Paper: Physics-Informed Convolutional Surrogates for Coupled Drift-Diffusion Equations: Reconstructing Full J-V Curves of Perovskite Solar Cells (Ozdincer, 2026)

Code: github.com/memo-ozdincer/perovskite-jv-surrogate

Dataset: huggingface.co/datasets/memo-ozdincer/perovskite-jv-comsol-150k

Model Description

A physics-constrained dilated convolutional network that reconstructs full current-voltage (J-V) curves of perovskite solar cells from 31 coupled drift-diffusion parameters spanning >20 orders of magnitude. The model is the Stage-2 component of a two-stage surrogate pipeline:

Stage 1 (Zhao et al., 2025 — included in matlab_stage1/): MATLAB neural networks predict scalar device metrics (V_oc, V_mpp, J_sc) from the 31 raw parameters.
Stage 2 (this model): A dilated 1D convolutional network reconstructs 8-point J-V curves from the 31 scaled parameters + Stage-1 scalar predictions.

The full 45-point J-V curve is recovered via monotone PCHIP interpolation from the 8 predicted points.

Architecture

Input: 31 params + 2 scalars (V_oc, V_mpp) = 33 features
  -> ParamMLP: 33 -> 256 -> 128 -> 128 (GELU, BatchNorm, Dropout=0.036)
  -> Broadcast across 8 voltage query points
  -> Concat with Gaussian RBF voltage encoding (18 bands, sigma=0.077)
  -> 8 x 256 sequence
  -> Conv Block 1: 256 -> 128, kernel=5, dilation=1 (residual)
  -> Conv Block 2: 128 -> 128, kernel=5, dilation=1 (residual)
  -> Conv Block 3: 128 -> 64,  kernel=5, dilation=2 (full receptive field > 8)
  -> Pointwise Linear: 64 -> 1
Output: 8-point J_sc-normalized J-V curve in [-1, 1]

Total parameters: ~0.49M

Physics-Constrained Loss

L = 0.98 * L_MSE + 0.005 * L_monotonicity + 0.005 * L_convexity + 0.01 * L_curvature

Monotonicity: Penalizes dJ/dV > 0 (current must decrease with voltage)
Convexity: Penalizes concave-up regions in the knee
Excess curvature: Bounds second finite differences to prevent oscillation

Performance

Evaluated on ~15k held-out test devices, averaged over 3 random seeds:

Metric	Mean	Median
R² (per-curve, ΔV-weighted)	0.9858 +/- 0.0009	0.9975 +/- 0.0004
MAE (A/m²)	4.75 +/- 0.26	2.96 +/- 0.34
RMSE (A/m²)	6.66 +/- 0.26	4.27 +/- 0.34
\|V_oc error\| (V)	0.0056 +/- 0.0058	0.00039 +/- 0.00016
\|I_sc error\| (A/m²)	0.59 +/- 0.53	0.36 +/- 0.62

Median V_oc error (0.39 mV) is an order of magnitude below experimental measurement uncertainty
>10,000x speedup over COMSOL finite-element simulation
Training: ~10 min on a single NVIDIA L40S GPU
Inference: ~10 s for ~15k devices

Per-Seed Breakdown

Seed	R² (median)	MAE (median)	V_oc error (median, mV)
123	0.9979	2.62	0.38
42	0.9976	2.96	0.23
456	0.9971	3.31	0.56

Repository Structure

perovskite-jv-surrogate/
├── README.md                           # This model card
├── checkpoint/
│   ├── hparams.yaml                    # Full hyperparameter configuration
│   ├── seed_123/
│   │   ├── best-model.ckpt            # PyTorch Lightning checkpoint
│   │   └── test_stats.json            # Test-set evaluation metrics
│   ├── seed_42/
│   │   ├── best-model.ckpt
│   │   └── test_stats.json
│   └── seed_456/
│       ├── best-model.ckpt
│       └── test_stats.json
├── preprocessing/
│   ├── seed_123/
│   │   ├── cnn_param_transformer.joblib    # Parameter normalization (sklearn)
│   │   ├── cnn_scalar_transformer.joblib   # Scalar normalization (sklearn)
│   │   └── cnn_preprocessed.npz            # Cached metadata (split indices, feature names)
│   ├── seed_42/
│   │   └── ...
│   └── seed_456/
│       └── ...
├── matlab_stage1/                      # Stage-1 scalar predictors (Zhao et al., 2025)
│   ├── NN_Perf.mat                     # Trained NN weights: V_oc, FF, PCE
│   ├── NN_RMPP.mat                     # Trained NN weights: MPP-related metrics
│   ├── NN_ROC.mat                      # Trained NN weights: additional metrics
│   ├── NN_predict.m                    # MATLAB inference script
│   └── NN_predict_v2.m                 # Alternative inference script
└── results/
    ├── champion_model.json             # Aggregated champion statistics
    ├── all_results.csv                 # Full 30-run ablation results (10 configs x 3 seeds)
    └── results_leaderboard.csv         # Ranked experiment performance

