# Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecasting

arXiv: https://arxiv.org/abs/2608.23119 · HTML: https://mlsanity.com/paper/2608.23119/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2306.08827/) (2023)
- [Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes](https://mlsanity.com/paper/2304.11247/) (2023)
- [Physics-Informed Echo State Networks](https://mlsanity.com/paper/2011.02280/) (2020)
- [Automatic-differentiated Physics-Informed Echo State Network (API-ESN)](https://mlsanity.com/paper/2101.00002/) (2020)
- [Physics-consistent machine learning: output projection onto physical manifolds](https://mlsanity.com/paper/2502.15755/) (2025)
- [Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability](https://mlsanity.com/paper/2506.22335/) (2025)

## Abstract (arXiv)

We study a hybrid proposal--correction architecture for reduced-order PDE forecasting in which a pure-state quantum reservoir computer (QRC) predicts latent coefficient dynamics and a PINN-based physics-informed corrector (PIC) refines local rollout windows. The method is evaluated on Burgers and Kuramoto--Sivashinsky (KS), with KS as the primary chaotic benchmark. On KS, QRC+PIC consistently improves over QRC alone in RMSE, NRMSE, and PDE residual, while Burgers highlights a regime in which simple baselines remain strong. These results suggest that QRC proposals with local physics-informed correction are a viable benchmark-dependent reduced-order forecasting strategy.