InFlow: entropic stochastic dual dynamic programming with HJB cross-certification for seasonal energy storage
Abstract
Seasonal reservoir operation requires optimization methods that remain reliable under strongly periodic and uncertain inflow dynamics. We present InFlow, a verification-oriented framework combining periodic stochastic dual dynamic programming (SDDP), entropic robustness, control-space Bellman annealing, and an independently discretized Hamilton-Jacobi-Bellman (HJB) benchmark. The entropic transition operator is interpreted as a KL-penalized worst-case expectation and linked to fixed-radius KL ambiguity sets through Lagrange duality. We establish a uniform soft-Bellman approximation bound and prove the validity of Gibbs-tilted SDDP cuts. The benchmark relies on a normalized seasonal Cox-Ingersoll-Ross inflow process whose positivity condition fails during the driest weeks, requiring explicit treatment of the degenerate boundary. Independent verification shows strong agreement between HJB storage gradients and HiGHS storage-balance duals, with water-value correlations of 0.995 and 0.996 for the standard and exact-cut-only implementations. Refining the HJB grid from 61^2 to 81^2 states changes the annual mean water value by only 0.6% and the peak value by less than 0.1%. Out-of-sample simulations based on 3,000 independent trajectories show that a robustness level of gamma=5 increases nominal mean cost by 4.6% while reducing CVaR90 by 11.2%. Under a dry-season stress scenario with inflows reduced by 40%, the mean-cost difference becomes statistically insignificant whereas CVaR90 improves by 11.5%. A robustness sweep confirms monotonicity of the risk-adjusted value. Finally, a two-reservoir cascade reproduces grid-oracle marginal water values with correlation 0.999 and recovers the predicted upstream-to-downstream value ratio of two. InFlow is intended as a transparent methodological benchmark rather than a calibrated operational reservoir model.
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BibTeX
@misc{affognona2026inflow,
title = {{InFlow: entropic stochastic dual dynamic programming with HJB cross-certification for seasonal energy storage}},
author = {Steeven B. Affognona and Babacar M. Ndiaye and Pierre Mendy and Cheikh M. F. Kebe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11339},
eprint = {2609.11339},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11339},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - InFlow: entropic stochastic dual dynamic programming with HJB cross-certification for seasonal energy storage
AU - Steeven B. Affognona
AU - Babacar M. Ndiaye
AU - Pierre Mendy
AU - Cheikh M. F. Kebe
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11339
UR - https://arxiv.org/abs/2609.11339
AB - Seasonal reservoir operation requires optimization methods that remain reliable under strongly periodic and uncertain inflow dynamics. We present InFlow, a verification-oriented framework combining periodic stochastic dual dynamic programming (SDDP), entropic robustness, control-space Bellman annealing, and an independently discretized Hamilton-Jacobi-Bellman (HJB) benchmark. The entropic transition operator is interpreted as a KL-penalized worst-case expectation and linked to fixed-radius KL ambiguity sets through Lagrange duality. We establish a uniform soft-Bellman approximation bound and prove the validity of Gibbs-tilted SDDP cuts. The benchmark relies on a normalized seasonal Cox-Ingersoll-Ross inflow process whose positivity condition fails during the driest weeks, requiring explicit treatment of the degenerate boundary. Independent verification shows strong agreement between HJB storage gradients and HiGHS storage-balance duals, with water-value correlations of 0.995 and 0.996 for the standard and exact-cut-only implementations. Refining the HJB grid from 61^2 to 81^2 states changes the annual mean water value by only 0.6% and the peak value by less than 0.1%. Out-of-sample simulations based on 3,000 independent trajectories show that a robustness level of gamma=5 increases nominal mean cost by 4.6% while reducing CVaR90 by 11.2%. Under a dry-season stress scenario with inflows reduced by 40%, the mean-cost difference becomes statistically insignificant whereas CVaR90 improves by 11.5%. A robustness sweep confirms monotonicity of the risk-adjusted value. Finally, a two-reservoir cascade reproduces grid-oracle marginal water values with correlation 0.999 and recovers the predicted upstream-to-downstream value ratio of two. InFlow is intended as a transparent methodological benchmark rather than a calibrated operational reservoir model.
ER -