(untitled) (CSIAM Transactions on Applied Mathematics, 2026)
Data- and mechanism-driven hybrid computing refers to the integration of traditional mechanism-based computing with data-driven methods. In this article, we present three typical patterns of this emerging paradigm: (1) mechanism-driven model optimization via data-driven refinement, (2) data-driven model construction with physical constraints, and (3) alternating optimization of mechanism-driven and data-driven models. We present several concrete examples to illustrate how hybrid computing improves accuracy, efficiency, and robustness across a variety of computational tasks.