Solving a Third Order ODE Boundary Value Problem with Soft Constraints

Problem

We will look at solving the ODE

Over \(t\in[0,1]\), with boundary values

Implementation

First import package. We will only import ode_Solvers as that is all that is needed.

import pinnde.ode_Solvers as ode_Solvers

Next, we declare our equation, order, inital values, t boundary, number of points, and epochs

eqn = "uttt - 2*utt + u"
order = 3
inits = [0, 0.93, 1, 0.7]
t_bdry = [0,1]
N_pde = 200
epochs = 1500

If we also want to change the default number of internal layers (4) and nodes (40) per layer in our PINN, we can declare them as well

layers = 6
nodes = 50

To solve, we simply call the corresponding solving function to our problem, and we will not delcare a constraint as it defaults to soft

mymodel = ode_Solvers.solveODE_BVP(eqn, order, inits, t_bdry, N_pde, epochs, 
                                        net_layers=layers, net_units=nodes)

If we want to quickly vizualize our data from training we can add after the solving function

mymodel.plot_epoch_loss()

mymodel.plot_solution_prediction()

All Code

import pinnde.ode_Solvers as ode_Solvers

eqn = "uttt - 2*utt + u"
order = 3
inits = [0, 0.93, 1, 0.7]
t_bdry = [0,1]
N_pde = 200
epochs = 1500
layers = 6
nodes = 50

mymodel = ode_Solvers.solveODE_BVP(eqn, order, inits, t_bdry, N_pde, epochs, 
                                        net_layers=layers, net_units=nodes)

mymodel.plot_epoch_loss()

mymodel.plot_solution_prediction()