Research

A study extending the approximation theorem of the conventional Fourier Neural Operator to non-Markovian processes and proposing an improved architecture for this purpose has been published in the Journal of Scientific Computing. In this study, the research team demonstrated, based on the ...

To improve the efficiency of Monte Carlo integration, this study proposes a machine learning algorithm for stratified sampling that divides the domain space based on the integrand's value, analogous to Lebesgue integration. By utilizing neural networks to learn complex isocontours and prec...

This research presents a new analytical framework for nonlinear stochastic partial differential equations with nonlocal diffusion and spatially correlated noise. By introducing a new condition on the random noise correlation, it significantly enlarges the range of nonlinear phenomena that ...

This work mathematically characterizes the existence and properties of Magnetohydrostatic (MHS) equilibrium states via the vanishing resistivity limit of resistive magnetic relaxation equations subject to stochastic forcing. The "magnetic relaxation process" proposed by H. K. Moffatt is a ...

 Traditional fluctuation–response relations break down far from equilibrium, leaving few general tools to predict how strongly a system reacts to small changes. In this study, we present a set of mathematical inequalities that connect fluctuations of physical quantities to their respo...