How to Implement ML Interpolation for Estimating Device Parameters Between Simulated Designs in SQuADDS

You can estimate device parameters between simulated designs in SQuADDS by using the Interpolator abstract class with concrete implementations like PhysicsInterpolator or GPInterpolator, which fit surrogate models on existing simulation data to predict missing design variables without running new expensive simulations.

SQuADDS (Superconducting Qubit Automated Design & Discovery System) provides a machine learning framework for interpolating between electromagnetic simulation results. When you need device parameters that fall between existing simulated points, you can leverage ML interpolation for estimating device parameters between simulated designs in SQuADDS to avoid costly re-simulation and accelerate your design workflow.

Understanding the SQuADDS Interpolation Architecture

The Analyzer Class

The Analyzer class, exposed via squadds/__init__.py, serves as the data backbone for all interpolation operations. It wraps simulation results into a pandas DataFrame (self.df) and provides query methods to filter the database. When initializing any interpolator, you must pass an Analyzer instance to give the model access to the underlying training data.

The Interpolator Abstract Base Class

All interpolation logic in SQuADDS inherits from the abstract Interpolator class defined in squadds/interpolations/interpolator.py. The base constructor (lines 8‑14) stores references to the analyzer and target parameters:

def __init__(self, analyzer, target_params):
    self.analyzer = analyzer
    self.target_params = target_params
    self.df = self.analyzer.df  # Direct access to simulation data

Subclasses must implement the get_design(self) method, which returns a pd.DataFrame containing the predicted device parameters.

Concrete Interpolator Implementations

SQuADDS provides several concrete implementations tailored to different physics regimes:

• PhysicsInterpolator (squadds/interpolations/physics.py): Leverages domain‑specific electromagnetic scaling laws and feature engineering via apply_physics_rules() to ensure predictions remain physically plausible (e.g., converting geometry to capacitance using known formulas).
• GPInterpolator (exposed via squadds/interpolations/utils.py): Wraps sklearn.GaussianProcessRegressor for non‑linear, probabilistic interpolation between design points, making it suitable for sparse datasets.

Step-by-Step Implementation Guide

Loading the Simulation Database

First, instantiate the Analyzer with your existing simulation results:

from squadds import Analyzer

analyzer = Analyzer.from_database("simulations.db")

This loads the electromagnetic simulation data into analyzer.df, making it available for model training.

Defining Target Parameters

Create a dictionary specifying the device specifications you need. These are the values you want to hit through interpolation:

target = {
    "freq_target_GHz": 5.2,
    "zeta_target_MHz": 3.0,
    "junction_cap_fF": 2.5,
}

Selecting and Configuring an Interpolator

Choose the interpolation strategy that best fits your physics. For physics‑aware estimation:

from squadds.interpolations.physics import PhysicsInterpolator

interp = PhysicsInterpolator(analyzer, target)

For a purely data‑driven Gaussian process approach:

from squadds.interpolations.utils import GPInterpolator

gp_interp = GPInterpolator(analyzer, target, kernel="RBF")

Generating the Interpolated Design

Call get_design() to fit the surrogate model and predict the missing geometric or electrical parameters:

design_df = interp.get_design()
print(design_df)

The returned pd.DataFrame contains the interpolated device parameters that fall between your simulated design points.

Code Examples for ML Interpolation

Physics-Based Interpolation

The PhysicsInterpolator leverages domain knowledge from squadds/interpolations/physics.py to ensure predictions respect electromagnetic scaling laws:

from squadds import Analyzer
from squadds.interpolations.physics import PhysicsInterpolator

# Load simulation database

analyzer = Analyzer.from_database("simulations.db")

# Define target specifications

target = {
    "freq_target_GHz": 5.2,
    "zeta_target_MHz": 3.0,
    "junction_cap_fF": 2.5,
}

# Initialize physics-based interpolator

interp = PhysicsInterpolator(analyzer, target)

# Generate interpolated design

design_df = interp.get_design()
print(design_df)

Source reference: The abstract Interpolator constructor is defined in [interpolator.py](https://github.com/lfl-lab/squadds/blob/master/squadds/interpolations/interpolator.py#L8-L14).

Gaussian Process Interpolation

For non‑linear interpolation between sparse simulation points, use the GPInterpolator exposed via squadds/interpolations/utils.py:

from squadds import Analyzer
from squadds.interpolations.utils import GPInterpolator

analyzer = Analyzer.from_database("simulations.db")
target = {"freq_target_GHz": 4.8, "chi_target_MHz": 1.8}

gp_interp = GPInterpolator(analyzer, target, kernel="RBF")
predicted = gp_interp.get_design()

Source reference: Helper functions and ML wrappers live in [utils.py](https://github.com/lfl-lab/squadds/blob/master/squadds/interpolations/utils.py); the GP class inherits from Interpolator.

