According to the World Economic Forum’s Future of Jobs report, 39% of existing skill sets will be transformed or become outdated within the next five years. For universities and colleges, that raises ...

Abstract: Neural Ordinary Differential Equations (NODEs) revolutionize the way we view residual networks as solvers for initial value problems (IVPs), with layer depth serving as the time step. In ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. In chemical reaction network theory, ordinary differential equations are used to model ...

Abstract: Solving ordinary differential equations (ODEs) is vital in diverse fields. However, it is difficult to obtain the exact analytical solutions of ODEs due to their changeable mathematical ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

This study centers on incorporating memory effects (the impact of past events on current states) into mathematical models for population dynamics. It introduces a framework based on the gamma ...

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 ...

Riccati equations are a natural next step after you’ve studied linear differential equations. Linear first-order ordinary differential equations look like this: I think I finally get why they’re ...