Hybrid Stochastic-PDE Simulation

Overview

This project provides a self-contained Python framework for simulating reaction-diffusion systems using Hybrid, Stochastic, and PDE models. It is designed for researchers and practitioners who want to explore hybrid stochastic-PDE dynamics in spatially distributed systems.

The framework implements the Spatial Regime Conversion Method (SRCM) for the Fisher-KPP adaptive switching problem (Test Case 4), as described in:

Cameron, Yates, and Smith, "Regime Conversion Method."

• Hybrid Model: Combines discrete stochastic simulations (SSA) with continuous PDEs for efficient and accurate modeling.
• Stochastic Model: Pure SSA simulation of particles in compartments.
• PDE Model: Pure partial differential equation simulation of the system.

The code is fully self-contained with hardcoded parameters for demonstration purposes.

Requirements

• Python 3.8+
• Base packages:
  • numpy
  • tqdm
  • os
  • json
  • ctypes
• production_project package (contains Hybrid, Stochastic, PDE classes)
• Optional: C compiler for hybrid model acceleration

Note: The hybrid model uses ctypes to call a compiled C library (.so) for speed. On macOS, this .so is provided. For Windows, you may need to recompile the library or simply disable C acceleration by setting use_c_functions=False.

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Usage

Run the main simulation script:

python main.py

How it works

main.py is a self-contained demonstration. Here’s what it does:

1. Set Simulation Parameters

domain_length = 5.0
h = 0.1
compartment_number = int(domain_length / h)
PDE_multiple = 8
total_time = 10
timestep = 0.008
particles_per_compartment_thresh = 50
gamma = 1.0
production_rate = 10.0
degradation_rate = 0.01
diffusion_rate = 1e-2
repeats = 10
number_particles_per_cell = 1

2. Set Initial Conditions

SSA_initial = np.zeros(compartment_number, dtype=np.int64)
SSA_initial[0] = number_particles_per_cell

3. Run Hybrid Simulation

hybrid_model = Hybrid(
    domain_length, compartment_number, PDE_multiple, total_time, timestep,
    particles_per_compartment_thresh, gamma, production_rate, degradation_rate,
    diffusion_rate, SSA_initial, use_c_functions=True
)

Hybrid_SSA, Hybrid_PDE, Hybrid_combined = hybrid_model.run_simulation(number_of_repeats=repeats)
hybrid_model.save_simulation_data(Hybrid_SSA, Hybrid_PDE, Hybrid_combined, datadirectory='data', filename='Hybrid_data')

4. Run Pure Stochastic Simulation

stochastic_model = Stochastic(
    domain_length, compartment_number, total_time, timestep,
    production_rate, degradation_rate, diffusion_rate, SSA_initial
)

SSA_grid = stochastic_model.run_simulation(number_of_repeats=repeats)
stochastic_model.save_simulation_data(SSA_grid, datadirectory='data', filename = 'pure_SSA_data')

5. Run Pure PDE Simulation

PDE_points = hybrid_model.PDE_M
PDE_initial = np.zeros(PDE_points)
PDE_initial[0:PDE_multiple] = number_particles_per_cell / hybrid_model.h

pde_model = PDE(
    domain_length, PDE_points, total_time, timestep,
    production_rate, degradation_rate, diffusion_rate, PDE_initial
)

PDE_grid = pde_model.run_simulation()
pde_model.save_simulation_data(PDE_grid, datadirectory='data', filename = 'PDE_data')

6. Completion Message

print("Simulation complete!")

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Visualisation

After running main.py, you can animate the results:

python animate.py

This will create visualisations of the hybrid simulation outputs. Make sure main.py has been run first so that the data/ folder contains the simulation outputs. You can change the datapath at the top of the animate.py script.

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Output

• data/Hybrid_data.npz: Hybrid simulation results including SSA, PDE, and combined grids.
• data/Hybrid_data_parameters.json: JSON file containing all simulation parameters.
• Additional outputs from stochastic and PDE simulations in the data/ folder.

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