Russell (Rust Scientific Library) helps develop high-performance computations involving linear algebra, sparse linear systems, numerical mathematics (continuation), differential equations, statistics, ...

FreeFEM is a partial differential equation solver for non-linear multi-physics systems in 2D and 3D using the finite element method. Problems involving partial differential equations from several ...

Optimal control problems are pervasive across numerous disciplines, including engineering, economics, biology, and medicine, where they play a crucial role in optimizing the performance of dynamic ...

Integer linear programming can help find the answer to a variety of real-world problems. Now researchers have found a much faster way to do it. The traveling salesperson problem is one of the oldest ...

Five steps to ensure that you don’t jump to solutions by Julia Binder and Michael D. Watkins When business leaders confront complex problems, there’s a powerful impulse to dive right into “solving” ...

Physics informed neural networks (PINNs), a type of machine learning approach, can be used to find the solution of differential equations by including all of the physics into the loss function and ...

Abstract: Nowadays, there are time-critical applications involving linear equations, such as the fault reconstruction problem, where hard response time constraints and robustness to external ...

The use of diagrams can be effective in solving mathematical word problems solving. However, students worldwide do not construct diagrams unprompted or have trouble using them. In the present study, ...

Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network. PINNs have emerged ...