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This research introduces Physics-SIMS-TS, a diffusion model specifically engineered to enforce monotonic decline constraints for oil and gas production forecasting, addressing the ill-posed nature of predicting long horizons from limited initial data. By integrating physical priors like isotonic projection with negative guidance against synthetic artifacts, the method achieves high accuracy while maintaining calibrated predictive intervals across thousands of wells. Although competitive with ensemble transformer baselines, the study highlights that enforcing domain-specific monotonicity comes at a negligible cost to mean squared error, offering a robust alternative for production-driven decision-making.
Monotone-Constrained Diffusion Models for Long-Horizon Production Forecasting
arXiv:2609.22643v1 Announce Type: new Abstract: Forecasting a long horizon from only the first observations of a sequence is ill-posed: many trajectories are consistent with the same short history. We study this problem in oil and gas production forecasting, where forecasts made after roughly the first fifth of a well's producing life drive development and abandonment decisions, and where a usable forecast must describe a monotone decline. We present Physics-SIMS-TS, a conditional diffusion forecaster that combines negative guidance against synthetic artifacts, decline-curve constraints and an isotonic projection applied during sampling, spatial training augmentation, and an ensembled stochastic sampler yielding a full predictive distribution. Across three jurisdictions and more than 35,000 wells, under a shared-space, validation-frozen protocol, Physics-SIMS-TS is the most accurate diffusion forecaster in the comparison and is competitive with, but not superior to, ensembled transformer forecasters. Its forecasts are monotone by construction at a cost of at most 0.5% in mean squared error, and its trajectory ensemble yields calibrated intervals after one dispersion factor is fitted per jurisdiction. On six standard benchmarks a reversible-instance-normalization variant of the backbone is the leading diffusion baseline. We also quantify four protocol choices on which the measured ranking depends. Code and evaluation artifacts are released.
Abstract:Forecasting a long horizon from only the first observations of a sequence is ill-posed: many trajectories are consistent with the same short history. We study this problem in oil and gas production forecasting, where forecasts made after roughly the first fifth of a well's producing life drive development and abandonment decisions, and where a usable forecast must describe a monotone decline. We present Physics-SIMS-TS, a conditional diffusion forecaster that combines negative guidance against synthetic artifacts, decline-curve constraints and an isotonic projection applied during sampling, spatial training augmentation, and an ensembled stochastic sampler yielding a full predictive distribution. Across three jurisdictions and more than 35,000 wells, under a shared-space, validation-frozen protocol, Physics-SIMS-TS is the most accurate diffusion forecaster in the comparison and is competitive with, but not superior to, ensembled transformer forecasters. Its forecasts are monotone by construction at a cost of at most 0.5% in mean squared error, and its trajectory ensemble yields calibrated intervals after one dispersion factor is fitted per jurisdiction. On six standard benchmarks a reversible-instance-normalization variant of the backbone is the leading diffusion baseline. We also quantify four protocol choices on which the measured ranking depends. Code and evaluation artifacts are released.
34 pages, 4 figures. Under review at the Journal of Machine Learning Research. Extended version of a paper at Canadian AI 2026 (PMLR 318, pp. 332-341)
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2609.22643 [cs.LG]
(or arXiv:2609.22643v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.22643 arXiv-issued DOI via DataCite (pending registration)
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