Reproducing kernel Hilbert space method is utilized in this paper as an efficient approach to solve singular fourth order ...

Data-driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data-driven techniques face the ...

Partial differential equations (PDEs) form the mathematical backbone for models in physics, engineering, biology and finance. They express relationships between the rates of change of a multivariable ...

A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...