Simulators Documentation

Overview

The simulators in this project are built to solve different Partial Differential Equations (PDEs). Each simulator extends the BaseSimulator class and implements the problem-specific logic for a particular PDE. Simulation results, including metadata and input-output pairs, are saved in an HDF5 format, making them suitable for training machine learning models like DeepONet and FNO.

Base Simulator

The BaseSimulator class serves as the foundation for all PDE simulators. It implements reusable methods for setting up, running, and saving simulations, ensuring a modular and extensible structure.

Key Features:

  • Metadata Management: Collects and saves metadata such as simulation parameters, execution time, and hardware information.

  • HDF5 File Handling: Stores simulation results hierarchically in an HDF5 file.

  • Reusability: Abstract methods allow flexibility for specific PDE implementations.

Example Constructor:

class BaseSimulator:
    def __init__(self, mesh_size: int = 32, output_path: str = "simulations.h5"):
        self.mesh_size = mesh_size
        self.output_path = output_path

Key Methods:

  • setup_problem(): Abstract method to set up the specific PDE problem.

  • run_simulation(): Executes a single simulation and stores results.

  • run_session(): Runs multiple simulations with varying parameters and saves them in the HDF5 format.

Poisson Simulator

The PoissonSimulator solves the Poisson equation using FEniCS, incorporating Dirichlet and Neumann boundary conditions. It supports parameterization of the source term and Neumann coefficient, enabling dynamic simulations for various configurations.

Key Parameters:

  • Source Strength: Controls the intensity of the source term.

  • Neumann Coefficient: Defines the boundary condition coefficient.

Example Usage:

from simulators.poisson_simulator import PoissonSimulator

simulator = PoissonSimulator(mesh_size=32, output_path="poisson_results.h5")
simulator.run_session(
    parameter_ranges={
        'source_strength': (10.0, 20.0),
        'neumann_coefficient': (5.0, 10.0)
    },
    num_simulations=10
)

Output Data:

  • Field Inputs: field_input_f (source term) and field_input_g (Neumann boundary).

  • Solutions: values containing PDE solutions at grid points.

  • Metadata: Parameter values, execution time, and hardware information.

Biharmonic Simulator

The BiharmonicSimulator solves the biharmonic equation using a discontinuous Galerkin method. It supports parameterization of the source term for flexible simulation setups.

Key Features:

  • Implements a penalty-based discontinuous Galerkin formulation.

  • Allows parameterization of the source term.

Key Parameter:

  • Source Coefficient: Controls the amplitude of the source term in the PDE.

Example Usage:

from simulators.biharmonic_simulator import BiharmonicSimulator

simulator = BiharmonicSimulator(mesh_size=32, output_path="biharmonic_results.h5")
simulator.run_session(
    parameter_ranges={'source_coefficient': (1.0, 5.0)},
    num_simulations=10
)

Output Data: - Field Inputs: field_input_f representing the source term. - Solutions: values containing the PDE solutions at grid points. - Metadata: Includes source coefficient, execution time, and hardware details.

HDF5 File Structure

The simulation results are saved in an HDF5 format with the following hierarchical structure:

simulations/
├── session_1/
│   ├── simulation_1/
│   │   ├── coordinates            # Spatial grid coordinates
│   │   ├── values                 # Solution values at grid points
│   │   ├── field_inpu             # Input field data
│   │   └── attributes/            # Metadata
│   │       ├── paramete
│   │       ├── mesh_size
│   │       ├── execution_time
│   └── attributes/
│       ├── number_of_simulations
│       ├── timestamp
│       └── hardware_info
├── session_2/
│   ...

This structure ensures interoperability and reusability of the data.

Advanced Usage

Custom Parameter Ranges

You can easily modify the parameter ranges for any simulator to explore different PDE configurations. For example:

parameter_ranges = {'source_strength': (5.0, 15.0), 'neumann_coefficient': (3.0, 7.0)}

Multiple Field Inputs

Both PoissonSimulator and BiharmonicSimulator support handling multiple input fields. Simply define the fields in the setup_problem method and store them using the HDF5 file handler.

Contact

For further assistance or feedback, contact the project maintainers: