Recently, two scientists have been awarded the Nobel Prize in Physics for their foundational discoveries and inventions that enable machine learning with artificial neural networks. These scientists are John Hopfield, an emeritus professor at Princeton University, and another distinguished scientist. Hopfield is renowned for his associative memory model, which laid the groundwork for the development of later artificial neural networks.

Hopfield's contributions extend beyond his theoretical models; he also has a deep understanding of computational science. His associative memory model not only helps computers recognize patterns but can also make predictions when data is incomplete. This capability is particularly important in many practical applications, such as image recognition, speech recognition, and natural language processing. Additionally, Hopfield's research has inspired many subsequent works, driving the development of the entire field.

The other laureate, often referred to as the 'Godfather of AI,' made significant contributions to the early research on artificial neural networks. His work not only advanced machine learning technologies but also laid the foundation for modern deep learning techniques. This scientist's contribution lies in proposing a training method for multi-layer neural networks, which significantly improved the performance of neural networks, enabling them to excel in complex tasks. His research findings have been widely applied in various fields, from autonomous vehicles to medical diagnostic systems.