Metal additive manufacturing (AM) offers tremendous benefits in producing intricately shaped parts and customized microstructures and properties of the final products, promoting its wide acceptance across various industries. The phase-field (PF) method for simulating microstructure evolution during metal AM has drawn increased attention due to its physics-based formulation and thermodynamically-consistent foundation. The PF method models the microstructure evolution by solving a set of governing partial differential equations (PDE). However, classic discretization methods like the finite difference method can be computationally expensive due to sufficiently small mesh size required, which not only brings challenges to forward simulation of a realistic physical domain (e.g., >1 mm) but also makes inverse design and control of microstructure intractable. To accelerate the forward PF simulation, we will discuss several approaches. First, a high-performance implementation of the PF method based on Google JAX is introduced, where GPU is used to boost the performance by 10-100 times when compared to CPU. Second, we show a physics-embedded graph network (PEGN) [1] approach, where an elegant graph representation of the grain structure is used to coarsen the discretization and achieve acceleration. Third, a composable deep learning surrogate model is proposed for large-scale PF simulation, e.g., an unprecedented 64-layer simulation of a 2 mm^3 cube for a powder bed fusion AM process. The inverse design/control of microstructure will be formulated under the framework of PDE-constrained learning. Design parameters of this optimization problem can live in a high-dimensional space, such as time-dependent manufacturing process parameters, e.g., variable laser power discretized in time-series format, parametrized with a neural network. The PDE-constrained learning problem will be effectively solved by gradient-based optimization algorithms, where gradients will be computed by differentiable programming method. When computing the gradients, several approaches will be compared, such as the continuous adjoint method (late discretization) and the discrete adjoint method (early discretization). A checkpointing strategy is implemented to avoid memory issue.