Model_Selection

Model Selection

Lotka-Volterra

Following Chris Rackauckas' approach [1], we reimplemented the following Lotka-Volterra equations, embedding the ODE into a neural network using Julia's library DiffEqFlux.

Neural ODE 1D

Diffusion Equation: defining a 2-D reaction-diffusion equation. It describes combustion dynamics, similar to WRF-Fire equations.

• Diffusion Equation with a NN

• Diffusion Equation with a CNN

• Numerical Diffusion Equation

• Diffusion Equation NeuralBenchmark. We employ an UPDE solved based on a NN combined with a CNN.

Fisher KPP

• Fisher KPP example with CNN resolution

• Fisher KPP example with RNN resolution

Heat equation

Poisson's Equation

Burger's equation

• Burger's equation

• Burger's equation: comparison between neural and numerical approach

• Non Linear Burger's equation

References

[1] Chris Rackauckas et al (2019). DiffEqFlux.jl - A Julia Library for Neural Differential Equations