Abstract: Multidisciplinary concurrent materials, geometry and manufacturing process optimization involves many computational challenges such as high-dimensionality associated with location dependency, material heterogeneity, multi-modal information, and nonlinear material behaviors such as large deformations and plasticity. The recent growth of using physics-based machine learning creates opportunities for incorporating data-driven methodologies with physical models into design. Furthermore, digital twin is an emerging technology in the era of Industry 4.0 that holds promises for real time optimization of manufacturing processes and quality control. We will present in this talk a digital twin framework with uncertainty quantification that facilitates a bidirectional information exchange between virtual and physical systems in complex manufacturing processes. Using laser directed-energy deposition (DED) as an example in additive manufacturing (AM), we will first present the development of a time-series machine learning (ML) model of DED process to predict temperatures across various spatial locations of the DED-built part while taking dynamic processing conditions as inputs. With the uncertainty quantification using Monte Carlo dropout methods and a reduced dimensional representation, we introduce a Bayesian Optimization (BO) method for Time Series Process Optimization. We will then present a simultaneous multi-step Robust Model Predictive Control (R-MPC) framework for real-time decision-making, using a multi-variate deep neural network (DNN), Time-Series Dense Encoder (TiDE), as the surrogate model, and quantile prediction to account for uncertainty associated with process disturbances. TiDE allows one-shot forward propagation and auto-differentiation for rapid decisions therefore proactive control over melt pool temperatures, while mitigating porosity defects by regulating laser power to maintain melt pool depth. Overall, the proposed R-MPC framework offers as a powerful tool for future Digital Twin applications and real-time