Physics-Integrated Inference for Signal Recovery in Non-Gaussian Regimes

High-performance room-temperature sensing is often limited by non-stationary $1/f$ fluctuations and non-Gaussian stochasticity. In spintronic devices, thermally activated N\'eel switching creates heavy-tailed noise that masks weak signals, defeating linear filters optimized for Gaussian statistics. Here, we introduce a physics-integrated inference framework that decouples signal morphology from stochastic transients using a hierarchical 1D CNN-GRU topology. By learning the temporal signatures of N\'eel relaxation, this architecture reduces the Noise Equivalent Differential Temperature (NEDT) of spintronic Poisson bolometers by a factor of six (233.78 mK to 40.44 mK), effectively elevating room-temperature sensitivity toward cryogenic limits. We demonstrate the framework's universality across the electromagnetic and biological spectrum, achieving a 9-fold error suppression in Radar tracking, a 40\% uncertainty reduction in LiDAR, and a 15.56 dB SNR enhancement in ECG. This hardware-inference coupling recovers deterministic signals from fluctuation-dominated regimes, enabling near-ideal detection limits in noisy edge environments.