Can Artificial Intelligence "formulate" Quantum Mechanics? An Illustration for Planck's Blackbody Radiation*

With the success of deep neural networks (DNN) in various applications, these methods have been uniformly proposed to solve scientific and engineering problems. To assess this premise, we investigated whether DNN formalisms can really formulate the underlying physics, by using the example of black body radiation (BBR). To resolve the “ultraviolet catastrophe” that incorrectly predicted black body emission of infinite energy at high frequency, Planck derived an “interpolation formula” which matched the experimental spectral intensity data using the assumption that radiation can only be emitted in quanta, connecting classical and quantum mechanics. To evaluate the ability of DNNs to similarly characterize BBR data, we evaluated multiple architectures, along with network dimensions, activation functions, learning rates, etc. Our analysis underscores the difficulty of extracting the physics of frequency correlation, independent of the amount of noise-free spectral data. By studying the functional forms that drive model predictions and examining the reasons for these difficulties, our findings, more broadly, exemplify the challenge of extracting physical laws using machine learning even with “hints”, and why physical intuition continues to be critical in scientific discoveries.