Related papers: Scattering with Neural Operators
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…
In this paper, we integrate neural networks and Gaussian wave packets to numerically solve the Schr\"odinger equation with a smooth potential near the semi-classical limit. Our focus is not only on accurately obtaining solutions when the…
Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that…
With the recent rise of neural operators, scientific machine learning offers new solutions to quantify uncertainties associated with high-fidelity numerical simulations. Traditional neural networks, such as Convolutional Neural Networks…
In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution…
Neutron and X-ray scattering represent two state-of-the-art materials characterization techniques that measure materials' structural and dynamical properties with high precision. These techniques play critical roles in understanding a wide…
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…
Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic…
We develop the analytic perturbation technique on the absolutely continuous spectrum and calculate the Scattering matrix for the Schr\"{o}dinger operator on the Quantum Network based on the Dirichlet-to Neumann map of an Intermediate…
Future quantum computers may serve as a tool to access non-perturbative real-time correlation functions. In this talk, we discuss the prospects of using these to study Compton scattering for arbitrary kinematics. The restriction to a…
In this work we approach the Schr\"odinger equation in quantum wells with arbitrary potentials, using the machine learning technique. Two neural networks with different architectures are proposed and trained using a set of potentials,…
Recent progress in AI has established neural operators as powerful tools that can predict the evolution of partial differential equations, such as the Navier-Stokes equations. Some complex problems rely on sophisticated algorithms to deal…
Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to…
In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified…
Scattering network is a convolutional network, consisting of cascading convolutions using pre-defined wavelets followed by the modulus operator. Since its introduction in 2012, the scattering network is used as one of few mathematical tools…
Data-driven, deep-learning modeling frameworks have been recently developed for forecasting time series data. Such machine learning models may be useful in multiple domains including the atmospheric and oceanic ones, and in general, the…
Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black…
With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by…
Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…
Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…