Usage

Inference with the training code

bash

git clone https://github.com/memo-ozdincer/perovskite-jv-surrogate.git
cd perovskite-jv-surrogate
pip install -r requirements.txt

bash scripts/run_paper_inference.sh \
    --params /path/to/params.txt \
    --voc /path/to/voc.txt \
    --vmpp /path/to/vmpp.txt \
    --checkpoint /path/to/best-model.ckpt \
    --cache-dir /path/to/preprocessing/seed_42 \
    --output-dir ./outputs

Loading the checkpoint directly

python

import torch
import sys
sys.path.insert(0, "src")
from train import PhysicsIVSystem

model = PhysicsIVSystem.load_from_checkpoint("best-model.ckpt", map_location="cpu")
model.eval()

# x: (batch, 33) tensor of scaled parameters + scalars
# v: (batch, 8) tensor of voltage query points
with torch.no_grad():
    j_pred = model(x, v)  # (batch, 8) normalized current predictions

Training Configuration

Parameter	Value
Optimizer	AdamW (beta1=0.9, beta2=0.999)
Learning rate	5.5e-3 (OneCycleLR, cosine to lr/150)
Weight decay	5.4e-5
Batch size	512
Precision	bf16-mixed (fp32 for Jacobian)
Max epochs	100
Early stopping	20 epochs patience on val loss
Gradient clipping	max_norm=1.0

MATLAB Stage-1 Models (Zhao et al.)

The matlab_stage1/ directory contains pre-trained MATLAB neural networks from Zhao et al. (2025), "Accelerating device characterization in perovskite solar cells via neural network approach," Applied Energy, 392:125922.

These models are NOT authored by the maintainer of this repository. They are included here for pipeline completeness and are redistributed with attribution. The Stage-1 models predict scalar device metrics (V_oc, FF, PCE) from the 31 raw COMSOL parameters using 3-layer ANNs with Bayesian regularization, achieving MSE < 3.1e-4 for V_oc. See the original publication for full details.

Usage (MATLAB):

matlab

load('NN_Perf.mat');
input = mapminmax('apply', X_P, PS_input);
output = net(input);
Perf = mapminmax('reverse', output, PS_output);
% Perf(1,:) = Voc, Perf(2,:) = FF, Perf(3,:) = PCE

Limitations

S-shaped curves: Devices with large interface band offsets (|ΔE_v^HP| >> k_BT) produce barrier-dominated transport that violates the monotone-sigmoid assumption. The model correctly refuses unphysical fits for these cases.
Extreme V_oc: Devices with V_oc < 0.5 V or V_oc > 1.2 V may have mislocated knee regions due to the fixed query-point grid.
High series resistance: R_s > 10³ Ohm cm² produces nearly linear J-V curves that the convexity penalty actively resists.
These failure modes affect <1% of devices and are physically interpretable (see paper Section 4.3).

Citation

bibtex

@article{ozdincer2026physics,
  title={Physics-Informed Convolutional Surrogates for Coupled Drift-Diffusion Equations: Reconstructing Full {J-V} Curves of Perovskite Solar Cells},
  author={Ozdincer, Mehmet},
  year={2026}
}

@article{zhao2025ae,
  title={Accelerating device characterization in perovskite solar cells via neural network approach},
  author={Zhao, X. and Huang, C. and Birgersson, E. and Suprun, N. and Tan, H.Q. and Zhang, Y. and Jiang, Y. and Shou, C. and Sun, J. and Peng, J. and Xue, H.},
  journal={Applied Energy},
  volume={392},
  pages={125922},
  year={2025}
}