Variational Quantum Physics-Informed Neural Networks for Hydrological PDE-Constrained Learning with Inherent Uncertainty Quantification
Prasad Nimantha Madusanka Ukwatta Hewage, Midhun Chakkravarthy, Ruvan Kumara Abeysekara
TLDR
This paper introduces HQC-PINN, a quantum-classical physics-informed neural network for hydrological prediction, offering faster training and fewer parameters.
Key contributions
- Proposes HQC-PINN, integrating variational quantum circuits into PINNs for hydrological PDE-constrained learning.
- Uses quantum measurement for inherent uncertainty quantification, avoiding explicit Bayesian inference.
- Achieves ~3x faster convergence and ~44% fewer parameters than classical PINNs with competitive accuracy.
- Introduces quantum transfer learning and shows physics constraints mitigate barren plateaus in VQCs.
Why it matters
This paper pioneers quantum-enhanced physics-informed learning for hydrological prediction. It demonstrates significant computational efficiency gains, like faster training and fewer parameters, compared to classical methods. This work opens a new avenue for quantum advantage in environmental science, particularly for complex, uncertainty-laden problems like flood forecasting.
Original Abstract
We propose a Hybrid Quantum-Classical Physics-Informed Neural Network (HQC-PINN) that integrates parameterized variational quantum circuits into the PINN framework for hydrological PDE-constrained learning. Our architecture encodes multi-source remote sensing features into quantum states via trainable angle encoding, processes them through a hardware-efficient variational ansatz with entangling layers, and constrains the output using the Saint-Venant shallow water equations and Manning's flow equation as differentiable physics loss terms. The inherent stochasticity of quantum measurement provides a natural mechanism for uncertainty quantification without requiring explicit Bayesian inference machinery. We further introduce a quantum transfer learning protocol that pre-trains on multi-hazard disaster data before fine-tuning on flood-specific events. Numerical simulations on multi-modal satellite and meteorological data from the Kalu River basin, Sri Lanka, show that the HQC-PINN achieves convergence in ~3x fewer training epochs and uses ~44% fewer trainable parameters compared to an equivalent classical PINN, while maintaining competitive classification accuracy. Theoretical analysis indicates that hydrological physics constraints narrow the effective optimization landscape, providing a natural mitigation against barren plateaus in variational quantum circuits. This work establishes the first application of quantum-enhanced physics-informed learning to hydrological prediction and demonstrates a viable path toward quantum advantage in environmental science.
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