edl-ml

ML-augmented electric double layer simulator for ion adsorption at charged electrode interfaces.

edl-ml couples a rigorous Gouy-Chapman-Stern physics core (nonlinear Poisson-Boltzmann solver, Grahame equation, self-consistent series capacitance) with a PyTorch MLP surrogate that reproduces C_dl(E) at ~10⁴× speedup — fast enough to live inside a Bayesian optimisation loop, a digital-twin dashboard, or a parameter-identifiability study.

Scientific motivation

The differential capacitance of an electric double layer controls ion adsorption, electrosorption energetics, pseudocapacitive storage, and the kinetics of electrocatalytic reactions. The Gouy-Chapman-Stern model predicts C_dl(E) from first principles but requires an inner-loop bisection over the self-consistent potential split and is awkward to differentiate through. An ML surrogate trained on GCS data provides a smooth, analytically differentiable, vectorised alternative suitable for large-scale screening and gradient-based process design.

Architecture

┌─────────────────────────┐      ┌────────────────────────────┐
│  physics                │      │  ml                        │
│                         │      │                            │
│  • Poisson-Boltzmann    │──────▶  • Latin hypercube dataset │
│    (first-integral ODE) │  GCS │  • StandardScaler          │
│  • Grahame equation     │──────▶  • MLP (torch)             │
│  • GCS self-consistent  │ data │  • AdamW + cosine LR       │
│    potential split      │      │  • Optuna TPE HPO          │
└─────────────────────────┘      │  • MLflow logging          │
                                 │  • Kernel SHAP + permutation│
                                 └────────────────────────────┘
                                                │
                                                ▼
                                 ┌──────────────────────────────┐
                                 │  viz / cli / docs            │
                                 │  • parity plots              │
                                 │  • residual distributions    │
                                 │  • loss curves               │
                                 │  • SHAP beeswarm             │
                                 │  • edl CLI                   │
                                 │  • mkdocs-material site      │
                                 └──────────────────────────────┘

Quickstart

git clone https://github.com/defnalk/edl-ml
cd edl-ml
make install-dev

# end-to-end pipeline
edl generate --n-samples 1000 --output data/processed/dataset.parquet
edl train    --data data/processed/dataset.parquet \
             --checkpoint data/models/model.pt \
             --mlflow-experiment edl-ml
edl evaluate --checkpoint data/models/model.pt \
             --data data/processed/dataset.parquet \
             --figures-dir reports/figures

Single-point simulation (no ML)

edl simulate --concentration 0.1 --valence 1 \
             --e-min -0.4 --e-max 0.4 --n-points 81

Python API

from edl_ml.physics import GCSParameters, gouy_chapman_stern
import numpy as np

params = GCSParameters(
    concentration_mol_l=0.1,
    valence=1,
    stern_thickness_m=3e-10,
    stern_permittivity=6.0,
)
E = np.linspace(-0.4, 0.4, 201)
sigma, psi_d, C_dl = gouy_chapman_stern(params, E)

Results

Reference pipeline trained on 1 000 LHS samples × 81 potentials = 81 000 rows, split 70/15/15 at the sweep level (no feature leakage):

Metric	Units	Test value
RMSE	µF/cm²	< 0.15
MAE	µF/cm²	< 0.10
R²	—	> 0.999
Inference	points/sec	> 10⁶

Figures are generated by edl evaluate and saved to reports/figures/.

Validation

The physics core is validated against closed-form results:

• Debye length matches 1 / sqrt(2 N_A e² z² c / ε_r ε₀ k_B T) exactly across concentration and valence.
• Numerical PB profile matches the analytical Gouy-Chapman expression ψ(x) = (4 k_B T / z e) arctanh(tanh(z e ψ_d / 4 k_B T) · exp(-κ x)) to < 10⁻⁸ V over a 40-Debye-length domain.
• Grahame surface charge reproduced to 1 ppm relative tolerance across randomised diffuse-layer potentials (hypothesis-driven property test).
• Self-consistency |E − (ψ_H + ψ_d)| < 10⁻⁹ V at every electrode potential in the sampling box.

Documentation

Full API and guides: defnalk.github.io/edl-ml.

Citation

@software{edl_ml,
  author  = {Ertugrul, Defne Nihal},
  title   = {edl-ml: ML-augmented electric double layer simulator},
  year    = {2026},
  url     = {https://github.com/defnalk/edl-ml},
  version = {0.1.0}
}

License

MIT. See LICENSE.