More information: Yingheng Tang et al, Optical neural engine for solving scientific partial differential equations, Nature Communications (2025). DOI: 10.1038/s41467-025-59847-3 ...

Course content The course provides an introduction to the theoretical basis for linear partial differential equations, focusing on elliptic equations and eigenvalue problems. The techniques and ...

Code associated with the paper: Learning data-driven discretizations for partial differential equations. Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey, Michael P. Brenner. Proceedings of the National ...

Books Received Published: 11 June 1932 Partial Differential Equations of Mathematical Physics E. T. WHITTAKER Nature 129, 850–851 (1932) Cite this article ...

Course content The course provides a thorough introduction to design, analysis (both theoretical and empirical), and programming of difference and elemental methods to solve differential equations. In ...

Introduction to analytical and numerical methods for finding solutions to differential equations involving two or more independent variables. Topics include linear partial differential equations, ...

We construct global-in-time solutions for semilinear parabolic rough partial differential equations. We work on a scale of Banach spaces tailored to the controlled rough path approach and derive ...

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

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

The book is devoted to boundary value problems for general partial differential equations. Efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of ...

Hannah Cairo has solved the so-called Mizohata-Takeuchi conjecture, a problem in harmonic analysis closely linked to other ...

Abstract This paper presents a single variable new first-order shear deformation plate theory with only one fourth-order partial governing differential equation. It may be noted that, first-order ...