Efficient hybrid explicit-implicit learning for multiscale problems
نویسندگان
چکیده
Splitting method is a powerful to handle application problems by splitting physics, scales, domain, and so on. Many algorithms have been designed for efficient temporal discretization. In this paper, our goal use concepts in designing machine learning and, at the same time, help incorporating data speeding them up. We propose assisted scheme which improves efficiency of meanwhile preserves accuracy. consider recently introduced multiscale algorithms, where problem solved on coarse grid. To approximate dynamics, only few degrees freedom are implicitly, while others explicitly. This concept allows identifying that need implicit treatment. we several strategies. First, part solution can be learned as it more difficult solve, explicit computed. provides speed-up incorporation approaches. Secondly, one design hybrid neural network architecture because handling parts requires much fewer communications among neurons done efficiently. Thirdly, solve grid component via PDEs or other approximation methods construct simpler networks solutions. discuss these options implement interpreting translation task. interpretation successfully enables us using Transformer since perform model reduction multiple time series learn connection between them. also find great platform predict with insufficient information target model: partially given through known approximates target. Our incorporate encode from two different then problems. conduct four numerical examples results show stable accurate.
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2022
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2022.111326