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 ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

Maths Class 12 Differential Equations MCQs: The Central Board of Secondary Education conducts the annual board exams for class 12, which are considered among the most important for students. The ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Runge-Kutta methods applied to stiff systems in singular perturbation form are shown to give accurate approximations of phase portraits near hyperbolic stationary points. Over arbitrarily long time ...

The use of neural networks to approximate optimal control variates is proposed in order to reduce the variance of Monte Carlo simulations for stochastic differential equations driven by Brownian ...

It can take years for humans to solve complex scientific problems. With AI, it can take a fraction of the time. Subscribe to our newsletter for the latest sci-tech news updates. Dr. Shuiwang Ji, a ...