Nature

Generative discovery of partial differential equations by learning from math handbooks

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 ...
Nature

Exact solutions for nonlinear partial differential equations via a fusion of classical methods and innovative approaches

This paper presents a new approach for finding exact solutions to certain classes of nonlinear partial differential equations (NLPDEs) by combining the variation of parameters method with classical ...
Risk

Partial differential equation (PDE)

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 ...
uni

Analysis of Partial Differential Equations

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...
uni

T6: Singularities and partial differential equations

In this topic, our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular ...