:orphan:

Paroto Examples
===============

This directory contains example files and configurations for the Paroto optimization framework.

📁 Contents
-----------

Python Examples
~~~~~~~~~~~~~~~

- **EXAMPLE_MODEL_USAGE.py** - Demonstrates different model fidelities and the model registry

  - Compares breakdown voltage models at different fidelity levels
  - Shows how to use the model registry
  - Exports architecture to STONE format

Subdirectories
~~~~~~~~~~~~~~

- **VDEF_optim/** - Voltage-gap-Distance-Energy-Frequency (VDEF) optimization

  - Complete parameter sweep example with OpenMDAO
  - Parallel execution (multiprocessing/MPI)
  - Advanced pairwise grid visualization
  - See VDEF_optim/README.rst for details

Configuration Files
~~~~~~~~~~~~~~~~~~~

- **config_example.yml** - Basic configuration template with all available options
- **config_low_fidelity.yml** - Fast exploration with low-fidelity models
- **config_with_models.yml** - Recommended balanced configuration (medium fidelity)
- **config_high_fidelity.yml** - High accuracy with physical models

Results
~~~~~~~

- **example_results/** - Sample output from running optimizations

  - cases.db - OpenMDAO case database
  - problem_summary.txt - Problem structure summary
  - config.json - Configuration used for the run

- **example_architecture.yml** - Generated STONE format architecture file

🚀 Quick Start
--------------

Run the Python Example
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: bash

   conda activate paroto
   python examples/EXAMPLE_MODEL_USAGE.py

Run Optimization with Different Fidelities
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: bash

   # Fast exploration (low fidelity)
   paroto-optimize --config examples/config_low_fidelity.yml --out results_low/

   # Recommended balance (medium fidelity)
   paroto-optimize --config examples/config_with_models.yml --out results_medium/

   # High accuracy (high fidelity)
   paroto-optimize --config examples/config_high_fidelity.yml --out results_high/

Single-Point Evaluation
~~~~~~~~~~~~~~~~~~~~~~~

Test a configuration without optimization:

.. code-block:: bash

   paroto-optimize --config examples/config_example.yml --out results/ --driver none

Model Validation
~~~~~~~~~~~~~~~~

Validate breakdown voltage models against experimental data:

.. code-block:: bash

   conda activate paroto
   python -m paroto.validation.validate_breakdown_models

This will:

- Compare all 5 breakdown models against Paschen curve data
- Validate temperature correction factors
- Test spark breakdown transition (G-S) with field enhancement
- Generate validation plots with statistical metrics

See paroto/validation/README.md for details.

📚 Documentation
----------------

For more details, see:

- Main documentation
- QUICK_START_MODELS.md - Quick start guide
- MODEL_SELECTION_GUIDE.md - Complete model selection guide

🎓 Recommended Learning Path
-----------------------------

1. **Start here**: Run EXAMPLE_MODEL_USAGE.py to understand model differences
2. **Single evaluation**: Try config_example.yml with --driver none
3. **DOE sweep**: Use config_low_fidelity.yml with --driver doe --generations 50
4. **Optimization**: Run config_with_models.yml with --driver gradient or --driver nsga2
5. **Validation**: Use config_high_fidelity.yml for final designs
6. **Advanced**: Explore VDEF_optim/ for comprehensive parameter space analysis

📊 Advanced Examples
--------------------

VDEF MDAO Parameter Space Exploration
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For a complete example of parameter space exploration using OpenMDAO with parallel execution
and advanced visualization:

.. code-block:: bash

   cd VDEF_optim/
   python example_vdef_mdao.py      # Run parameter sweep
   python analyze_vdef_pairwise.py  # Generate pairwise grid visualization

See VDEF_optim/README.rst for complete documentation.



