Related papers: Stochastic Representation of Time-Evolving Neural …
Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…
Interacting spin networks are fundamental to quantum computing. Data-based tomography of time-independent spin networks has been achieved, but an open challenge is to ascertain the structures of time-dependent spin networks using time…
Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…
The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined by a hypersingular integral with a (possibly…
An exact stochastic model for the thermalisation of quantum states is proposed. The model has various physically appealing properties. The dynamics are characterised by an underlying Schrodinger evolution, together with a nonlinear term…
Starting from the 3D Gross-Pitaevskii equation we revisit the dimensional reduction to an effective one-dimensional wave-equation that describes the longitudinal dynamics of a Bose condensate in an axially-symmetric external potential.…
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing…
There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
This article proposes and analyzes explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (SPDEs) with polynomial nonlinearities such as, e.g.,…
Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and…
Simulating quantum many-body dynamics on classical computers is a challenging problem due to the exponential growth of the Hilbert space. Artificial neural networks have recently been introduced as a new tool to approximate quantum-many…
We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central…
The quantum dynamic equation (QDE) of machine learning is obtained based on Schr\"odinger equation and potential energy equivalence relationship. Through Wick rotation, the relationship between quantum dynamics and thermodynamics is also…
We develop a quantum algorithm for solving high-dimensional time-fractional heat equations. By applying the dimension extension technique from [FKW23], the $d+1$-dimensional time-fractional equation is reformulated as a local partial…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-form solution to the dynamical equation, valid for all…
Deep neural network (DNN) and auto differentiation have been widely used in computational physics to solve variational problems. When DNN is used to represent the wave function to solve quantum many-body problems using variational…
A general {\it ab-initio} and non-perturbative method to solve the time-dependent Schr\"odinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasi-one-electron or…
Nonlinear molecular excitations in DNA have traditionally been modelled using the nonlinear Schr\"odinger equation (NLSE). An alternative approach is based on the plane-base rotator model and the SU(2)/U(1) generalized spin coherent states,…