Vascular homeostasis is the preferred state that blood vessels try to maintain against external mechanical and chemical stimuli. The vascular adaptive behavior around the homeostatic state is closely related to cardiovascular disease progressions such as arterial aneurysms. In this work, we develop a multi-physics computational framework that couples vascular growth & remodeling (G&R), wall mechanics and hemodynamics to describe the overall vascular adaptive behavior. The coupled simulation is implemented in patient-specific geometries to predict aneurysm progression. Lyapunov stability analysis of the governing equations for vascular adaptation is conducted to obtain a stabilizing criterion for aneurysm rupture. Also, to facilitate patient-specific computations, an algorithm is proposed to generate vascular homeostatic states by incorporating non-uniform residual stress and specifying optimal collagen fiber deposition angles. Since the accuracy and effectiveness of the computational models relies on properly estimating the unknown/hidden model parameters, we also demonstrate recent progress on improving data filtering techniques for inverse problems derived from model calibration. First, iterative ensemble Kalman filter (IEnKF) is applied to solve the inverse problems. The convergence of standard IEnKF is discussed and we show that the poor convergence of IEnKF is caused by the covariance shrinkage effect of the standard Kalman updates. An ensemble resampling based method is proposed to resolve this issue by perturbing the covariance shrinking via ensemble resampling and ensuring "correct" update directions by keeping the first and second moments of the resampling distribution unchanged. In the case of ill-posed inverse problems, we demonstrate that solution non-uniqueness can be overcome by incorporating additional constraints in a Bayesian inference framework. Constraints are imposed by defining a constraint likelihood function, and the method is demonstrated in both exact Bayesian and approximate Bayesian inference scenarios.