Complex Algorithms for Data-Driven Model Learning in Science and Engineering

Abstract

In their first centuries, scientific and engineering develop-ments were dominated by empirical understanding which encapsulated the first paradigm of scientific discovery. After the Renaissance, the scientific revolution and the develop-ment of calculus led to a new scientific viewpoint wherebyphysical principles, laws of nature, and engineering models were established by proposing new theoretical constructs thatcould be verified through specific experiments. This was thesecond paradigm of scientific discovery. More recently, thecomputational era, or the third paradigm of discovery, has allowed us to solve complex and nonlinear scientific and engi-neering problems that were beyond our analytically tractable methodologies. Today, there is a new fourth paradigm ofdiscovery, which is a data-driven science and engineering framework whereby complex models and physical laws are directly inferred from data.