Kenji Fukushima

Gert Aarts, Kenji Fukushima, Tetsuo Hatsuda et al.

The integration of deep learning techniques and physics-driven designs is reforming the way we address inverse problems, in which accurate physical properties are extracted from complex data sets. This is particularly relevant for quantum chromodynamics (QCD), the theory of strong interactions, with its inherent limitations in observational data and demanding computational approaches. This perspective highlights advances and potential of physics-driven learning methods, focusing on predictions of physical quantities towards QCD physics, and drawing connections to machine learning(ML). It is shown that the fusion of ML and physics can lead to more efficient and reliable problem-solving strategies. Key ideas of ML, methodology of embedding physics priors, and generative models as inverse modelling of physical probability distributions are introduced. Specific applications cover first-principle lattice calculations, and QCD physics of hadrons, neutron stars, and heavy-ion collisions. These examples provide a structured and concise overview of how incorporating prior knowledge such as symmetry, continuity and equations into deep learning designs can address diverse inverse problems across different physical sciences.

Yuji Hirono, Akinori Tanaka, Kenji Fukushima

Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability flow ODEs) sampling schemes remain unclear. We introduce a novel formulation of diffusion models using Feynman's path integral, which is a formulation originally developed for quantum physics. We find this formulation providing comprehensive descriptions of score-based generative models, and demonstrate the derivation of backward stochastic differential equations and loss functions.The formulation accommodates an interpolating parameter connecting stochastic and deterministic sampling schemes, and we identify this parameter as a counterpart of Planck's constant in quantum physics. This analogy enables us to apply the Wentzel-Kramers-Brillouin (WKB) expansion, a well-established technique in quantum physics, for evaluating the negative log-likelihood to assess the performance disparity between stochastic and deterministic sampling schemes.

Kenji Fukushima, Shotaro Shiba Funai, Hideaki Iida

Images of line drawings are generally composed of primitive elements. One of the most fundamental elements to characterize images is the topology; line segments belong to a category different from closed circles, and closed circles with different winding degrees are nonequivalent. We investigate images with nontrivial winding using the unsupervised machine learning. We build an autoencoder model with a combination of convolutional and fully connected neural networks. We confirm that compressed data filtered from the trained model retain more than 90% of correct information on the topology, evidencing that image clustering from the unsupervised learning features the topology.