The Impact of Data-Driven Deep Learning Methods on Solving Complex Problems Once Beyond the Reach of Traditional Approaches
This blog is intended for mathematicians with limited background in physics and computational biology. Recent advancements in data-driven deep learning have transformed mathematics by enhancing—and sometimes surpassing—traditional methods. By leveraging datasets, deep learning techniques are redefining problem-solving and providing powerful tools to tackle challenges once considered impossible. This marks a new paradigm, driven by data, advanced computation, and adaptive learning, pushing the boundaries of what can be achieved. The profound impact of data-driven deep learning was recognized by the 2024 Nobel Prizes in Physics and Chemistry. The Nobel Prize in Physics honored John Hopfield and Geoffrey Hinton for their groundbreaking contributions to neural networks. Hopfield developed an early model of associative memory in neural networks, known as the Hopfield network , which is based on the concept of energy minimization. The energy function is represented by: \[E(\mathbf{...