An Algebra of Machine Learners with Applications

Abstract

Machine learning (ML) methods are increasingly being applied to solve complex, data-driven problems in diverse areas, by exploiting the physical laws derived from first principles such as thermal hydraulics and the abstract laws developed recently for data and computing infrastructures. These physical and abstract laws encapsulate, typically in compact algebraic forms, the critical knowledge that complements data-driven ML models. We present a unified perspective of these laws and ML methods using an abstract algebra $(\mathcal{A}; \oplus , \otimes )$, wherein the performance estimation and classification tasks are characterized by the additive ⊕ operations, and the diagnosis, reconstruction, and optimization tasks are characterized by the difference ⊗ operations. This abstraction provides ML codes and their performance characterizations that are transferable across different areas. We describe practical applications of these abstract operations using examples of throughput profile estimation tasks in data transport infrastructures, and power-level and sensor error estimation tasks in nuclear reactor systems.