Image relighting has emerged as a problem of significant research interest inspired by augmented reality applications. Physics-based traditional methods, as well as black box deep learning models, have been developed. The existing deep networks have exploited training to achieve a new state of the art; however, they may perform poorly when training is limited or does not represent problem phenomenology, such as the addition or removal of dense shadows. We propose a model which enriches neural networks with physical insight. More precisely, our method generates the relighted image with new illumination settings via two different strategies and subsequently fuses them using a weight map (w). In the first strategy, our model predicts the material reflectance parameters (albedo) and illumination/geometry parameters of the scene (shading) for the relit image (we refer to this strategy as intrinsic image de-composition (IID)). The second strategy is solely based on the black box approach, where the model optimizes its weights based on the ground-truth images and the loss terms in the training stage and generates the relit output directly (we refer to this strategy as direct). While our proposed method applies to both one-to-one and any-to-any relighting problems, for each case we introduce problem-specific components that enrich the model performance: 1) For one-to-one relighting we incorporate normal vectors of the surfaces in the scene to adjust gloss and shadows accordingly in the image. 2) For any-to-any relighting, we propose an additional multiscale block to the architecture to enhance feature extraction. Experimental results on the VIDIT 2020 and the VIDIT 2021 dataset (used in the NTIRE 2021 relighting challenge) reveals that our proposal can outperform many state-of-the-art methods in terms of well-known fidelity metrics and perceptual loss.