HyDLPy is a cutting-edge Python framework that seamlessly integrates traditional process-based hydrological models with modern deep learning techniques. Built on PyTorch and PyTorch Lightning, it enables researchers and practitioners to construct hybrid models that combine the interpretability of physics-based approaches with the flexibility and predictive power of neural networks.

⚠️ WARNING: This is a private library for internal use only. It is highly unstable and the API is subject to change without notice. DO NOT USE IN PRODUCTION.

• 🔬 Symbolic Model Definition: Define hydrological processes using SymPy equations with automatic compilation to PyTorch
• 🧠 Hybrid Architecture: Combine process-based models with neural networks for enhanced performance
• ⚡ High Performance: GPU-accelerated computations with automatic differentiation support
• 🔧 Modular Design: Flexible, plug-and-play components for different modeling needs
• 📊 Built-in Models: Pre-implemented HBV, XAJ, and ExpHydro models ready to use
• 🌐 Advanced Routing: Sophisticated river routing with differentiable Muskingum-Cunge method
• 📈 Comprehensive Metrics: Multiple loss functions and evaluation metrics for hydrological modeling
• 🔌 PyTorch Lightning Integration: Easy training, validation, and deployment workflows

HyDLPy follows a modular architecture that allows for flexible combination of different components:

graph TB
    A[Input Data] --> B[Static Parameter Estimator]
    A --> C[Dynamic Parameter Estimator]
    A --> D[Hydrology Core]
    B --> D
    C --> D
    D --> E[Routing Module]
    E --> F[Streamflow Prediction]
    
    subgraph "Neural Components"
        B
        C
    end
    
    subgraph "Physics-Based Core"
        D
    end
    
    subgraph "Routing"
        E
    end

The heart of the framework - a differentiable, physics-based hydrological model defined using symbolic equations:

• Symbolic Definition: Use SymPy to define complex hydrological processes
• Automatic Compilation: Equations are automatically compiled to optimized PyTorch functions
• Topological Sorting: Dependencies are automatically resolved for correct computation order
• Parameter Management: Built-in parameter bounds and optimization support

Neural network components that learn to estimate model parameters:

• Static Parameter Estimator: MLPs that estimate parameters from basin characteristics
• Dynamic Parameter Estimator: LSTMs/GRUs that estimate time-varying parameters from meteorological data
• Flexible Architecture: Support for various neural network architectures

Advanced river routing capabilities:

• Differentiable Muskingum-Cunge (DMC): Physics-based routing with automatic differentiation
• Neural Routing: MLP-based routing for complex river networks
• Flexible Integration: Easy to add custom routing methods

Ready-to-use implementations of popular hydrological models:

• HBV Model: Complete implementation of the HBV conceptual model
• XAJ Model: Xinanjiang model for humid regions
• ExpHydro: Experimental model for research and development

• Python 3.11 or higher
• PyTorch 2.8 or higher
• CUDA (optional, for GPU acceleration)

pip install hydlpy

git clone https://github.com/chooron/hydlpy.git
cd hydlpy
pip install -e .

• torch>=2.8 - PyTorch for deep learning computations
• pytorch-lightning>=2.5 - High-level PyTorch wrapper for training
• sympy>=1.14 - Symbolic mathematics for model definition
• pydantic>=2.11 - Data validation and settings management

import torch
from hydlpy.model import DplHydroModel

# Create configuration (ExpHydro example)
config = {
    "hydrology_model": {
        "name": "exphydro",
        "input_names": ["prcp", "pet", "temp"],
    },
    # Estimated parameters must exactly match hydrology model parameters (static ∪ dynamic)
    "static_estimator": {
        "name": "mlp",
        "estimate_parameters": ["Tmin", "Tmax", "Df", "Smax"],
        "input_names": ["attr1", "attr2", "attr3", "attr4", "attr5", "attr6"],
    },
    "dynamic_estimator": {
        "name": "lstm",
        "estimate_parameters": ["Qmax", "f"],
        "input_names": ["attr1", "attr2", "attr3"],
    },
    "warm_up": 100,
    "hru_num": 8,
    "optimizer": {"lr": 1e-3},
}

model = DplHydroModel(config)

