Variational Quantum Physics-Informed Neural Networks for Hydrological PDE-Constrained Learning with Inherent Uncertainty Quantification

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.

Beyond Weather Correlation: A Comparative Study of Static and Temporal Neural Architectures for Fine-Grained Residential Energy Consumption Forecasting in Melbourne, Australia

Accurate short-term residential energy consumption forecasting at sub-hourly resolution is critical for smart grid management, demand response programmes, and renewable energy integration. While weather variables are widely acknowledged as key drivers of residential electricity demand, the relative merit of incorporating temporal autocorrelation - the sequential memory of past consumption; over static meteorological features alone remains underexplored at fine-grained (5-minute) temporal resolution for Australian households. This paper presents a rigorous empirical comparison of a Multilayer Perceptron (MLP) and a Long Short-Term Memory (LSTM) recurrent network applied to two real-world Melbourne households: House 3 (a standard grid-connected dwelling) and House 4 (a rooftop solar photovoltaic-integrated household). Both models are trained on 14 months of 5-minute interval smart meter data (March 2023-April 2024) merged with official Bureau of Meteorology (BOM) daily weather observations, yielding over 117,000 samples per household. The LSTM, operating on 24-step (2-hour) sliding consumption windows, achieves coefficients of determination of R^2 = 0.883 (House 3) and R^2 = 0.865 (House 4), compared to R^2 = -0.055 and R^2 = 0.410 for the corresponding weather-driven MLPs - differences of 93.8 and 45.5 percentage points. These results establish that temporal autocorrelation in the consumption sequence dominates meteorological information for short-term forecasting at 5-minute granularity. Additionally, we demonstrate an asymmetry introduced by solar generation: for the PV-integrated household, the MLP achieves R^2 = 0.410, revealing implicit solar forecasting from weather-time correlations. A persistence baseline analysis and seasonal stratification contextualise model performance. We propose a hybrid weather-augmented LSTM and federated learning extensions as directions for future work.