Solving multiscale dynamical systems by deep learning
CoRR(2024)
摘要
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary
differential equations (ODEs) with wide-ranging characteristic timescales,
arise across diverse fields of science and engineering, but their numerical
solvers often encounter severe efficiency bottlenecks. This paper introduces a
novel DeePODE method, which consists of a global multiscale sampling method and
a fitting by deep neural networks to handle multiscale systems. DeePODE's
primary contribution is to address the multiscale challenge of efficiently
uncovering representative training sets by combining the Monte Carlo method and
the ODE system's intrinsic evolution without suffering from the “curse of
dimensionality”. The DeePODE method is validated in multiscale systems from
diverse areas, including a predator-prey model, a power system oscillation, a
battery electrolyte auto-ignition, and turbulent flames. Our methods exhibit
strong generalization capabilities to unseen conditions, highlighting the power
of deep learning in modeling intricate multiscale dynamical processes across
science and engineering domains.
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