[1] On the solvability of a space-time fractional nonlinear Schrödinger system. Partial Differential Equations in Applied Mathematics (2024). [2] Exponential Scattering for a Damped Hartree Equation.

A collection of resources about partial differential equations, deep learning, graph neural networks, dynamic system simulation. We also roughly categorize the resources into the following categories ...

This repository is provided as a tutorial for the implementation of integration algorithms of first and second order ODEs through recurrent neural networks in Python. The first order example ...

In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one-dimensi ...

The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the state space dynamics from measurement data. Building on the ...

Hermite approximation in multiple dimensions is investigated. As an example, a spectral scheme and a pseudospectral scheme for the Logistic equation are constructed, respectively. The stability and ...

1906 Topics equation, differential, equations, solution, integral, linear, method, sin, general, arbitrary, differential equations, differential equation, general solution, partial differential, ...

This paper presents a method to compute the normal forms of differential equations whose Jacobian evaluated at an equilibrium includes a double zero or a triple zero eigenvalue. The method combines ...

Abstract Records for observing dynamics are usually complied by a form of time series. However, time series can be a challenging type of dataset for deep neural networks to learn. In deep neural ...