Monotone-Constrained Diffusion Models for Long-Horizon Production Forecasting
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.
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BibTeX
@misc{abraha2026monotoneconstrained,
title = {{Monotone-Constrained Diffusion Models for Long-Horizon Production Forecasting}},
author = {Temesgen Mikael Abraha and Yves Lucet},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22643},
eprint = {2609.22643},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22643},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monotone-Constrained Diffusion Models for Long-Horizon Production Forecasting
AU - Temesgen Mikael Abraha
AU - Yves Lucet
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22643
UR - https://arxiv.org/abs/2609.22643
AB - 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.
ER -