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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to load a complete system architecture from a STONE format YAML file and run a simulation.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_EXAMPLE_MODEL_USAGE_thumb.png
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  :ref:`sphx_glr_auto_examples_EXAMPLE_MODEL_USAGE.py`

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      <div class="sphx-glr-thumbnail-title">Example: Load and run Paroto system from STONE configuration.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates how to use the validation module to compare breakdown voltage models against experimental data.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_VALIDATION_EXAMPLE_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VALIDATION_EXAMPLE.py`

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      <div class="sphx-glr-thumbnail-title">Example: Running breakdown voltage model validation.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the new ProblemGraph abstraction layer that provides a unified interface for all visualization backends (Mermaid, Cytoscape, NetworkX).">

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  .. image:: /auto_examples/images/thumb/sphx_glr_example_problem_graph_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_example_problem_graph.py`

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      <div class="sphx-glr-thumbnail-title">Example: Using ProblemGraph abstraction for unified visualization.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the hierarchical visualization capabilities of Paroto, showing how primary design parameters flow through models to constraints.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_gallery_hierarchical_viz_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_hierarchical_viz.py`

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      <div class="sphx-glr-thumbnail-title">Gallery Example: Hierarchical Parameter Visualization.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="==========================================">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_generator_operating_window_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_generator_operating_window.py`

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      <div class="sphx-glr-thumbnail-title">Automatic Constraint Boundary Exploration.</div>
    </div>


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.. toctree::
   :hidden:

   /auto_examples/EXAMPLE_MODEL_USAGE
   /auto_examples/VALIDATION_EXAMPLE
   /auto_examples/example_problem_graph
   /auto_examples/gallery_hierarchical_viz
   /auto_examples/plot_generator_operating_window

VDEF MDAO Optimization Example
===============================

This folder contains a comprehensive example of using the paroto library for
**Voltage-gap-Distance-Energy-Frequency** (VDEF) optimization in plasma torch design,
using **Multidisciplinary Analysis and Optimization (MDAO)** with OpenMDAO.

Overview
--------

The example demonstrates:

- **Parameter sweep** of plasma torch operating conditions
- **Constraint satisfaction** (25 kW power target, breakdown voltage limits)
- **Parallel execution** using Python multiprocessing (Windows) or MPI (Linux)
- **Data persistence** using SQLite databases
- **Advanced visualization** with pairwise grid (corner plot) analysis

Files
-----

1. example_vdef_mdao.py
~~~~~~~~~~~~~~~~~~~~~~~

Main parameter sweep script that explores the plasma torch design space.

**Features:**

- Uses OpenMDAO's ``TorchDesignGroup`` with physics-based models
- Explores 3D parameter space: **V**\ oltage × gap-**D**\ istance × **F**\ requency
- Computes **E**\ nergy per pulse as output (satisfying power constraint)
- Implements power constraint (25 kW) via balance component
- Tracks convergence status for all evaluations
- Saves results to SQLite database (``parameter_sweep_cases.sql``)

**Usage:**

.. code-block:: bash

   # Run parameter sweep (default: multiprocessing)
   python example_vdef_mdao.py

   # Generate N2 diagram only
   python example_vdef_mdao.py --n2

**Parameters Explored (VDEF):**

- **Voltage** (V): HV voltage: 5 - 80 kV (15 levels)
- **gap** (D): Gap distance: 6 - 30 mm (8 levels)
- **Energy** (E): Energy per pulse (computed output)
- **Frequency** (F): Pulse frequency: 5 - 200 kHz (10 levels)
- **Total evaluations**: 1,200 cases (15 × 8 × 10)

**Outputs:**

- ``parameter_sweep_cases.sql``: SQLite database with all results
- ``parameter_space_visualization.png``: Standard 6-panel visualization
- Console output with convergence statistics

2. analyze_vdef_pairwise.py
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Post-processing script that creates pairwise grid (corner plot) visualization.

**Features:**

- Loads results from SQLite database
- Creates comprehensive pairwise grid showing:

  - All 2D parameter combinations
  - 1D marginal distributions (histograms)
  - Three-way classification: Feasible / Converged-Infeasible / Non-converged

- Eliminates 2D projection ambiguity
- Color-coded by energy per pulse

**Usage:**

.. code-block:: bash

   # Run after example_vdef_mdao.py has generated data
   python analyze_vdef_pairwise.py

**Output:**

- ``pairwise_grid_visualization.png``: Comprehensive corner plot

3. generate_n2_diagram.py
~~~~~~~~~~~~~~~~~~~~~~~~~~

Utility script to generate OpenMDAO N2 diagram showing system architecture.

