Title: APILaNet: Adaptive Physics-Informed Latent Network for Single-Sensor Forecasting
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Physics-informed learning, conservation laws, adaptive loss weighting, latent field, monotone neural mapping, time-series forecasting

Abstract: Forecasting conservation-governed dynamics is often constrained by sparse sensing: in practice, we may have only a single downstream sensor and noisy exogenous variables. In this work we design an Adaptive Physics-Informed Latent Network (APILaNet) that learns a latent field and enforces conservation of physics law in the weak form using a learned, normalized space--time measure. Normalization makes physics enforcement insensitive to quadrature resolution and concentrates it on transient violations. A monotone, Lipschitz measurement layer maps latent variables to observed targets, improving identifiability from a single sensor. An adaptive, bounded scheduler scales the physics and smoothness loss terms with meaningful representations, emphasizing conservation of physics laws during events while preserving training stability. Learning a space-time measure for weak-form enforcement, combined with a monotone mapping and adaptive scheduling, enables accurate, data-efficient single-sensor forecasting in physics-governed systems. We evaluate APILaNet through a hydrological case study, APILaNet outperforms strong sequence baselines and reduces MSE during extreme events, while improving Nash--Sutcliffe efficiency. Code will be released upon acceptance.

TL;DR: A physics-informed latent network with adaptive weighting and a learned weak-form measure enables robust single-sensor forecasting under sparse sensing, outperforming SOTA models