Compute the physics-informed residual loss (Norouzi et al. 2025)

Evaluates four physics constraints against the current model weights:

S1 (L_lin): Second derivative \(|\partial^2\theta/\partial pF^2|\) in the dry end \(pF \in [5, 7.6]\) should be near zero (linearity).
S2 (L_pos): \(\theta(pF = 6.2) \geq 0\) (non-negativity).
S3 (L_neg): \(\theta(pF = 7.6) \leq 0\) (non-positivity).
S4 (L_sat): First derivative \(|\partial\theta/\partial pF|\) near zero in the saturated plateau \(pF \in [-2, -0.3]\).

Usage

compute_physics_loss(
  theta_model,
  res_tensors,
  lambda3 = 1,
  lambda4 = 1000,
  lambda5 = 1000,
  lambda6 = 1,
  pf_left = -2,
  pf_right = 7.6,
  training = TRUE
)

Arguments

theta_model: A Keras model with two inputs: Xseq and pf_norm.
res_tensors: A named list with four sublists (set1 – set4), each containing Xseq and pf tensors (output of residual_to_tensors()).
lambda3: Weight for S1 linearity loss (default 1.0).
lambda4: Weight for S2 non-negativity loss (default 1000.0).
lambda5: Weight for S3 non-positivity loss (default 1000.0).
lambda6: Weight for S4 saturation loss (default 1.0).
pf_left: Left boundary of the normalised pF domain (default -2).
pf_right: Right boundary (default 7.6).
training: Logical passed to the model call (default TRUE).

Value

A named list of TensorFlow scalars: L_phys, L_lin, L_pos, L_neg, L_sat.