Scientists at Rice University have found that Fourier analysis, a 200-year-old technique, can reveal crucial information about how deep neural networks (DNN) learn to perform tasks involving complex physics, such as climate and turbulence modelling.

The researchers discovered that the technique can connect what a DNN has learned to the physics of the complex system that the DNN is modelling. In the paper published in PNAS Nexus, the researchers used Fourier analysis to study a DNN that was trained to recognise complex flows of air and water and predict how those flows would change over time. By taking the Fourier transform of the equation, they found that what the neural network had learned was a combination of low-pass filters, high-pass filters and Gabor filters. The researchers claim that their findings could lead to more reliable climate change projections, by providing a rigorous framework to explain and guide the use of deep neural networks for complex dynamical systems such as climate. (Read more here)

The framework could also increase the trustworthiness of scientific deep learning by enabling generalisation. The researchers' method is different from those commonly used to understand neural networks, which they say have not shown much success for natural and engineering system applications. The team's approach was to use a tool that is common for studying physics and apply it to the study of a neural network that has learned to do physics. Fourier analysis is a favourite technique of physicists and mathematicians for identifying frequency patterns in space and time.

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🧱 Unlocking the Key to Quantum Computing

A Breakthrough in Heterostructure Layering

Researchers from the Penn State Center for Nanoscale Science (CNS) have discovered that a new form of heterostructure of layered two-dimensional (2D) materials could help quantum computing overcome key barriers to its widespread application. A topological qubit, based on topological superconductors, is expected to be more robust against the negative effect of a classical environment, which causes error in the operation of a quantum computer.

A topological qubit relates to topology in mathematics, where a structure is undergoing physical changes such as being bent or stretched, and still holds the properties of its original form. It is a theoretical type of qubit and has not been realized yet, but the basic idea is that the topological properties of certain materials can protect the quantum state from being disturbed by the classical environment. The researchers have taken a step in this direction by developing a type of layered material called a heterostructure. The heterostructure in the study consists of a layer of a topological insulator material and a superconducting material layer. However, such a topological insulator/superconductor heterostructure is difficult to create because different materials have different lattice structures.

Therefore, the researchers are using a synthesis technique known as confinement heteroepitaxy, which involves inserting a layer of epitaxial graphene between the gallium layer and the topological insulator material layer. This technique is being explored at Materials Research Science and Engineering Centers (MRSEC) and is potentially scalable, making it an attractive option for future quantum computing.