Abstract: Analytically solving complex or large-scale differential equations is often difficult or even impossible, making numerical integration methods indispensable. However, as all numerical ...

Abstract: Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential ...

The registration is now closed. The Autumn School on Scientific Machine Learning and Numerical Methods aims to equip PhD students, postdocs, and early-career researchers with foundational and advanced ...

The Fisher–Kolmogorov–Petrovsky–Piskunov equation is a diffusive logistic model for the population density of an invasive species. This paper presents a one-level numerical simulation of the ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

This paper proposes a new deep-learning-based algorithm for high-dimensional Bermudan option pricing. To the best of our knowledge, this is the first study of the arbitrary-order discretization scheme ...

Simo Särkkä and Arno Solin (2019). Applied Stochastic Differential Equations. Cambridge University Press. Cambridge, UK. The book can be ordered through Cambridge University Press or, e.g., from ...

Learn methods for interpolation, numerical integration and derivation, and finite difference methods for differential equations. You can use these live scripts as demonstrations in lectures, class ...

This research work investigates the use of Artificial Neural Network (ANN) based on models for solving first and second order linear constant coefficient ordinary differential equations with initial ...

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 ...

More than 70 years ago, researchers at the forefront of artificial intelligence research introduced neural networks as a revolutionary way to think about how the brain works. In the human brain, ...