**Usage:**

.. code-block:: bash

   python generate_n2_diagram.py

**Output:**

- ``n2.html``: Interactive N2 diagram

4. plot_generator_operating_window.py
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Demonstrates automatic constraint boundary exploration for the generator.

**Usage:**

.. code-block:: bash

   python plot_generator_operating_window.py



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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="This script loads pre-computed parameter sweep results and creates a pairwise grid (corner plot) showing: - All 2D projections of parameter combinations - 1D marginal distributions (histograms) - Three-way classification: Feasible, Converged-Infeasible, Non-converged">

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  .. image:: /auto_examples/VDEF_optim/images/thumb/sphx_glr_analyze_vdef_pairwise_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VDEF_optim_analyze_vdef_pairwise.py`

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      <div class="sphx-glr-thumbnail-title">Analysis script: Pairwise grid visualization of parameter space.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to: 1. Set up the problem directly in Python (no STONE config) 2. Use RepetitivePulseBreakdownModel with:    - Pulse duration effects (ionization avalanche kinetics: e + M → e + e + M+)    - Memory effects from repeated pulsing    - Field enhancement factors 3. Explore feasible parameter space with power and breakdown constraints 4. Visualize the solution space 5. Run parameter sweeps in parallel using OpenMDAO&#x27;s DOEDriver">

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  .. image:: /auto_examples/VDEF_optim/images/thumb/sphx_glr_example_vdef_mdao_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VDEF_optim_example_vdef_mdao.py`

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      <div class="sphx-glr-thumbnail-title">Example: Direct MDAO problem setup for plasma torch parameter space exploration.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script creates an interactive HTML N2 diagram showing the system architecture and data flow for the plasma torch MDAO problem.">

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  .. image:: /auto_examples/VDEF_optim/images/thumb/sphx_glr_generate_n2_diagram_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VDEF_optim_generate_n2_diagram.py`

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      <div class="sphx-glr-thumbnail-title">Generate N2 diagram for the VDEF MDAO example.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script loads results from the VDEF parameter sweep and visualizes the generator operating window with actual design points overlaid.">

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  .. image:: /auto_examples/VDEF_optim/images/thumb/sphx_glr_plot_generator_operating_window_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VDEF_optim_plot_generator_operating_window.py`

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      <div class="sphx-glr-thumbnail-title">Plot Generator Operating Window from VDEF Parameter Sweep.</div>
    </div>


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    </div>

VedEf Operating Window - 5D Parameter Space Exploration
========================================================

This directory contains a comprehensive example for exploring the operating window of a pulsed
plasma torch with 5 design parameters and multiple physics-based constraints.

Overview
--------

The **VedEf** optimization explores 5 design parameters using **ARC002 parameter naming convention**:

- **G_UMAX_OUT** (kV): Generator voltage (High voltage)
- **G_e** (mm): Interelectrode gap distance
- **TP_D_OUT** (mm): Torch outlet diameter
- **G_F** (kHz): PRF - Pulse Frequency
- **G_Ep** (J): Energy per pulse
- **TP_QM** (kg/h): Mass flow rate per torch

All parameters follow the ARC002 parameter registry standard for consistency across
the project and compatibility with experimental specifications.

Files
-----

Integration Layer (Example-Specific)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

- ``1_model_vedef_design_group.py`` - VedEfDesignGroup model definition

  Defines the **VedEfDesignGroup** class that integrates all models for 5D exploration.
  This is the reusable model component containing physics models, constraints, and connections.

- ``1_setup_vedef_problem.py`` - Problem factory function

  Provides **setup_vedef_problem()** convenience function that creates a fully configured
  OpenMDAO Problem with default parameter values. Used by all analysis scripts for consistency.

  **Note:** These are application-specific integration files, not core library components.
  They connect the 5 parameters, 7 physics models/systems, and 10 constraints for this example.

