Physics-Informed Neural Operator (PINO) for ODEs

PINOODE(chain,
    opt,
    bounds;
    init_params = nothing,
    strategy = nothing
    kwargs...)

Algorithm for solving paramentric ordinary differential equations using a physics-informed neural operator, which is used as a solver for a parametrized ODEProblem.

Positional Arguments

• chain: A neural network architecture, defined as a AbstractLuxLayer or Flux.Chain. Flux.Chain will be converted to Lux using adapt(FromFluxAdaptor(false, false), chain)
• opt: The optimizer to train the neural network.
• bounds: A dictionary containing the bounds for the parameters of the parametric ODE.
• number_of_parameters: The number of points of train set in parameters boundaries.

Keyword Arguments

• init_params: The initial parameters of the neural network. By default, this is nothing, which thus uses the random initialization provided by the neural network library.
• strategy: The strategy for training the neural network.
• additional_loss: additional loss function added to the default one. For example, add training on data.
• kwargs: Extra keyword arguments are splatted to the Optimization.jl solve call.

References

• Sifan Wang "Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets"
• Zongyi Li "Physics-Informed Neural Operator for Learning Partial Differential Equations"