Dual-Encoder Physics-Informed Variational Autoencoders for robust forward and inverse SDE solving under noisy measurements

Real-world measurements for stochastic differential equations (SDEs) are often corrupted by heterogeneous or high-intensity noise, which poses significant challenges for deep learning-based solvers. In this study, we propose a Dual-Encoder Physics-Informed Variational AutoEncoder (DE-PIVAE) framework that explicitly disentangles latent noise from physical variables. Unlike previous single-encoder PI-VAE approaches, our model employs one encoder to learn the underlying clean physical signal and an additional noise encoder to capture the statistical properties of measurement noise from limited sensor data. The framework incorporates physical constraints into end-to-end training and enables more accurate reconstruction of the true system states under noisy observations. We consider a broad spectrum of noisy scenarios, including different noise types, varying noise intensities, partial sensor corruption, and noise distribution misspecification. Experimental results show that DE-PIVAE achieves superior performance compared to baseline solvers, with its advantage becoming more pronounced under higher noise.