3 Hermite spectral scheme for the logistic model This section is for application of the Hermite spectral approximation to the Logistic equation in two-dimensions. We construct a Hermite spectral ...

Learning data-driven discretizations for partial differential equations Code associated with the paper: Learning data-driven discretizations for partial differential equations. Yohai Bar-Sinai, ...

machine-learning neural-network ode neural-networks partial-differential-equations differential-equations ordinary-differential-equations differentialequations pde pinn scientific-machine-learning ...

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

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

In this paper, the concept of multirate partial differential equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The ...

We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy ...

University of Utah engineers encode partial differential equations in light and feed them into newly designed optical neural engine, or ONE, to accelerate machine learning.

In this paper, lump solutions of nonlinear partial differential equations, the generalized (2 + 1)-dimensional KP equation and the Jimbo–Miwa equation, are studied by using the Hirota bilinear method ...