Physics-Informed Neural Networks in Native R with torch • pinnr

Physics-informed neural networks in native R.

pinnr trains neural networks that satisfy differential equations. Use it to solve ordinary and partial differential equations, or to estimate the unknown parameters of a model from observations. It runs on R’s torch, with no Python dependency, and it accepts ODE models written for deSolve without changes.

Why pinnr?

R has excellent classical solvers for differential equations, but physics-informed neural networks have so far required Python libraries such as DeepXDE, or R packages built for a single application. pinnr provides a general, R-native interface:

Use your deSolve models directly. pinn_ode() takes the same function(t, y, parms) you already wrote.
Estimate parameters from data. List unknown constants and supply observations; they are learned with the network. States can be partly observed, at different times, with missing values.
Write PDEs as R functions. Residuals are plain functions with arguments matched by name, and d(u, x, x) for derivatives.
Conditions for real problems. Dirichlet, Neumann, initial and custom (Robin, periodic, …) conditions, plus exact “hard” constraints through output transforms.
Practical training. Adam followed by optional L-BFGS, Latin hypercube sampling with resampling, time marching for long ODE horizons, GPU support, reproducible seeds, and stopping early with Esc without losing the model.

Installation

Install the pre-built package from R-universe:

install.packages("pinnr", repos = c("https://obasanmii.r-universe.dev",
                                    "https://cloud.r-project.org"))
torch::install_torch()   # once, if you have not used torch before

or the development version from GitHub:

# install.packages("remotes")
remotes::install_github("Obasanmii/pinnr")

On Intel Macs running macOS 14 or older, torch 0.17.0 cannot load its backend (its Intel build of LibTorch requires macOS 15). Install torch 0.16.3 instead, then run torch::install_torch().

Example: estimating epidemic parameters

library(pinnr)

sir <- function(t, y, parms) {
  with(as.list(c(y, parms)), {
    dS <- -beta * S * I
    dI <- beta * S * I - gamma * I
    dR <- gamma * I
    list(c(dS, dI, dR))
  })
}
y0 <- c(S = 0.99, I = 0.01, R = 0)

# simulate observations of I and R with deSolve
ref <- as.data.frame(deSolve::ode(y0, 0:100, sir, c(beta = 0.3, gamma = 0.1)))
obs <- ref[ref$time %% 5 == 0, c("time", "I", "R")]

prob <- pinn_ode(sir, y0 = y0, times = 0:100,
                 unknown = c(beta = 0.5, gamma = 0.2), data = obs)
fit <- pinn_fit(prob, epochs = 5000, seed = 1)
coef(fit)
#>  beta gamma
#> ~0.30 ~0.10

Example: the heat equation

heat <- pinn_problem(
  domain = pinn_domain(x = c(0, 1), t = c(0, 1)),
  outputs = "u",
  residual = function(u, x, t, a, d) d(u, t) - a * d(u, x, x),
  conditions = list(
    pinn_initial(function(x) sin(pi * x), time = "t"),
    pinn_dirichlet(where = list(x = "both"), value = 0)
  ),
  parms = list(a = 0.1)
)
fit <- pinn_fit(heat, epochs = 5000)
plot(fit, type = "solution")

See vignette("pinnr") or the website for a full walkthrough.

Main functions

Function	Purpose
`pinn_ode()`	Problem from a `deSolve`-style ODE model
`pinn_problem()`, `pinn_domain()`	General PDE problem on a rectangular domain
`pinn_dirichlet()`, `pinn_neumann()`, `pinn_initial()`, `pinn_condition()`	Conditions
`pinn_fit()`	Train the network
`predict()`, `residuals()`, `coef()`, `plot()`, `summary()`	Inspect a fit
`pinn_save()`, `pinn_load()`	Store fits on disk

Limitations

pinnr is young. Domains are rectangles (time intervals, lines, boxes), residuals must use tensor-friendly operations, and, as with all PINNs, training is slower than a classical solver for problems those solvers handle well. PINNs are most useful for inverse problems, sparse or noisy data, and settings where a smooth, differentiable surrogate is helpful.

Contributing

Bug reports and pull requests are welcome; see CONTRIBUTING.md. Please open an issue to discuss larger changes first.

Citation

If you use pinnr in your work, please cite it; see citation("pinnr") or CITATION.cff. The method is from Raissi, Perdikaris and Karniadakis (2019), Journal of Computational Physics 378, 686-707, https://doi.org/10.1016/j.jcp.2018.10.045.