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Introduction to soilFlux

Physics-Informed CNN1D for Soil Water Retention Curves

Hugo Rodrigues

2026-03-21

1 Overview

Note: All code in this vignette requires TensorFlow and Keras to be installed. See ?soilFlux for installation instructions. The outputs shown are representative examples from a training run on the swrc_example dataset.

The soilFlux package implements a physics-informed one-dimensional convolutional neural network (CNN1D-PINN) for estimating the complete soil water retention curve (SWRC) as a continuous function of matric potential. The architecture and physics constraints are adapted from Norouzi et al. (2025).

1.1 What is the SWRC?

The soil water retention curve describes the relationship between volumetric water content (\(\theta\), m³/m³) and matric potential (expressed as pF = log₁₀(h [cm])). It is a key input to most hydrological and land-surface models.

1.2 Key features

Feature	Description
Monotone by construction	θ decreases with pF by architecture (cumulative integral of positive slopes)
Physics-informed	Four residual constraints enforce known physical behaviour
Continuous output	Predicts θ at any pF value, not just standard pressure heads
Multi-covariate	Uses texture (sand/silt/clay fractions), bulk density, SOC, and depth
Ready to save/load	Weights persisted via Keras HDF5 for spatial prediction

2 Quick-start

2.1 Installation

# Install development version from GitHub
remotes::install_github("hugo-rodrigues/soilFlux")

# Required Python backend (once per machine)
tensorflow::install_tensorflow()

2.2 Minimal example

library(soilFlux)

# 1. Load and prepare data --------------------------------------------------
data("swrc_example")   # example dataset bundled with the package

df <- prepare_swrc_data(
  swrc_example,
  depth_col = "depth",
  fix_bd    = TRUE,
  fix_theta = TRUE
)

# Train / validation / test split (by PEDON_ID)
ids      <- unique(df$PEDON_ID)
set.seed(42)
tr_ids   <- sample(ids, floor(0.7 * length(ids)))
val_ids  <- sample(setdiff(ids, tr_ids), floor(0.15 * length(ids)))
te_ids   <- setdiff(ids, c(tr_ids, val_ids))

train_df <- df[df$PEDON_ID %in% tr_ids,  ]
val_df   <- df[df$PEDON_ID %in% val_ids, ]
test_df  <- df[df$PEDON_ID %in% te_ids,  ]

# 2. Fit model --------------------------------------------------------------
fit <- fit_swrc(
  train_df   = train_df,
  x_inputs   = c("clay", "silt", "bd_gcm3", "soc", "Depth_num"),
  val_df     = val_df,
  epochs     = 60,
  batch_size = 256,
  lambdas    = norouzi_lambdas("norouzi"),
  verbose    = TRUE
)

# 3. Evaluate ---------------------------------------------------------------
m <- evaluate_swrc(fit, test_df)
print(m)

# 4. Dense SWRC curves ------------------------------------------------------
dense <- predict_swrc_dense(fit, newdata = test_df, n_points = 500)

# 5. Plot -------------------------------------------------------------------
plot_swrc(dense, obs_points = test_df,
          obs_col   = "theta_n",
          facet_row = "Depth_label",
          facet_col = "Texture")

3 Data preparation

3.1 Expected columns

prepare_swrc_data() expects (at minimum):

Column	Description	Units
`PEDON_ID`	Unique profile identifier	—
`depth`	Depth interval (e.g. `"0-5"`)	cm
`matric_head`	Matric head	cm
`water_content`	Volumetric water content	m³/m³ or %
Covariates	e.g. `clay`, `silt`, `bd`, `soc`	%, g/cm³

3.2 Unit handling

The package automatically detects and corrects common unit issues:

# Bulk density: if median > 10, assumes kg/m3 and converts to g/cm3
fix_bd_units(c(1200, 1450, 1300))   # kg/m3 -> g/cm3

# Theta: if max > 1.5, assumes % and divides by 100
theta_unit_factor(c(30, 40, 25))    # returns 100

4 Model architecture

4.1 Monotone integral layer

The model output is:

\[\hat{\theta}(\text{pF}) = \theta_s - \int_0^{\text{pF}} \text{softplus}(s(t)) \, dt\]

where \(s(t)\) is a 1-channel Conv1D output. Because softplus > 0 always, the integral is strictly increasing, so \(\hat{\theta}\) is strictly decreasing — monotonicity is guaranteed by construction, not by post-processing.

4.2 Inputs to the model

Each observation is encoded as a 3-D sequence: * Shape: [N, K, p+1] * K = number of knot points (default 64) * p = number of covariates * Last channel = knot position in [0, 1]

This design broadcasts each covariate across all knot positions, allowing the Conv1D layers to learn shape-from-texture mappings.

5 Physics constraints

Four residual constraints from Norouzi et al. (2025) are embedded in the loss function:

Set	Constraint	pF range	Default weight
S1	Linearity at dry end: ∣∂²θ/∂pF²∣ → 0	[5.0, 7.6]	λ₃ = 1
S2	Non-negativity: θ(pF = 6.2) ≥ 0	fixed	λ₄ = 1000
S3	Non-positivity: θ(pF = 7.6) ≤ 0	fixed	λ₅ = 1000
S4	Flat plateau: ∣∂θ/∂pF∣ → 0	[−2.0, −0.3]	λ₆ = 1

Plus two data-loss weights:

Term	Description	Default
λ₁	Wet-end data loss (pF ≤ 4.2)	1
λ₂	Dry-end data loss (pF > 4.2)	10

# Exact replication of Norouzi et al. (2025) Table 1
norouzi_lambdas("norouzi")

# Smoother dry-end (lambda3 = 10)
norouzi_lambdas("smooth")

6 Saving and loading models

# Save
save_swrc_model(fit, dir = "./models", name = "model_5")

# Check it exists
swrc_model_exists("./models", "model_5")

# Reload (in a new session, after library(soilFlux))
fit2 <- load_swrc_model("./models", "model_5")
pred <- predict_swrc(fit2, newdata = test_df)

7 Visualisation

7.1 SWRC curves

dense <- predict_swrc_dense(fit, newdata = test_df, n_points = 500)

plot_swrc(
  pred_curves  = dense,
  obs_points   = test_df,
  obs_col      = "theta_n",
  facet_row    = "Depth_label",
  facet_col    = "Texture",
  line_colour  = "steelblue4",
  point_colour = "black"
)

7.2 Predicted vs. observed

pred_df <- data.frame(
  theta_n         = test_df$theta_n,
  theta_predicted = predict_swrc(fit, test_df),
  Texture         = test_df$Texture
)
plot_pred_obs(pred_df, group_col = "Texture")

7.3 Training history

plot_training_history(fit)

8 Texture classification

classify_texture(
  sand = c(70, 20, 10),
  silt = c(15, 50, 30),
  clay = c(15, 30, 60)
)

# Add as a column to a data frame
add_texture(df, sand_col = "sand_total")

# Texture triangle (requires ggtern)
texture_triangle(df, color_col = "Texture")

9 Session information

sessionInfo()

10 References

Norouzi, A. M., Feyereisen, G. W., Papanicolaou, A. N., & Wilson, C. G. (2025). Physics-Informed Neural Networks for Estimating a Continuous Form of the Soil Water Retention Curve. Journal of Hydrology.

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