Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus
نویسندگان
چکیده
Abstract This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential equations (PDEs) by using an asymptotic expansion with deep learning-based algorithm. In particular, mathematical justification on is provided. Numerical examples Kolmogorov PDEs show effectiveness our method.
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ژورنال
عنوان ژورنال: Partial Differential Equations And Applications
سال: 2023
ISSN: ['2662-2971', '2662-2963']
DOI: https://doi.org/10.1007/s42985-023-00240-4