Solving Differential Equations Using Neural Network Solution Bundles

Understand

The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions.

• Most standard approaches numerically integrate ODEs producing a single solution whose values are computed at discrete times.
• When many varied solutions with different initial conditions to the ODE are required, the computational cost can become significant.
• We propose that a neural network be used as a solution bundle, a collection of solutions to an ODE for various initial states and system parameters.