pinnr: Physics-Informed Neural Networks in Native R

pinnr trains neural networks whose outputs satisfy a differential equation. A network \(u_\theta(x)\) is fitted by minimising a weighted sum of

• the mean squared equation residual at collocation points inside the domain,

• the mean squared violation of boundary and initial conditions, and

• the mean squared misfit to observed data, when data are supplied.

Details

Unknown constants in the equation can be estimated jointly with the network weights, which turns the same machinery into a tool for parameter discovery (an inverse problem).

The main entry points are:

• pinn_ode() builds a problem from a deSolve-style derivative function.

• pinn_problem() builds a problem for any partial differential equation on a rectangular domain defined with pinn_domain(), with conditions from pinn_dirichlet(), pinn_neumann(), pinn_initial() and pinn_condition().

• pinn_fit() trains the network.

• predict(), coef(), residuals() and plot() inspect the result.

References

Raissi, M., Perdikaris, P. and Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707. doi:10.1016/j.jcp.2018.10.045

See also

Useful links:

• https://github.com/Obasanmii/pinnr

• Report bugs at https://github.com/Obasanmii/pinnr/issues

Author

Maintainer: Samson Obasanmi obasanmisamson722@gmail.com (ORCID)

Authors:

• Samson Obasanmi obasanmisamson722@gmail.com (ORCID)