The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to
a series of computational techniques for numerical solutions. Although numerous latest …

This is the first of a two-part paper. We formulate a data-driven method for constructing finite-
volume discretizations of an arbitrary dynamical system's underlying Liouville/Fokker …

Numerous physics theories are rooted in partial differential equations (PDEs). However, the
increasingly intricate physics equations, especially those that lack analytic solutions or …

The eigenspectrum of the Koopman operator enables the decomposition of nonlinear
dynamics into a sum of nonlinear functions of the state space with purely exponential and …

We apply dynamic mode decomposition (DMD) to elementary cellular automata (ECA).
Three types of DMD methods are considered, and the reproducibility of the system dynamics …

We perform a Koopman spectral analysis of elementary cellular automata (ECA). By lifting
the system dynamics using a one-hot representation of the system state, we derive a matrix …

私たちの身のまわりで起こる種々の現象は多様な要素が複雑に結びついて生じるために,
それ自身を直接考察することは容易ではない. そこで人類は現象に強く関わる一部の性質だけに …