  **Architecture Update (Nov 2025):** Refactored to use:

  - ``HighVoltageGeneratorSystem`` instead of simple HV window ExecComp
  - ``TorchFlowSystem`` instead of separate flow_rate and residence_time ExecComps
  - ``BrownianArcMobilityModel`` for physics-based mobility modeling
  - Explicit intermediate variables (T_0, breakdown_voltage, flow_velocity, etc.)

Main Example
~~~~~~~~~~~~

- ``example_operating_window_5d.py`` - 5D parameter sweep with parallel execution
- ``visualize_operating_window.py`` - Static matplotlib visualization of operating windows
- ``dashboard_operating_window.py`` - Interactive Plotly Dash dashboard
- ``generate_vedef_diagram.py`` - Mermaid diagram generation

Validation and Compliance
~~~~~~~~~~~~~~~~~~~~~~~~~~

- ``validate_arc002_compliance.py`` - Validates parameter names against ARC002 registry

  Checks that all critical design parameters:

  - Are defined in the ARC002 parameter registry
  - Are associated with the correct Equipment_Class (Generator, PlasmaTorch, etc.)
  - Follow the standard naming convention

  **Usage:**

  .. code-block:: bash

     python examples/VedEf_optim/validate_arc002_compliance.py

  **ARC002 Registry Utilities:** ``paroto/validation/arc002.py``

Utilities
~~~~~~~~~

- Uses ``paroto/utils/mermaid_generator.py`` for flowchart generation
- Uses ``paroto/utils/cytoscape_layout.py`` for interactive graph layouts

Physics Models
--------------

New Models Created
~~~~~~~~~~~~~~~~~~

1. Initial Temperature Model (``PulseInitialTemperatureModel``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Computes the initial gas temperature before each pulse, accounting for:

- **Energy-to-temperature conversion** via sub-model:

  - ``ConstantCpEnergyModel`` (Low fidelity, default)
  - ``CanteraEnergyModel`` (High fidelity, optional)

- Cylindrical thermal diffusion with characteristic time τ = (d_a/2)² / (4α)
- Exponential relaxation between pulses

**Location:** ``paroto/core/models/initial_temperature.py``

**Sub-models:** ``paroto/core/models/energy_to_temperature.py``

**Gallery:** ``examples/gallery/plot_initial_temperature_model_example.py``,
``plot_energy_to_temperature_example.py``

**Validation:** ``paroto/validation/validate_initial_temperature.py``

2. Coverage Model (``ArcCoverageModel``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Ensures complete gas treatment by the arc, as if the arc was painting the cross-flow gas:

- Constraint: π × e × d_a² / 4 × f ≥ v × S
- Outputs coverage fraction and constraint satisfaction
- Critical for ensuring all gas passes through the thermal treatment zone

**Location:** ``paroto/core/models/coverage.py``

**Gallery:** ``examples/gallery/plot_coverage_model_example.py``

**Validation:** ``paroto/validation/validate_coverage.py``

3. Arc Density Constraint Model (``ArcDensityConstraintModel``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Limits energy density in the arc volume:

- Constraint: ρ_E = E_p / V_arc < ρ_E_max
- Prevents arc instabilities from excessive energy concentration
- **Note:** Max energy density threshold requires experimental validation

**Location:** ``paroto/core/models/arc_density.py``

**Gallery:** ``examples/gallery/plot_arc_density_model_example.py``

4. Arc Mobility Model (``BrownianArcMobilityModel``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Models arc attachment point movement as Brownian motion:

- Affects reignition probability and thermal loading distribution
- Computes RMS displacement, mobility factor, and thermal spread factor
- Based on characteristic velocity and time between pulses

**Location:** ``paroto/core/models/arc_mobility.py``

**Gallery:** ``examples/gallery/plot_mobility_model_example.py``

**Validation:** ``validation/validate_mobility.py``

Existing Systems Integrated
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

5. High Voltage Generator System (``HighVoltageGeneratorSystem``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Models power electronics constraints:

