Parametric Frequency Sweep (PFS)#

NeurEco’s Parametric Frequency Sweep (PFS) solution builds models that predict complex-valued frequency responses based on input parameters. PFS is designed for frequency domain modeling, parametric model order reduction, and transfer function interpolation.

On this page

What PFS Solves#

PFS models learn the relationship between:

  • Input parameters (frequency + design variables) -> Complex frequency response

This is particularly useful for:

  • Electromagnetic simulations: Predicting S-parameters, antenna responses, filter characteristics

  • Structural dynamics: Frequency response functions (FRFs), transfer functions

  • Acoustic modeling: Sound transmission, vibration analysis

  • Model order reduction: Creating fast-running surrogate models from expensive frequency sweeps

Key Characteristics#

Complex-Valued Outputs

Unlike other NeurEco templates, PFS models output complex numbers (magnitude and phase), making them suitable for frequency domain analysis.

Rational Function Approximation

PFS uses rational functions internally, which naturally capture poles and zeros in frequency response data. The denominator size indicates model complexity.

First Column = Frequency

The first column of input data must always be the frequency — this is a strict requirement, not optional. Even when evaluating at a single constant frequency, the frequency column must be present. Additional columns contain design parameters.

When to Use PFS#

Use PFS When

Consider Alternatives When

Outputs are complex-valued (magnitude + phase)

Outputs are real-valued only

Frequency is a key input variable

No frequency dependence

Data exhibits resonant behavior (poles/zeros)

Response is smooth and simple

You need to interpolate frequency responses

You need time-domain predictions

File Extension#

PFS models use the .efnn extension (e.g., my_model.efnn).

Getting Started#

Quick Example#

from NeurEco import NeurEcoFrequential as Frequential
import numpy as np

# Load data (frequency + parameters -> complex response)
x_train = np.load('inputs_train.npy')   # Shape: (n_samples, n_inputs), first col = frequency
y_train = np.load('targets_train.npy')  # Shape: (n_samples, n_outputs), dtype: complex128

# Build model
model = Frequential.PFS()
config = Frequential.PFSBuildConfig(
    input_data=x_train,
    output_data=y_train,
    write_model_to="./my_pfs_model.efnn",
)
model.build(config)

# Evaluate
predictions = model.evaluate(x_test)
print(f"Output dtype: {predictions.dtype}")  # complex128