Related papers: On Representing Electronic Wave Functions with Sig…

The electronic Schr\"odinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wavefunctions, depend on 3N variables, three spatial…

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent…

Function fitting/approximation plays a fundamental role in computer graphics and other engineering applications. While recent advances have explored neural networks to address this task, these methods often rely on architectures with many…

Feed-forward neural networks are a novel class of variational wave functions for correlated many-body quantum systems. Here, we propose a specific neural network ansatz suitable for systems with real-valued wave functions. Its…

Neural functional networks (NFNs) have recently gained significant attention due to their diverse applications, ranging from predicting network generalization and network editing to classifying implicit neural representation. Previous NFN…

Electromagnetic wave propagation through complex inhomogeneous walls introduces significant distortions to through-wall radar signatures. Estimation of wall thickness, dielectric, and conductivity profiles may enable wall effects to be…

Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…

Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…

The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…

Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

Equivariant Graph Neural Networks (eGNNs) trained on density-functional theory (DFT) data can potentially perform electronic structure prediction at unprecedented scales, enabling investigation of the electronic properties of materials with…

In this paper we present a framework for the design and implementation of offset equivariant networks, that is, neural networks that preserve in their output uniform increments in the input. In a suitable color space this kind of networks…

Neural Functional Networks (NFNs) have gained increasing interest due to their wide range of applications, including extracting information from implicit representations of data, editing network weights, and evaluating policies. A key…

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of…

Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow…

A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…

In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.…

Neural networks often require large amounts of data to generalize and can be ill-suited for modeling small and noisy experimental datasets. Standard network architectures trained on scarce and noisy data will return predictions that violate…