Koji Koyamada

Koji Koyamada

In this study, we investigate the capability of physics-informed neural networks (PINNs) to preserve global physical structures by comparing standard PINNs with a Trefftz-based PINN (Trefftz-PINN). The target problem is the reproduction of mag-netic field-line structures in a helical fusion reactor configuration. Using identical training data sampled from exact solutions, we perform comparisons under matched mean squared error (MSE) levels. Visualization of magnetic field lines reveals that standard PINNs may exhibit structural collapse across magnetic surfaces even when the MSE is sufficiently small, whereas Trefftz-PINNs successfully preserve the global topology of magnetic field lines. Furthermore, the proposed framework is extended to computational fluid dynamics (CFD) problems, where streamline structures of veloc-ity fields are analyzed. Similar tendencies are observed, demonstrating that Trefftz-PINNs provide superior structure preservation compared to standard PINNs. These results indicate that minimizing numerical error alone does not guarantee physical consistency, and that constraining the solution space prior to learning is an effective strategy for physics-consistent surrogate modeling.

Mai Cong Hung, Ryohei Nakatsu, Naoko Tosa et al.

GANs (Generative adversarial networks) is a new AI technology that can perform deep learning with less training data and has the capability of achieving transformation between two image sets. Using GAN we have carried out a comparison between several art sets with different art style. We have prepared several image sets; a flower photo set (A), an art image set (B1) of Impressionism drawings, an art image set of abstract paintings (B2), an art image set of Chinese figurative paintings, (B3), and an art image set of abstract images (B4) created by Naoko Tosa, one of the authors. Transformation between set A to each of B was carried out using GAN and four image sets (B1, B2, B3, B4) was obtained. Using these four image sets we have carried out psychological experiment by asking subjects consisting of 23 students to fill in questionnaires. By analyzing the obtained questionnaires, we have found the followings. Abstract drawings and figurative drawings are clearly judged to be different. Figurative drawings in West and East were judged to be similar. Abstract images by Naoko Tosa were judged as similar to Western abstract images. These results show that AI could be used as an analysis tool to reveal differences between art genres.