Model predictive control can be considered a form of suboptimal control technique that works well if the system model is known and sufficient compute is available for online computations. In practice, we may not have exact knowledge of the system dynamics, and the computation may be too costly. To accelerate solution to these systems, we propose a learning-based framework that combines 1) function encoder to approximate the system dynamics for parametric families of differential equations in a geometrically interpretable way, and to rapidly identify dynamics online from a single trajectory in a zero-shot (retraining free) manner, and 2) differentiable predictive control for offline pretraining of parametric control policies. Efficacy of the proposed method is verified across a range of nonlinear systems with varying dimensionality. Time permitting, I will briefly motivate a physics-guided conditioning method for message-passing graph neural networks to achieve material-adaptive granular flows in low-data regimes.