Fit a Neural ODE depth profile (Pillar 2, deep variant)

Models the vector field $dy/dz = f_\theta(z, y)$ where $f_\theta$ is a small MLP (default 2 x 16 + tanh). The forward model is a fixed-step RK4 integrator that runs end-to-end on torch, so training drives the MLP weights — and, optionally, the surface value $y_0$ — by back-propagating through the whole integration (a proper Neural ODE, Chen et al. 2018).

Usage

piml_neural_ode_fit(
  depths,
  values,
  y_surface = NULL,
  hidden = c(16L, 16L),
  n_steps = 4L,
  epochs = 500L,
  lr = 0.01,
  seed = NULL,
  verbose = FALSE
)

Arguments

depths: Numeric vector of horizon mid-depths.
values: Numeric vector of observed values, same length.
y_surface: Optional numeric; if supplied, $y_0$ is fixed (no learnable parameter) — used when you trust a specific 0 cm reading.
hidden: Integer vector with MLP hidden-layer widths.
n_steps: Integer, RK4 steps between successive observation depths. Higher = more accurate, slower.
epochs, lr: Integer and numeric — training hyperparameters for Adam.
seed: Optional integer — forwarded to torch::torch_manual_seed for reproducibility.
verbose: Logical; print training loss every 50 epochs.

Value

A edaphos_piml_neural_ode object (S3).

Details

Compared to piml_profile_fit(), the Neural ODE variant can capture non-monotone profiles (E horizons below an A, bulge in a Bt) that the parametric exponential-asymptote ODE cannot represent.