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Six $3 Million Prizes Awarded for Outstanding Discoveries in Life Sciences, Fundamental Physics and Mathematics ...

GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that ...

Abstract: Due to the problem that local binary fitting model is easy to fall into local extremum, based on the hypothesis that the brightness of the image on both sides of the target boundary has ...

Physics-aware machine learning integrates domain-specific physical knowledge into machine learning models, leading to the development of physics-informed neural networks (PINNs). PINNs embed physical ...

This repository allows you to solve forward and inverse problems related to partial differential equations (PDEs) using finite basis physics-informed neural networks (FBPINNs). To improve the ...

Abstract: Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), ...

Researchers have made a breakthrough in the ability to solve engineering problems. In a new paper published in Nature entitled, “A scalable framework for learning the geometry-dependent solution ...

ABSTRACT: This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. As soon as an appropriate mathematical model is developed, it can ...

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 ...