Real-world engineering design and calibration often become slow, intractable and reduced in scope due to frequent iterations over high-dimensional expensive black-box (HEB) class of models. One way to mitigate this challenge is to incorporate multi-fidelity models with variable complexity and accuracy into the design framework. This paper proposes a machine learning based multi-fidelity modeling (MFM) and information-theoretic sequential sampling strategy for optimization, where the associated models can have complex discrepancies among each other. From the perspective of statistical learning, the advantages of MFM based optimization over a single high fidelity surrogate, specifically under complex constraints, are discussed with benchmark optimization problems involving noisy data. The proposed framework, based on modeling of the varied fidelity information sources via Gaussian processes, is augmented with efficient active learning strategies which involve sequential selection of optimal points in a multi-scale architecture. Key applications of this methodology are demonstrated on practical engineering problems such as high-dimensional design optimization of compressor rotor and calibration of expensive microstructure prediction model, where the proposed framework promises improved efficiency of the underlying processes.