Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecasting
2026-08-24 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explore a two-part method for predicting how complex systems change over time using equations called PDEs. First, they use a quantum reservoir computer (QRC) to make initial guesses about hidden system behaviors. Then, a physics-based neural network corrects these guesses to improve accuracy. Testing on both the Burgers and Kuramoto-Sivashinsky equations, they find that combining QRC with the correction step works better than QRC alone for the more chaotic Kuramoto-Sivashinsky system. Their results show that this hybrid approach can be a practical way to forecast simplified models depending on the problem.
quantum reservoir computingreduced-order modelingpartial differential equationsphysics-informed neural networksBurgers equationKuramoto-Sivashinsky equationchaotic systemslatent dynamicsRMSEmodel correction
Authors
Krishna Bhatia, Harsh, Shalini Devendrababu
Abstract
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.