Decoder-DeepONet (DDON)

Model and code of Decoder DeepONet (DDON) for electric-field reconstruction from EFISH measurements. This model is specifically designed for vertically polarized EFISH signals (for a vertically polarized probe beam).

Citation

If you use DDON, the web tool, or results generated with this model, please cite:

Yang, Z., Sugeng, E. S., Alicherif, M. and Chng, T. L. (2026). An interpretable operator-learning model for electric field profile reconstruction in discharges based on the EFISH method. Plasma Sources Science and Technology, 35(2), 025035.

DOI: 10.1088/1361-6595/ae413f

Choose how to use DDON

1. Online Web App — no installation

Run DDON directly in a web browser:

Launch the DDON E-field Reconstruction Web App

The web app supports preprocessed CSV and MATLAB MAT inputs. Inference is performed locally in the browser using ONNX Runtime Web.

For DDON, the EFISH polarization is fixed to vertical.

2. Local Packaged Inference — lightweight ONNX Runtime

This mode is recommended if you want to run DDON locally, especially for predictions of multiple EFISH profiles, without installing TensorFlow:

pip install ddon-efish

View ddon-efish on PyPI

MATLAB MAT input (Recommended)

The recommended input is a MATLAB MAT file containing:

• Profile_Px.Px: $[z,P_x]$, size $(109,2)$
• Profile_Px.u: phase-mismatch parameter $u$, size $(109,1)$
• Profile_Px.Ex: normalized benchmark electric field $E_x$, size $(109,1)$, optional

A typical MATLAB input file can be prepared as:

Profile_Px.Px = [z(:), Px(:)];   % 109 x 2
Profile_Px.u  = u * ones(109,1); % 109 x 1
Profile_Px.Ex = Ex(:);           % 109 x 1, optional

save('Efish_vertical.mat', 'Profile_Px');

Python example using the MATLAB MAT file:

from ddon import DDON
from scipy.io import loadmat
import numpy as np

mat = loadmat(
    "Efish_vertical.mat",
    squeeze_me=True,
    struct_as_record=False
)

Profile = mat["Profile_Px"]

values = np.asarray(Profile.Px)       # [z, Px], shape (109, 2)
u = np.asarray(Profile.u).reshape(-1)[0]

model = DDON()

E = model.predict(
    values=values,
    u=u
)

print(E)

CSV input (optional)

from ddon import DDON
import numpy as np

values = np.loadtxt("input.csv", delimiter=",")

model = DDON()

E = model.predict(
    values=values,
    u=-0.35
)

print(E)

The verified ONNX model is downloaded automatically on first use and cached locally. This mode requires NumPy, SciPy, and ONNX Runtime.

3. Full Python Research Code — To be released

The full TensorFlow research implementation, including the original prediction, evaluation, and analysis workflow, is not included in the current public release and will be released separately in the future.

Full research implementation

The original TensorFlow research scripts are currently withheld from the public repository. The public web app and lightweight ONNX package remain available for inference.

Model file

The current DDON TensorFlow model is available from the DDON release:

Download DDON-v1.0.0.h5

For the original TensorFlow sample, place the model under the model log directory.

Input preprocessing and E-field prediction

1. Interpolate the EFISH profile to the recommended grid:

   $z/z_R = [-50:2:-24 , -22:1:-16 , -15:0.5:-1.5 , -1:0.2:1 , 1.5:0.5:15 , 16:1:22 , 24:2:50]$

   or

   $z/z_R = [-50:1:-2 , -1:0.2:1 , 2:1:50]$.

   The first grid is recommended and should be tried first.

2. Normalize the coordinate using $z_{\mathrm{scale}}=50$:

   $z' = (z/z_R)/50$,

   so that $z' \in [-1,1]$. Crop the input EFISH profile if the normalized/scaled range extends beyond this interval.

   Sampling points outside the experimental range may be set to zero. The input range should preferably cover at least $4.2\times\mathrm{FWHM}$ of the normalized EFISH profile.

3. Normalize the measured EFISH profile and, if available, the benchmark electric-field profile:

   $P_x^{\mathrm{norm}} = P_x/\max(P_x)$,

   $E_x^{\mathrm{norm}} = E_x/\max(E_x)$.

4. Estimate the physical phase-mismatch parameter:

   $u=\Delta k \times z_R$.

   Input the physical value of $u$ directly. Do not normalize $u$ before input.

   The current DDON model automatically applies the required internal normalization,

   $u' = u/(-1)$,

   before inference.

5. Import the preprocessed data and obtain the DDON prediction.

MATLAB input structure

Web and ONNX model

The browser and lightweight local modes use an ONNX version of DDON that is numerically verified against the TensorFlow model during the GitHub Actions conversion workflow.

License and copyright

© 2026 Zhijian Yang. All rights reserved.