# Prepare input data (shapes must match input_names)
time_len, basin_num = 200, 20
batch = {
    "x_phy": torch.rand((time_len, basin_num, 3)),      # [T, B, F]
    "x_nn_norm": torch.rand((time_len, basin_num, 3)),  # reserved
    "xc_nn_norm": torch.rand((time_len, basin_num, 3)), # inputs for dynamic estimator
    "c_nn_norm": torch.rand((basin_num, 6)),            # inputs for static estimator
}

with torch.no_grad():
    outputs = model(batch)
    # outputs is a dict of fluxes and states, e.g. outputs["flow"], outputs["soilwater"]
    print(list(outputs.keys())[:5])

from hydlpy.hydrology import HydrologicalModel, HydroParameter, HydroVariable, variables
from sympy import S, Min, Max, Eq, tanh

# Define parameters with bounds
Tmin = HydroParameter("Tmin", default=-1.0, bounds=(-5.0, 5.0))
Smax = HydroParameter("Smax", default=250.0, bounds=(100.0, 400.0))

# Define variables
temp = HydroVariable("temp")
prcp = HydroVariable("prcp")
snowpack = HydroVariable("snowpack")
soilwater = HydroVariable("soilwater")

# Define intermediate fluxes
rainfall, snowfall, melt, flow = variables("rainfall, snowfall, melt, flow")

# Define equations
fluxes = [
    Eq(rainfall, (tanh(5.0 * (Tmin - temp)) + 1.0) * 0.5 * prcp),
    Eq(snowfall, (tanh(5.0 * (temp - Tmin)) + 1.0) * 0.5 * prcp),
    Eq(melt, (tanh(5.0 * (temp - Tmin)) + 1.0) * 0.5 * Min(snowpack, 2.5 * (temp - Tmin))),
    Eq(flow, Max(soilwater - Smax, 0))
]

dfluxes = [
    Eq(snowpack, snowfall - melt),
    Eq(soilwater, rainfall + melt - flow)
]

# Create the model
model = HydrologicalModel(fluxes=fluxes, dfluxes=dfluxes, hru_num=16)

# Run the model
states = torch.randn(16, 2)  # [H, S]
forcings = torch.randn(16, 2)  # [H, F]

fluxes_out, new_states = model(forcings.unsqueeze(0).unsqueeze(1), states)
print(f"Fluxes shape: {fluxes_out.shape}")
print(f"New states shape: {new_states.shape}")

import pytorch_lightning as pl
from hydlpy.data import HydroDataModule

# Create data module
# data_module = HydroDataModule(...)

# Create trainer
trainer = pl.Trainer(
    max_epochs=100,
    accelerator="gpu" if torch.cuda.is_available() else "cpu",
    devices=1
)

# Train the model
# trainer.fit(model, data_module)

HyDLPy comes with several pre-implemented hydrological models ready for immediate use:

The HBV (Hydrologiska Byråns Vattenbalansavdelning) model is a conceptual rainfall-runoff model widely used in Nordic countries.

Key Features:

• Snow accumulation and melt processes
• Soil moisture accounting
• Three-layer response function
• Temperature-based snow/rain separation

Parameters:

• TT: Temperature threshold for snow/rain separation
• CFMAX: Degree-day factor for snowmelt
• FC: Field capacity of soil
• BETA: Shape parameter for soil moisture function
• k0, k1, k2: Recession coefficients

The Xinanjiang (XAJ) model is designed for humid regions and features a unique runoff generation mechanism.

Key Features:

• Three-layer soil moisture storage
• Free water storage concept
• Nash cascade routing
• Evapotranspiration calculation

Parameters:

• Wum, Wlm, Wdm: Upper, lower, and deep layer storage capacities
• b: Shape parameter for runoff generation
• Smax: Free water storage capacity
• Ki, Kg: Interflow and groundwater recession coefficients

An experimental model designed for research and development purposes.

Key Features:

• Simplified snow processes
• Basic soil moisture accounting
• Configurable parameter bounds
• Ideal for testing new concepts

For detailed documentation, examples, and API reference, visit:

• 📖 Full Documentation
• 🔬 Model Building Guide
• 💡 Examples and Tutorials

This project is licensed under the MIT License - see the LICENSE file for details.

• HydroModels.jl: Original Julia implementation by chooron
• PyTorch Team: For the excellent deep learning framework
• SymPy Community: For symbolic mathematics capabilities
• Hydrological Research Community: For decades of model development and validation

• 💬 GitHub Discussions - Community support and questions
• 🐛 Issue Tracker - Bug reports and feature requests
• 📧 Email: [email protected]