- Operating window: f × V² × t_pulse / Z ≤ P_max
- Replaces simple ExecComp with full system model
- Outputs: operating_window_power, hv_operating_window_satisfied

**Location:** ``paroto/systems/generator.py``

6. Torch Flow System (``TorchFlowSystem``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Models gas dynamics:

- Mass conservation: ṁ = ρ × v × S
- Residence time calculation
- Reynolds number and pressure drop
- Replaces simple ExecComps with physics-based flow model

**Location:** ``paroto/systems/torch/flow.py``

Auto-Generated Architecture Diagrams
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The VeDeF example now includes automatic Mermaid diagram generation that introspects
the OpenMDAO problem structure to visualize the complete architecture:

- Run ``generate_auto_diagram.py`` to create diagrams showing actual data flow
- Shows parameters (green), models (blue), intermediates (orange), constraints (red)
- Eliminates manual diagram maintenance - always reflects current implementation

**Script:** ``examples/VedEf_optim/generate_auto_diagram.py``

**Generator:** ``utils/mermaid_generator.py`` - ``generate_problem_graph()`` function



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    <div class="sphx-glr-thumbcontainer" tooltip="This is an application-specific OpenMDAO Group for the VedEf operating window example. It integrates all models and constraints for the 5-parameter exploration.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_1_model_vedef_design_group_thumb.png
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  :ref:`sphx_glr_auto_examples_VedEf_optim_1_model_vedef_design_group.py`

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      <div class="sphx-glr-thumbnail-title">VedEf Design Group for 5-parameter operating window exploration.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates the hierarchical parameter visualization module, showing the 5 primary parameters, models, and 10 constraints in multiple formats: - Hierarchical Mermaid diagram (showing parameter levels and data flow) - NetworkX graph export (for external tools like yEd, Gephi, D3.js)">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_1_problem_generate_diagram_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_1_problem_generate_diagram.py`

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      <div class="sphx-glr-thumbnail-title">Generate hierarchical visualization for VedEf operating window models.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This module provides the canonical Problem instance for the VedEf operating window example. All analysis and optimization scripts should import and use setup_vedef_problem() to ensure consistency.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_1_setup_vedef_problem_thumb.png
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  :ref:`sphx_glr_auto_examples_VedEf_optim_1_setup_vedef_problem.py`

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      <div class="sphx-glr-thumbnail-title">VedEf Operating Window Problem Setup.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script attempts to find a working set of parameters by: 1. Starting with nominal values 2. Testing individual parameter variations 3. Diagnosing which constraints are violated">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_find_working_params_thumb.png
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  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_find_working_params.py`

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      <div class="sphx-glr-thumbnail-title">Find working VedEf parameters through systematic search.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example explores the 5-dimensional parameter space: - V (kV): High voltage - e (mm): Electrode gap distance - d_t (mm): Torch diameter - f (kHz): Pulse frequency - E_p (mJ): Energy per pulse">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_parameter_sweep_5d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_parameter_sweep_5d.py`

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      <div class="sphx-glr-thumbnail-title">Example: 5D Operating Window Exploration for VedEf Parameters.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Minimal test to diagnose VedEf model issues.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_simple_test_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_simple_test.py`

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      <div class="sphx-glr-thumbnail-title">Minimal test to diagnose VedEf model issues.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Smart parameter search for VedEf - targeting power and temperature constraints.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_smart_search_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_smart_search.py`

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      <div class="sphx-glr-thumbnail-title">Smart parameter search for VedEf - targeting power and temperature constraints.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Search focusing on achieving temperature rise for mobility constraint.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_temperature_focused_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_temperature_focused.py`

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      <div class="sphx-glr-thumbnail-title">Search focusing on achieving temperature rise for mobility constraint.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This dashboard provides real-time interactive exploration of the 5D parameter space with constraint visualization and model connectivity graph.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_3_analysis_dashboard_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_3_analysis_dashboard.py`

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      <div class="sphx-glr-thumbnail-title">Interactive Dash Dashboard for VedEf Operating Window Exploration.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Analyze power constraint violations to find near-feasible operating points.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_3_analysis_power_constraint_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_3_analysis_power_constraint.py`

