A hybrid Physics-Informed Neural Network (PINN) framework coupled with HYSPLIT Lagrangian transport for atmospheric CO₂ flux inversion over Europe using the ICOS observation network.
- Decoupled formulation
C = H(α·F_fossil + β·F_bio)separates fossil and biospheric CO₂ fluxes by exploiting distinct spatial structures of priors (structural separation, not formal physical separation) - LOSO correlation r = 0.612 ± 0.015 on 19 rural ICOS stations
- 12× improvement over classical Bayesian inversion on identical data (LOSO 0.612 vs 0.033)
- r = 0.992 spatial correlation with the independent CAMS operational system (validation)
- MC Dropout uncertainty: α = 1.010 ± 0.078, β = 0.971 ± 0.023 (lower bounds)
- Temporal generalization tested: JJA withholding shows Δr = -0.002
| Document | Pages | Language | Description |
|---|---|---|---|
long_report.pdf |
45 | English | Complete technical report |
long_report_fr.pdf |
48 | Français | Rapport technique complet |
short_paper.pdf |
13 | English | AMT/ACP-style paper |
short_paper_fr.pdf |
13 | Français | Article style AMT/ACP |
Sources (Markdown) are also available in docs/ for editing/recompilation.
DATA.md— Data sources and preprocessingMETHODOLOGY.md— Mathematical formulationLIMITATIONS.md— Known limitations and caveatsPUBLISH.md— Publication and citation guide
pinn-inversion-co2/
├── docs/ # Reports (PDF + MD) and technical documentation
├── figures/ # 21 PNG figures used in reports
├── scripts/ # Python scripts for training, validation, ablation
├── results/ # (empty - see Zenodo archive for trained models)
├── references.bib # 30 bibliographic references
├── CITATION.cff # Citation metadata
├── LICENSE # MIT
├── README.md # This file
└── requirements.txt # Python dependencies
# Clone
git clone https://github.com/Mahamat-A/pinn-inversion-co2.git
cd pinn-inversion-co2
# Install dependencies
pip install -r requirements.txt
# Run V12b training (final configuration)
python scripts/v12b_filtered.py
# MC Dropout uncertainty quantification
python scripts/mc_dropout.py
# CAMS validation
python scripts/validation_cams.pySee docs/DATA.md for downloading required input data (ICOS, ERA5, CT2022, CAMS, EDGAR).
| Version | Innovation | LOSO r |
|---|---|---|
| V6 | Decoupled fossil/bio | 0.417 |
| V11 | Weekly footprints | 0.487 |
| V12b | Urban filtering (final) | 0.612 ± 0.015 |
- V14 (additive γ, 481 params) → LOSO 0.489 — over-parameterized
- V15 (80 regions, 961 params) → LOSO 0.133 — catastrophic collapse
- → Demonstrates the ~240-parameter ceiling at 19 stations × 52 weeks
- vs CAMS spatial: r = 0.992
- vs CT2022 spatial: r = 0.999
- Forward C_mod vs C_obs: r = 0.422 (best stations > 0.70)
This work is presented with explicit acknowledgment of its limitations:
-
Structural, not physical separation — The α/β decoupling exploits the distinct spatial structures of EDGAR (fossil) and VPRM (biosphere) priors. It is not a formal physical separation, which would require co-tracers like ¹⁴CO₂. If prior geographies are wrong, the system cannot detect it.
-
Urban station filtering — 6 of 25 stations excluded because HYSPLIT at 50 km cannot resolve urban plumes. This is a standard limitation of regional inversion systems at comparable resolution.
-
MC Dropout uncertainty — Reported intervals are lower bounds. Full Bayesian PINN would likely yield wider credible intervals (~±0.12 to ±0.15 instead of ±0.078).
-
Heatwave signal marginal — The JJA β reduction is directionally consistent with heatwave-induced sink reduction but only at 1.4σ — not a formal detection. Multi-year analysis (2018, 2020) needed for robust attribution.
See docs/LIMITATIONS.md and Section 8 of the long report for detailed discussion.
@software{mahamat2026pinn,
author = {Mahamat, Ali Ousmane},
title = {{PINN Inversion CO₂: A physics-informed framework
for European atmospheric CO₂ flux inversion}},
year = 2026,
publisher = {Zenodo},
version = {v1.1.0},
doi = {10.5281/zenodo.19638205},
url = {https://github.com/Mahamat-A/pinn-inversion-co2}
}- v1.1.0 (2026-04) — Reports added (EN/FR long + short), figures, expanded scripts, reformulated abstracts with explicit caveats on structural decoupling, MC Dropout calibration, urban filtering, and heatwave signal marginality
- v1.0.1 (2026-04) — Initial Zenodo release with core scripts
- v1.0.0 (2026-04) — Initial commit
Ali Ousmane Mahamat (Moud) — Indépendant (ex-GSMA, CNRS / URCA)
MIT — see LICENSE.
This work builds on my 2022 M2 thesis at GSMA, CNRS / Université de Reims Champagne-Ardenne. Thanks to ICOS, NOAA, ECMWF, JRC, and Copernicus for open data access.