相关论文: Augmentation of Universal Potentials for Broad App…

We study the Dirichlet problem for the stationary Schr\"odinger fractional Laplacian equation $(-\Delta)^s u + V u = f$ posed in bounded domain $ \Omega \subset \mathbb R^n$ with zero outside conditions. We consider general nonnegative…

Atomistic simulations often rely on interatomic potentials to access greater time- and length- scales than those accessible to first principles methods such as density functional theory (DFT). However, since a parameterised potential…

It is important in many applications to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of the paper is to provide an elementary…

The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…

Universal machine learning force fields (UMLFFs) promise to revolutionize materials science by enabling rapid atomistic simulations across the periodic table. However, their evaluation has been limited to computational benchmarks that may…

This paper integrates deep neural networks (DNNs) into structural economic models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic structure and machine learning are complements in empirical…

The widespread usage of high-definition screens on edge devices stimulates a strong demand for efficient image restoration algorithms. The way of caching deep learning models in a look-up table (LUT) is recently introduced to respond to…

We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational…

A relation between the deformed Hulth\'en potential and the Eckart one is used to write the bound-state wavefunctions of the former in terms of Jacobi polynomials and to calculate their normalization coefficients. The shape invariance…

Surface phenomena are increasingly becoming important in exploring nanoscale materials growth and characterization. Consequently, the need for atomistic based simulations is increasing. Nevertheless, relying entirely on quantum mechanical…

This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are…

DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite dimensional Banach spaces. We analyze DeepONets and prove estimates on the resulting approximation and generalization errors. In…

Dimensional analysis, superposition principle, and continuity of electric potential are used to study electric potential of a uniformly charged square sheet at its plane. It is shown that knowing the electric potential on the diagonal and…

Conventional hypernetworks are typically engineered around a specific base-model parameterization, so changing the target architecture often entails redesigning the hypernetwork and retraining it from scratch. We introduce the…

Learning to learn is a powerful paradigm for enabling models to learn from data more effectively and efficiently. A popular approach to meta-learning is to train a recurrent model to read in a training dataset as input and output the…

The low-index surfaces of Au and Pt all tend to reconstruct, a fact that is of key importance in many nanostructure, catalytic, and electrochemical applications. Remarkably, some significant questions regarding their structural energies…

Machine learned chemical potentials have shown great promise as alternatives to conventional computational chemistry methods to represent the potential energy of a given atomic or molecular system as a function of its geometry. However,…

The Earth's subsurface is a cornerstone of modern society, providing essential energy resources like hydrocarbons, geothermal, and minerals while serving as the primary reservoir for $CO_2$ sequestration. However, full physics numerical…

Deep structured-prediction energy-based models combine the expressive power of learned representations and the ability of embedding knowledge about the task at hand into the system. A common way to learn parameters of such models consists…

The success of deep neural networks (DNNs) is attributable to three factors: increased compute capacity, more complex models, and more data. These factors, however, are not always present, especially for edge applications such as autonomous…