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      <div class="sphx-glr-thumbnail-title">Analyze power constraint violations to find near-feasible operating points.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Recommend parameter ranges to achieve 25 kW target power.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_3_analysis_recommend_parameters_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_3_analysis_recommend_parameters.py`

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      <div class="sphx-glr-thumbnail-title">Recommend parameter ranges to achieve 25 kW target power.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script loads results from the parameter sweep and creates static matplotlib visualizations showing 2D slices through the 5D parameter space with constraint boundaries.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_3_analysis_visualize_window_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_3_analysis_visualize_window.py`

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      <div class="sphx-glr-thumbnail-title">Visualization of 5D Operating Window with 2D Slices.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This script introspects the problem graph to show: - Nodes organized by hierarchy level - Node types (parameters, models, constraints) - Connections between levels - Graph statistics">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_analyze_problem_graph_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_analyze_problem_graph.py`

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      <div class="sphx-glr-thumbnail-title">Analyze and visualize the VedEf problem graph structure.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates how to use the ARC002 validation utilities to check that a Problem&#x27;s parameters align with the ARC002 parameter registry.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_validate_arc002_compliance_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_validate_arc002_compliance.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Validate VedEf Problem Compliance with ARC002 Parameter Registry.</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Paroto Model Gallery
====================

This gallery contains minimal, standalone examples demonstrating individual models from the
paroto library. Each example is self-contained (20-30 lines) and can be run independently.

Quick Start
-----------

Each example can be run directly:

.. code-block:: bash

   python plot_initial_temperature_model_example.py
   python plot_coverage_model_example.py
   python plot_arc_density_model_example.py
   python plot_pulsed_breakdown_example.py
   python plot_mobility_model_example.py
   python plot_generator_system_example.py
   python plot_torch_flow_system_example.py

Gallery Index
-------------

1. Initial Temperature Model
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**File:** plot_initial_temperature_model_example.py

Demonstrates the ``PulseInitialTemperatureModel`` which computes initial gas temperature
accounting for:

- Energy-to-temperature conversion (via sub-model)
- Cylindrical thermal diffusion
- Relaxation between pulses

**Output:** Temperature evolution plot showing instantaneous jump and exponential decay.

1b. Energy to Temperature Conversion
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**File:** plot_energy_to_temperature_example.py

Demonstrates both energy conversion models:

- ``ConstantCpEnergyModel`` - Simple, constant specific heat (low fidelity)
- ``CanteraEnergyModel`` - Temperature-dependent properties (high fidelity)

**Output:** Comparison of both models showing temperature rise differences.

2. Coverage Model
~~~~~~~~~~~~~~~~~

**File:** plot_coverage_model_example.py

Demonstrates the ``ArcCoverageModel`` which ensures complete gas treatment by the arc:

- Coverage fraction calculation
- Constraint satisfaction check
- Recommendations for incomplete coverage

**Output:** Text summary of coverage analysis.

3. Arc Density Constraint Model
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**File:** plot_arc_density_model_example.py

Demonstrates the ``ArcDensityConstraintModel`` which limits energy density in the arc:

- Energy density calculation
- Constraint margin
- Safety assessment

**Output:** Text summary of energy density check.

4. Pulsed Breakdown Model
~~~~~~~~~~~~~~~~~~~~~~~~~~

**File:** plot_pulsed_breakdown_example.py

Demonstrates the ``RepetitivePulseBreakdownModel`` showing memory effects:

- Breakdown voltage for 1, 10, 100 pulses
- Transition from single-pulse to DC breakdown
- Memory effect from repetitive pulsing

**Output:** Text summary showing voltage reduction with pulse number.

5. Arc Mobility Model
~~~~~~~~~~~~~~~~~~~~~~

**File:** plot_mobility_model_example.py

Demonstrates the ``BrownianArcMobilityModel`` for arc displacement:

- RMS displacement calculation
- Mobility factor
- Thermal load spreading

**Output:** Text summary of arc movement characteristics.

6. High Voltage Generator System
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**File:** plot_generator_system_example.py

Demonstrates the ``HighVoltageGeneratorSystem`` for operating window constraints:

- Operating window power calculation
- Constraint satisfaction check
- Generator capability assessment

**Output:** Text summary of generator operating point.

7. Torch Flow System
~~~~~~~~~~~~~~~~~~~~~

