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Fit a 1-D Fourier Neural Operator for depth-profile operators

Source: R/pilar8_neural_operators.R
no_fno_fit.Rd

Learns the solution map u(z) -> y(z) from a collection of (covariate trajectory, target profile) pairs. The trained operator predicts the depth profile at new sites without re-fitting.

Usage

no_fno_fit(
  depths,
  targets,
  covariates,
  n_modes = 4L,
  width = 8L,
  n_blocks = 2L,
  epochs = 200L,
  lr = 0.01,
  seed = NULL,
  backend = c("r", "torch"),
  device = c("cpu", "mps", "cuda")
)

Arguments

depths

Numeric vector of depths (common grid, length n_depths). Depth must be equally spaced for the DFT to be exact; if not equally spaced, the implementation falls back to a FFT on the reindexed series.

targets

Matrix of observed profile values, shape (n_obs, n_depths). Each row is one site.

covariates

Matrix of depth-dependent covariate values, shape (n_obs, n_depths, n_channels) – the covariate trajectory that drives the operator. A 2-D matrix is accepted and treated as n_channels = 1.

n_modes

Integer; number of Fourier modes retained in each spectral convolution. Default 4L.

width

Integer; number of latent channels. Default 8L.

n_blocks

Integer; number of FNO blocks. Default 2L.

epochs

Integer; SGD epochs.

lr

Learning rate.

seed

RNG seed.

backend

"r" (default, pure-R ELM-style) or "torch" (full autograd via torch::optim_adam; requires the torch Suggests dependency). v2.7.0 upgrade.

device

"cpu" (default), "mps" (Apple Silicon) or "cuda" when backend = "torch".

Value

An edaphos_no_fno fit.