# Accelerating Underground Pumped Hydro Energy Storage Scheduling with Decision-Focused Learning

arXiv: https://arxiv.org/abs/2512.20880 · HTML: https://mlsanity.com/paper/2512.20880/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [Mixed-Integer Nonlinear Differentiable Predictive Control for Underground Pumped Hydro Energy Storage Systems](https://mlsanity.com/paper/2609.17964/) (2026)

## Abstract (arXiv)

Underground pumped hydro energy storage (UPHES) systems play a critical role in grid-scale energy storage for renewable integration, yet optimal day-ahead scheduling remains computationally prohibitive due to nonlinear turbine performance characteristics and discrete operational modes. This paper presents a decision-focused learning (DFL) framework that addresses the computational-accuracy trade-off in UPHES day-ahead scheduling. The proposed methodology employs neural networks to predict penalty weights that guide recursive linearization, transforming the intractable MINLP into a sequence of convex quadratic programs trained end-to-end via differentiable optimization layers. Case studies across 19 representative Belgian electricity market scenarios demonstrate that the DFL framework effectively navigates the trade-off between solution quality and computation time. As a refiner, DFL adds approximately 1.2 s of post-processing to improve profit by 1.1% over piecewise MIQP baselines. As a real-time scheduler initialized with a fast global linear MIQP, the end-to-end time is 3.87 s (a 300-fold speedup) while maintaining profitability within 3.6% of the piecewise MIQP benchmark. An MIP-free deployment mode, which warm-starts from a historical schedule database and thus needs no mixed-integer solve, retains 92% of benchmark profit on held-out price scenarios.