### Scientific AI’s black field isn’t any match for the 200-year-old methodology

*Fourier transforms reveal how the deep neural community learns advanced physics.*

Certainly one of computational physics’ oldest instruments, a 200-year-old mathematical approach generally known as Fourier evaluation, could reveal essential insights into how a type of synthetic intelligence known as a deep neural community learns to carry out duties involving advanced physics like local weather modeling. and turbulence, in keeping with a brand new research.

The invention by mechanical engineering researchers at Rice College is described in an open entry research revealed within the journal *PNAS nexus*a sister publication of *Proceedings of the Nationwide Academy of Sciences*.

That is the primary rigorous framework to clarify and information using deep neural networks for advanced dynamical techniques comparable to local weather, stated research correspondent creator Pedram Hassanzadeh. It might considerably speed up using scientific deep studying in local weather science and result in far more dependable local weather change projections.

Within the paper, Hassanzadeh, Adam Subel and Ashesh Chattopadhyay, each alumni, and Yifei Guan, a postdoctoral analysis affiliate, detailed their use of Fourier evaluation to review a deep studying neural community that was skilled to acknowledge advanced flows of air within the environment or water within the ocean and predict how these flows will change over time. Their evaluation revealed not solely what the neural community had realized, but in addition allowed us to straight relate what the community had realized to the physics of the advanced system it was modeling, Hassanzadeh stated.

Deep neural networks are notoriously obscure and are sometimes considered black bins, he stated. It is a main concern with utilizing deep neural networks in scientific purposes. The opposite is generalizability: these networks can’t work for a system apart from the one they had been skilled for.

Hassanzadeh stated the analytical framework introduced by his workforce within the paper opens up the black field, permits us to look into it to know what the networks have realized and why, and likewise permits us to narrate it to the physics of the system being realized.

Subel, the research’s lead creator, started the analysis as a Rice undergraduate and is now a graduate scholar at

” data-gt-translate-attributes=”[{” attribute=””>New York University. He said the framework could be used in combination with techniques for transfer learning to enable generalization and ultimately increase the trustworthiness of scientific deep learning.

While many prior studies had attempted to reveal how deep learning networks learn to make predictions, Hassanzadeh said he, Subel, Guan and Chattopadhyay chose to approach the problem from a different perspective.

The common

He said Fourier analysis, which was first proposed in the 1820s, is a favorite technique of physicists and mathematicians for identifying frequency patterns in space and time.

People who do physics almost always look at data in the Fourier space, he said. It makes physics and math easier.

For example, if someone had a minute-by-minute record of outdoor temperature readings for a one-year period, the information would be a string of 525,600 numbers, a type of data set physicists call a time series. To analyze the time series in Fourier space, a researcher would use trigonometry to transform each number in the series, creating another set of 525,600 numbers that would contain information from the original set but look quite different.

Instead of seeing temperature at every minute, you would see just a few spikes, Subel said. One would be the cosine of 24 hours, which would be the day and night cycle of highs and lows. That signal was there all along in the time series, but Fourier analysis allows you to easily see those types of signals in both time and space.

Based on this method, scientists have developed other tools for time-frequency analysis. For example, low-pass transformations filter out background noise, and high-pass filters do the inverse, allowing one to focus on the background.

Hassanzadehs team first performed the Fourier transformation on the equation of its fully trained deep-learning model. Each of the models approximately 1 million parameters act like multipliers, applying more or less weight to specific operations in the equation during model calculations. In an untrained model, parameters have random values. These are adjusted and honed during training as the algorithm gradually learns to arrive at predictions that are closer and closer to the known outcomes in training cases. Structurally, the model parameters are grouped in some 40,000 five-by-five matrices, or kernels.

When we took the Fourier transform of the equation, that told us we should look at the Fourier transform of these matrices, Hassanzadeh said. We didnt know that. Nobody has done this part ever before, looked at the Fourier transforms of these matrices and tried to connect them to the physics.

And when we did that, it popped out that what the neural network is learning is a combination of low-pass filters, high-pass filters and Gabor filters, he said.

The beautiful thing about this is, the neural network is not doing any magic, Hassanzadeh said. Its not doing anything crazy. Its actually doing what a physicist or mathematician might have tried to do. Of course, without the power of neural nets, we did not know how to correctly combine these filters. But when we talk to physicists about this work, they love it. Because they are, like, Oh! I know what these things are. This is what the neural network has learned. I see.

Subel said the findings have important implications for scientific deep learning, and even suggest that some things scientists have learned from studying machine learning in other contexts, like classification of static images, may not apply to scientific machine learning.

We found that some of the knowledge and conclusions in the machine learning literature that were obtained from work on commercial and medical applications, for example, do not apply to many critical applications in science and engineering, such as climate change modeling, Subel said. This, on its own, is a major implication.

Reference: Explaining the physics of transfer learning in data-driven turbulence modeling by Adam Subel, Yifei Guan, Ashesh Chattopadhyay and Pedram Hassanzadeh, 23 January 2023, *PNAS Nexus*.

DOI: 10.1093/pnasnexus/pgad015

Chattopadhyay received his Ph.D. in 2022 and is now a research scientist at the Palo Alto Research Center.

The research was supported by the Office of Naval Research (N00014- 20-1-2722), the National Science Foundation (2005123, 1748958) and the Schmidt Futures program. Computational resources were provided by the National Science Foundation (170020) and the National Center for Atmospheric Research (URIC0004).