La « boîte noire » de l’IA scientifique ne fait pas le poids face à une méthode vieille de 200 ans
Les transformées de Fourier révèlent comment un réseau neuronal profond apprend la physique complexe.
L’un des outils les plus anciens de la physique computationnelle – une technique mathématique vieille de 200 ans connue sous le nom de Analyse de Fourier — pourrait révéler des informations importantes sur la façon dont une forme d’intelligence artificielle appelée réseau neuronal profond apprend à effectuer des tâches impliquant une physique complexe telle que la modélisation du climat et de la turbulence, selon une nouvelle étude.
La découverte, faite par des chercheurs en génie mécanique de l’Université Rice, est décrite dans une étude librement accessible publiée dans la revue Nexus PNASqui est une publication sœur de Actes de l’Académie nationale des sciences.
« Il s’agit du premier cadre rigoureux pour expliquer et guider l’utilisation des réseaux de neurones profonds pour des systèmes dynamiques complexes tels que le climat », a déclaré l’auteur correspondant de l’étude, Pedram Hassanzadeh. « Cela pourrait considérablement accélérer l’utilisation de l’apprentissage scientifique en profondeur dans la science du climat et conduire à des prévisions plus fiables du changement climatique. »
Dans l’article, Hassanzadeh, Adam Sobel et Ashish Chattopadhyay, tous deux anciens étudiants, et Yivi Gauan, chercheur postdoctoral, détaillent leur utilisation de l’analyse de Fourier pour étudier un réseau neuronal d’apprentissage en profondeur qui a été formé pour reconnaître les flux complexes d’air dans le atmosphère. ou l’eau dans l’océan et prédire comment ces flux vont changer au fil du temps. Leur analyse, a déclaré Hassanzadeh, a révélé « non seulement ce que le réseau neuronal a appris, mais nous a également permis de relier ce que le réseau a appris directement à la physique du système complexe qu’il modélisait ».
Réseaux de neurones profonds Notoirement difficile à comprendre Ils sont souvent considérés comme des « boîtes noires ». « C’est l’une des principales préoccupations lors de l’utilisation de réseaux de neurones profonds dans des applications scientifiques. L’autre est la généralisabilité : ces réseaux ne peuvent pas fonctionner avec un système autre que celui pour lequel ils ont été formés. »
Le cadre analytique que son équipe présente dans l’article, a déclaré Hassanzadeh, « ouvre la boîte noire, nous permettant de regarder à l’intérieur pour comprendre ce que les réseaux ont appris et pourquoi, et nous permettant également de relier cela à la physique du système qui a été appris ». . »
Sobel, l’auteur principal de l’étude, a commencé la recherche en tant qu’étudiant de premier cycle à Rice et est maintenant étudiant diplômé à l’Université du Michigan.[{ » 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 machine learning tools for understanding neural networks have not shown much success for natural and engineering system applications, at least such that the findings could be connected to the physics,” Hassanzadeh said. “Our thought was, ‘Let’s do something different. Let’s use a tool that’s common for studying physics and apply it to the study of a neural network that has learned to do physics.”
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.
Hassanzadeh’s team first performed the Fourier transformation on the equation of its fully trained deep-learning model. Each of the model’s 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 didn’t 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. “It’s not doing anything crazy. It’s 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).