It’s July 20, 1969. Neil Armstrong and Buzz Aldrin are about to land on the moon. They will be the first humans to set foot on Earth’s only natural satellite. Suddenly, the onboard computer flashes: ...

Abstract: Data plays a pivotal role in the groundbreaking advancements in artificial intelligence. The quantitative analysis of data significantly contributes to model training, enhancing both the ...

Nearly 200 years ago, the physicists Claude-Louis Navier and George Gabriel Stokes put the finishing touches on a set of equations that describe how fluids swirl. And for nearly 200 years, 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 ...

The control of general nonlinear systems is a challenging task in particular for large-scale models as they occur in the semi-discretization of partial differential equations (PDEs) of, say, fluid ...

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 ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

In many physical systems, the governing equations are known with high confidence, but direct numerical solution is prohibitively expensive. Often this situation is alleviated by writing effective ...

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 ...