Integrating with Layout Generation

The get_design() method returns a pandas DataFrame where each row represents a complete device design with geometric and electrical parameters. You can pass these parameters directly to layout generators in squadds/components/ (such as AirbridgeGenerator in squadds/components/airbridge/airbridge_generator.py) by converting the DataFrame row to a dictionary:

from squadds.components.airbridge.airbridge_generator import AirbridgeGenerator
from squadds.interpolations.physics import PhysicsInterpolator

analyzer = Analyzer.from_database("simulations.db")
target = {"freq_target_GHz": 5.0}
interp = PhysicsInterpolator(analyzer, target)

design = interp.get_design()
airbridge = AirbridgeGenerator(**design.iloc[0].to_dict())
gds = airbridge.generate()
gds.write("interpolated_airbridge.gds")

This demonstrates a seamless hand‑off from ML interpolation to GDS file generation.

Key Source Files and Implementation Details

File	Purpose	Link
squadds/interpolations/interpolator.py	Abstract base class that all interpolators derive from.	https://github.com/lfl-lab/squadds/blob/master/squadds/interpolations/interpolator.py
squadds/interpolations/physics.py	Physics‑guided interpolator implementation (features domain‑specific transformations).	https://github.com/lfl-lab/squadds/blob/master/squadds/interpolations/physics.py
squadds/interpolations/utils.py	Utility functions for preprocessing, scaling, and ML model wrappers.	https://github.com/lfl-lab/squadds/blob/master/squadds/interpolations/utils.py
squadds/__init__.py (exposes Analyzer)	Central object that loads simulation results into a pandas DataFrame.	https://github.com/lfl-lab/squadds/blob/master/squadds/__init__.py
squadds/components/... (e.g., airbridge_generator.py)	Layout generators that accept the interpolated design output.	https://github.com/lfl-lab/squadds/tree/master/squadds/components

These files together form the backbone of ML‑enabled interpolation in SQuADDS, allowing rapid estimation of device parameters without additional costly simulations.

Summary

• SQuADDS stores electromagnetic simulation results in a pandas DataFrame accessible via the Analyzer class.
• The Interpolator abstract base class in squadds/interpolations/interpolator.py defines the interface for all ML interpolation methods, storing self.analyzer and self.target_params.
• Concrete implementations like PhysicsInterpolator (physics‑aware) and GPInterpolator (Gaussian process) fit surrogate models on existing data to predict design variables between simulated points.
• The get_design() method returns a pd.DataFrame that integrates directly with layout generators for seamless GDS creation.
• This architecture eliminates the need for expensive re‑simulation when targeting parameter sets that fall between existing design points.

Frequently Asked Questions

What is the difference between PhysicsInterpolator and GPInterpolator in SQuADDS?

The PhysicsInterpolator leverages domain‑specific electromagnetic scaling laws and feature engineering from squadds/interpolations/physics.py to ensure predictions remain physically plausible (e.g., converting geometry to capacitance using known formulas). In contrast, the GPInterpolator uses a pure data‑driven Gaussian Process regressor from sklearn to model non‑linear relationships between design parameters without explicit physics constraints, making it more flexible but potentially less constrained by physical laws.

How does the Interpolator class handle missing or sparse simulation data?

The concrete interpolator implementations rely on preprocessing utilities in squadds/interpolations/utils.py (specifically prepare_dataframe()) to align columns, normalize numeric fields, and drop NaN values before model fitting. For sparse datasets, the GPInterpolator is particularly robust because Gaussian Process regression naturally handles uncertainty and can interpolate effectively with limited training points, while the PhysicsInterpolator uses analytical scaling laws to constrain the search space even when simulation data is sparse.

Can I use custom ML models with the SQuADDS interpolation framework?

Yes, you can extend the abstract Interpolator class defined in squadds/interpolations/interpolator.py to implement custom ML models. You must override the __init__(self, analyzer, target_params) method (which stores self.analyzer and self.target_params) and implement the get_design(self) method to return a pd.DataFrame with your predicted parameters. This allows integration of custom regressors (e.g., neural networks, random forests) while maintaining compatibility with the SQuADDS Analyzer and layout generation pipeline.

How do I integrate interpolated designs with physical layout generation in SQuADDS?

The get_design() method returns a pandas DataFrame where each row represents a complete device design with geometric and electrical parameters. You can pass these parameters directly to layout generators in squadds/components/ (such as AirbridgeGenerator in squadds/components/airbridge/airbridge_generator.py) by converting the DataFrame row to a dictionary using design.iloc[0].to_dict(). This creates a seamless workflow from ML interpolation to GDS file generation without manual parameter mapping.

{
  "mcpServers": {
    "instagit": {
      "command": "npx",
      "args": ["-y", "instagit@latest"]
    }
  }
}