APILaNet: Adaptive Physics-Informed Latent Network for Single-Sensor Forecasting

Forecasting river dynamics from sensor networks is often limited by sparse and noisy observations: in many catchments, operational monitoring provides only a single gauge and uncertain rainfall inputs. We propose an Adaptive Physics-Informed Latent Network (APILaNet), a trustworthy physics-constrained forecasting model that learns a 1-D latent dynamical field while enforcing mass conservation through a weak-form residual weighted by a learned, normalized space–time measure. The normalization stabilizes training across discretizations and concentrates constraint enforcement on transient, event-driven regimes. To improve identifiability under single-gauge supervision, APILaNet uses a monotone Lipschitz measurement layer to map latent states to observed levels, and a bounded event-aware scheduler that increases conservation and smoothness regularization during high-impact periods while preserving optimization stability. Across synthetic 1-D conservation benchmarks and multi-catchment hydrological forecasting, APILaNet improves accuracy relative to strong sequence baselines and yields markedly lower error during extreme events, with consistent gains in Nash–Sutcliffe efficiency.