Tsuyoshi Yoneda

Ryota Kawasumi, Tsuyoshi Yoneda

In this paper, we clarify the crucial difference between a deep neural network and the Fourier series. For the multiple Fourier series of periodization of some radial functions on $\mathbb{R}^d$, Kuratsubo (2010) investigated the behavior of the spherical partial sum and discovered the third phenomenon other than the well-known Gibbs-Wilbraham and Pinsky phenomena. In particular, the third one exhibits prevention of pointwise convergence. In contrast to it, we give a specific deep neural network and prove pointwise convergence.

Takuya Jinno, Takahito Mitsui, Kengo Nakai et al.

In recent years, the application of machine learning approaches to time-series forecasting of climate dynamical phenomena has become increasingly active. It is known that applying a band-pass filter to a time-series data is a key to obtaining a high-quality data-driven model. Here, to obtain longer-term predictability of machine learning models, we introduce a new type of band-pass filter. It can be applied to realtime operational prediction workflows since it relies solely on past time series. We combine the filter with reservoir computing, which is a machine-learning technique that employs a data-driven dynamical system. As an application, we predict the multi-year dynamics of the El Niño-Southern Oscillation with the prediction horizon of 24 months using only past time series.

Tsuyoshi Yoneda

We present a new inverse-time formulation of vortex stretching in the Navier-Stokes equations, based on a PDE framework inspired by score-based diffusion models. By absorbing the ill-posed backward Laplacian arising from time reversal into a drift term expressed through a score function, the inverse-time dynamics are formulated in a Lagrangian manner. Using a discrete Lagrangian flow of an axisymmetric vortex-stretching field, the score function is learned with a neural network and employed to construct backward-time particle trajectories. Numerical results demonstrate that information about initial positions is rapidly lost in the compressive direction, whereas it is relatively well preserved in the stretching direction.

Chikara Nakayama, Tsuyoshi Yoneda

We consider arbitrary bounded discrete time series originating from dynamical system with recursivity. More precisely, we provide an explicit construction of recurrent neural networks which effectively approximate the corresponding discrete dynamical systems.

Chikara Nakayama, Tsuyoshi Yoneda

We consider composite functions in the elementary algebraic framework. Without any use of the Fourier transform, we find almost periodic orbits which suitably characterizes certain composite functions. In particular, we provide special composite functions that tend asymptotically to almost periodic orbits.