Physics-Informed ETo Modeling: PINN vs LightGBM vs Neural Network

Reference evapotranspiration (ETo) drives irrigation scheduling and agricultural water management. This project shows, end to end, how to model ETo with three approaches and compare them fairly:

Model	Type	Uses physics?
LightGBM	Gradient-boosted trees	No (data-driven baseline)
Data-only NN	Neural network	No
PINN	Physics-Informed Neural Network	Yes (FAO-56 Penman-Monteith)

The PINN embeds the FAO-56 Penman-Monteith equation directly into the training loss, so the network is rewarded for agreeing with established agronomy

• not just with the (noisy) training data.

This repo uses fully synthetic, reproducible data generated from real physics, so anyone can clone and run it with no data-licensing concerns.

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Key Result

The interesting story appears when data are scarce and noisy - the realistic situation for many farms and weather stations. Here the physics constraint helps the PINN generalize better than a purely data-driven model.

Scarce + noisy regime (1 station, 1 year, high label noise):

Model	RMSE ↓	MAE ↓	R² ↑
LightGBM	0.840	0.612	0.827
Data-only NN	0.773	0.576	0.853
PINN	0.762	0.574	0.857

Data-rich regime (4 stations, 3 years, low noise) - all models are strong, differences shrink:

Model	RMSE ↓	MAE ↓	R² ↑
LightGBM	0.188	0.147	0.990
Data-only NN	0.196	0.150	0.990
PINN	0.195	0.150	0.990

Takeaway: physics information matters most when data are limited or noisy. With abundant clean data, a good tree model is already excellent.

(Units are mm/day. Your exact numbers may vary slightly by machine / library version. Regenerate everything with the commands below.)

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Repository Structure

.
├── main.py                 # End-to-end pipeline (run this)
├── src/
│   ├── physics.py          # FAO-56 Penman-Monteith (NumPy) - the "ground truth"
│   ├── data.py             # Synthetic weather + ETo dataset generator
│   ├── models_lgbm.py      # LightGBM baseline (falls back to scikit-learn)
│   ├── models_pinn.py      # PINN + data-only NN (PyTorch, differentiable physics)
│   └── evaluate.py         # Metrics + plots
├── notebook.ipynb          # Intro PINN notebook (simple ODE example)
├── PINN_Tutorial.md        # Step-by-step PINN primer (the simple ODE)
├── STEP_BY_STEP.md         # Step-by-step guide for THIS ETo project
├── requirements.txt
├── LICENSE                 # MIT
└── README.md

Outputs (data/, results/, results_scarce/) are generated on run and are git-ignored.

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Quick Start

1. Install

git clone https://github.com/GreenSmart-DSS/physics-informed-eto.git
cd physics-informed-eto

python -m venv .venv
# Windows:  .venv\Scripts\activate
# macOS/Linux:  source .venv/bin/activate

pip install -r requirements.txt

2. Run the full comparison

python main.py

This will:

1. Generate a synthetic ETo dataset (data/eto_synthetic.csv).
2. Train LightGBM, a data-only NN, and a PINN.
3. Print a metrics table and save plots + metrics.csv to results/.

3. Reproduce the scarce-data experiment

python main.py --stations 1 --years 1 --noise 0.8 --physics-weight 2.0 \
    --outdir results_scarce --datadir data_scarce

Command-line options

Flag	Default	Meaning
--stations	4	number of virtual weather stations
--years	3	years of daily data per station
--noise	0.15	std-dev of ETo label noise [mm/day]
--epochs	800	NN / PINN training epochs
--physics-weight	1.0	weight of the physics loss term in the PINN
--seed	42	random seed (reproducibility)
--outdir	results	where plots + metrics are written
--datadir	data	where the generated dataset is written

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How It Works

The physics: FAO-56 Penman-Monteith

ETo is computed from eight daily inputs:

t_max, t_min   air temperature [°C]
rh_mean        relative humidity [%]
wind_2m        wind speed at 2 m [m/s]
rs             solar radiation [MJ m⁻² day⁻¹]
elevation      station elevation [m]
latitude       [decimal degrees]
doy            day of year [1..365]

via the standard FAO-56 equation (src/physics.py):

        0.408·Δ·(Rn − G) + γ·(900 / (T + 273))·u₂·(es − ea)
ETo = ────────────────────────────────────────────────────────
                    Δ + γ·(1 + 0.34·u₂)

The synthetic dataset

src/data.py simulates seasonal, internally-consistent weather (temperature follows an annual sinusoid, solar radiation is capped by clear-sky physics, humidity anti-correlates with temperature, etc.), computes the true ETo with the physics engine, then adds Gaussian sensor noise to create the training label. This gives a realistic yet fully reproducible learning problem.

The PINN loss

src/models_pinn.py re-implements Penman-Monteith in PyTorch so it is differentiable. The network is trained on:

L = L_data + λ · L_physics

  L_data    = MSE( NN(x), noisy ETo label )      # fit the observations
  L_physics = MSE( NN(x), Penman-Monteith(x) )   # obey the equation

Setting λ = 0 recovers an ordinary data-only NN, which is exactly the baseline we compare against. Increasing λ (--physics-weight) makes the model lean harder on physics - most useful when data are scarce/noisy.

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Outputs

After a run, results/ contains:

• metrics.csv - RMSE, MAE, R², MBE for every model
• metrics_bar.png - grouped bar chart comparing the models
• scatter_<model>.png - predicted-vs-observed scatter (with 1:1 line)
• loss_<model>.png - training-loss curves for the neural models

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Learning Path

New to PINNs? Follow this order:

1. PINN_Tutorial.md - learn the PINN idea on a tiny ODE (dy/dx + 2y = 0).
2. notebook.ipynb - run that same example interactively.
3. STEP_BY_STEP.md - walk through this ETo project module by module.
4. main.py - run the full comparison and read the code.

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Extending the Project

• Swap the synthetic data for a real station dataset (keep the 8 feature columns and an eto label column).
• Add hard physical bounds (e.g. energy-balance limits) as extra loss terms.
• Turn a physical parameter (like the wind/aerodynamic coefficient) into a trainable nn.Parameter to solve an inverse problem.
• Try other tabular baselines (XGBoost, CatBoost, Random Forest).

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Reference

Allen, R.G., Pereira, L.S., Raes, D., Smith, M. (1998). Crop evapotranspiration - Guidelines for computing crop water requirements. FAO Irrigation and drainage paper 56, Rome.

License

MIT - see LICENSE.