Our vision is to develop novel artificial intelligence (AI) methods to model and understand complex systems, and more specifically the visual brain, Earth and climate systems, and their human interactions. Our approach to signal, image, and vision processing combines statistical learning theory with the understanding of the underlying physics, processes and biological vision. The problems posed in these disciplines require similar mathematical tools, where model inversion, uncertainty estimation, and causal inference play a central role. Our research on AI pivots around three main pillars: encoding domain knowledge in machine learning, understanding model representations and predictions, as well as learning causal relations from observational data.