<p>Efficient and uncertainty-aware modeling of dynamic systems is essential for design, analysis, health monitoring, and the operation of digital twins. This work introduces a Probabilistic Latent Dynamics Network (PLDN), which is designed to address the dual challenge of learning high-dimensional system dynamics while enabling scalable and timely uncertainty quantification. The proposed PLDN leverages an unsupervised Deep Operator Network (DeepONet) to perform dimension reduction, projecting high-dimensional system responses into a compact latent coefficient space that preserves essential dynamics. A key advantage of this representation is the use of a basis-function superposition structure that enables analytical and interpretable mapping from latent-to-physical space, eliminating the need for learning complex decoders. Built upon this reduced space, the probabilistic model captures both epistemic uncertainty via Monte Carlo Dropout and aleatoric uncertainty via heteroscedastic regression. The resulting framework supports closed-form propagation of predictive mean and variance, significantly reducing computational overhead during inference. The proposed PLDN emphasizes scalability and inference speed, making it highly suitable for large-scale, real-time digital twin applications. The proposed method is validated through three dynamic system case studies, demonstrating strong predictive performance along with substantial gains in efficiency for both training and uncertainty estimation. These properties position PLDN as a practical building block for enabling digital twins at scale.</p>