> [Researchers applied Fourier analysis] to the study of neural networks that have learned to do physics > [The researchers] detailed their use of to study a

> [Researchers applied Fourier analysis] to the study of neural networks that have learned to do physics > [The researchers] detailed their use of to study a deep learning neural network that was trained to recognize complex flows ... and to predict how [they] would change over time > «Deep neural networks are infamously hard to understand and are often considered "black boxes" ... That is one of the major concerns with using deep neural networks in scientific applications. The other is generalizability: These networks cannot work for a system that is different from the one for which they were trained. [... Instead, the analytic framework presented] opens up the black box, lets us look inside to understand what the networks have learned and why, and also lets us connect that to the physics of the system that was learned» > [For example, Fourier analysis allows to plot variations in temperatures abstracting from the superimposed variations of "night and day"] Original research article: Explaining the physics of transfer learning in data-driven turbulence modeling - https://academic.oup.com/pnasnexus/advance-article/doi/10.1093/pnasnexus/pgad015/6998042 https://academic.oup.com/pnasnexus/advance-article/doi/10.10... > Transfer learning (TL), which enables neural networks (NNs) to generalize out-of-distribution via targeted re-training, is becoming a powerful tool in scientific machine learning (ML) applications such as weather/climate prediction and turbulence modeling. Effective TL requires knowing 1) how to re-train NNs? and 2) what physics are learned during TL? Here, we present novel analyses and a framework addressing (1)-(2) for a broad range of multi-scale, nonlinear, dynamical systems. Our approach combines spectral (e.g., Fourier) analyses of such systems with spectral analyses of convolutional NNs, revealing physical connections between the systems and what the NN learns (a combination of low-, high-, band-pass filters and Gabor filters). Integrating these analyses, we introduce a general framework that identifies the best re-training procedure for a given problem based on physics and NN theory. As test case, we explain the physics of TL in subgrid-scale modeling of several setups of 2D turbulence. Furthermore, these analyses show that in these cases, the shallowest convolution layers are the best to re-train, which is consistent with our physics-guided framework but is against the common wisdom guiding TL in the ML literature. Our work provides a new avenue for optimal and explainable TL, and a step toward fully explainable NNs, for wide-ranging applications in science and engineering, such as climate change modeling