**File:** plot_torch_flow_system_example.py

Demonstrates the ``TorchFlowSystem`` for flow calculations:

- Flow velocity computation
- Residence time calculation
- Pressure drop estimation

**Output:** Text summary of flow characteristics.

Related Resources
-----------------

Full Validation Scripts
~~~~~~~~~~~~~~~~~~~~~~~

For detailed temporal behavior and comprehensive validation:

- paroto/validation/validate_initial_temperature.py - 4 plots showing T(t) evolution
- paroto/validation/validate_pulsed_breakdown.py - Memory effects and transitions
- paroto/validation/validate_coverage.py - Coverage vs frequency analysis
- paroto/validation/validate_mobility.py - Displacement and lensing risk

Complete Examples
~~~~~~~~~~~~~~~~~

For integrated system examples:

- examples/VedEf_optim/example_operating_window_5d.py - 5D parameter sweep
- examples/VedEf_optim/dashboard_operating_window.py - Interactive dashboard
- examples/VDEF_optim/example_vdef_mdao.py - MDAO optimization

Model Documentation
-------------------

Each model class includes comprehensive docstrings with:

- Physics equations in LaTeX format
- Input/output descriptions
- Usage examples
- References to gallery and validation scripts

Requirements
------------

- Python 3.11+
- OpenMDAO >= 3.27
- NumPy
- Matplotlib (for examples with plots)
- paroto library installed (``pip install -e .`` from repo root)

Notes
-----

⚠️ **AI-Generated Equations Warning**: The physics equations in these models are AI-generated
and not yet validated for production use. They serve as demonstrations of the model framework
and should be validated against experimental data before use in real applications.

Contributing
------------

To add a new gallery example:

1. Create a minimal 20-30 line script
2. Include clear comments and output
3. Add entry to this README
4. Reference the gallery example in the model's docstring



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the ArcDensityConstraintModel which enforces energy density limits in the plasma arc to prevent excessive thermal loading.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_arc_density_model_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_arc_density_model_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Arc Density Constraint Model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the basic usage of ArcCoverageModel for gas coverage calculation without plotting, suitable for quick validation.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_coverage_model_basic_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_coverage_model_basic_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Arc Coverage Model (Basic)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the ArcCoverageModel which ensures complete gas treatment by the arc through coverage fraction calculation.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_coverage_model_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_coverage_model_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Arc Coverage Model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates both ConstantCpEnergyModel and CanteraEnergyModel for converting energy deposition to temperature increase in the plasma arc.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_energy_to_temperature_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_energy_to_temperature_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Energy to Temperature Conversion</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the HighVoltageGeneratorSystem which calculates operating window constraints for the pulse power generator.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_generator_system_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_generator_system_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">High Voltage Generator System</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the PulseInitialTemperatureModel which computes initial gas temperature accounting for energy-to-temperature conversion, cylindrical thermal diffusion, and relaxation between pulses.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_initial_temperature_model_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_initial_temperature_model_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Initial Temperature Model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the BrownianArcMobilityModel which calculates arc displacement due to Brownian motion and thermal effects.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_mobility_model_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_mobility_model_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Arc Mobility Model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the RepetitivePulseBreakdownModel which calculates breakdown voltage with memory effects from repetitive pulsing.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_pulsed_breakdown_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_pulsed_breakdown_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Pulsed Breakdown Model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the TorchFlowSystem which calculates flow velocity, residence time, and pressure drop in the plasma torch.">

.. only:: html

  .. image:: /auto_examples/gallery/images/thumb/sphx_glr_plot_torch_flow_system_example_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_gallery_plot_torch_flow_system_example.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Torch Flow System</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /auto_examples/VDEF_optim/index.rst
   /auto_examples/VedEf_optim/index.rst
   /auto_examples/gallery/index.rst


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`