Can a small neural surrogate trained on noisy synthetic observations become more consistent with the known greenhouse-gas accounting equation when that equation is included directly in the training objective?
The benchmark generates synthetic activity and emission-factor pairs. The noiseless target follows the auditable relationship:
emissions = activity × emission factor
The same one-hidden-layer neural network is trained twice from identical initial weights. The data-only model minimises prediction error against noisy observations. The physics-informed model minimises the same error plus a penalty for disagreement with the physical equation. Both are tested on held-out interpolation data and on an extrapolation range outside the training distribution.
Run the locked default experiment with:
ghg-scimlThe command writes machine-readable metrics to outputs/sciml_benchmark.json and a
prediction-versus-physical-target figure to figures/sciml_benchmark.svg.
With seed 2026, 600 synthetic training samples, 15% observation noise and a physics weight of 1.5, the physics-informed model reduced interpolation RMSE from 9.69 to 6.22 kg CO2e (35.8%). On the deliberate extrapolation split, RMSE fell from 455.98 to 400.56 kg CO2e (12.2%). The remaining extrapolation error is substantial. The result therefore supports the limited claim that the constraint improves consistency in this setup; it does not show that a small neural network can extrapolate reliably.
This is a deliberately small educational experiment. It demonstrates the mechanics of a physics-informed loss, deterministic evaluation and out-of-range testing. The data are synthetic; the governing equation is simple; and the neural network is implemented directly with NumPy for transparency. It is not evidence that the model is suitable for real emissions inventories, inverse problems, industrial control or scientific foundation models. A next study would use an established deep-learning framework, multiple random seeds, stronger baselines, partial/noisy physics, genuine spatiotemporal data and uncertainty-aware neural operators.