Real-time digital twins rely on synchronizing virtual models with physical systems to monitor evolving states. A critical enabler for this synchronization is virtual sensing—the reconstruction of full-field transient responses from sparse sensor measurements. However, achieving accurate reconstruction is particularly challenging for systems governed by Nonlinear Partial Differential Equations (PDEs) [1]. Standard physics-informed learning approaches often treat time as a spatial dimension, violating temporal causality and leading to convergence issues in transient analysis. Furthermore, the accuracy of the solution is highly sensitive to measurement locations; arbitrary sensor configurations often fail to capture the essential energy of the evolving nonlinear system [2]. To address these limitations, we propose a novel framework that synergizes Optimal Sensor Placement (OSP) with a causality-aware, FEM-guided machine learning architecture. The methodology operates in three integrated stages. First, an OSP strategy identifies sensor locations that maximize the observability of the transient nonlinear modes. Second, to strictly enforce temporal causality, we embed a physics-based time-integration scheme (e.g., Newmark-beta) directly into the neural network’s loss function. This constraint ensures that the predicted state at any time step depends solely on the history of the system, effectively preventing non-physical error propagation. Finally, the network is initialized with global matrices from a baseline Finite Element Method (FEM), serving as a linear physical prior while the network learns the nonlinear residual operators. The framework is validated using numerical simulations and experimental data of systems exhibiting complex transient nonlinear behaviors. The results demonstrate that incorporating temporal causality constraints and optimal sensing significantly enhances reconstruction accuracy and stability compared to standard non-causal models. This study provides a robust, physics-faithful pathway for solving transient nonlinear PDEs in data-scarce applications.