold representation. Each SN block implements a "sum of shifted univariate functions" using…

Vibrational spectroscopy is a key technique to elucidate microscopic structure and dynamics. Without the aid of theoretical approaches, it is however, often difficult to understand such spectra at a microscopic level. Ab initio molecular…

We examine the necessary and sufficient complexity of neural networks to approximate functions from different smoothness spaces under the restriction of encodable network weights. Based on an entropy argument, we start by proving lower…

We present a deep learning approach to estimation of the bead parameters in welding tasks. Our model is based on a four-hidden-layer neural network architecture. More specifically, the first three hidden layers of this architecture utilize…

We investigate whether a neural network approach can reproduce and predict the electron-nucleus cross sections in the kinematical domain of present and future accelerator-based neutrino oscillation experiments. For this purpose, we consider…

Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…

Sidescan sonar intensity encodes information about the changes of surface normal of the seabed. However, other factors such as seabed geometry as well as its material composition also affect the return intensity. One can model these…

In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the…

In this article, we study approximation properties of the variation spaces corresponding to shallow neural networks with a variety of activation functions. We introduce two main tools for estimating the metric entropy, approximation rates,…

Rapid advancements in machine-learning methods have led to the emergence of machine-learning-based interatomic potentials as a new cutting-edge tool for simulating large systems with ab initio accuracy. Still, the community awaits universal…

We present design and implementation of a novel neural network potential (NNP) and its combination with an electrostatic embedding scheme, commonly used within the context of hybrid quantum-mechanical/molecular-mechanical (QM/MM)…

Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks,…

Computational screening for new and improved catalyst materials relies on accurate and low-cost predictions of key parameters such as adsorption energies. Here, we use recently developed compressed sensing methods to identify descriptors…

We prove a semiclassical resolvent estimate for a broad class of non-self-adjoint, non-elliptic pseudodifferential operators in the low-lying spectral regime. The proof relies on improved ellipticity properties for the symbol of the…