One model to solve them all: 2BSDE families via neural operators
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911246925692928 |
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| author | Furuya, Takashi Kratsios, Anastasis Possamaï, Dylan Raonić, Bogdan |
| author_facet | Furuya, Takashi Kratsios, Anastasis Possamaï, Dylan Raonić, Bogdan |
| contents | We introduce a mild generative variant of the classical neural operator model, which leverages Kolmogorov--Arnold networks to solve infinite families of second-order backward stochastic differential equations ($2$BSDEs) on regular bounded Euclidean domains with random terminal time. Our first main result shows that the solution operator associated with a broad range of $2$BSDE families is approximable by appropriate neural operator models. We then identify a structured subclass of (infinite) families of $2$BSDEs whose neural operator approximation requires only a polynomial number of parameters in the reciprocal approximation rate, as opposed to the exponential requirement in general worst-case neural operator guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One model to solve them all: 2BSDE families via neural operators Furuya, Takashi Kratsios, Anastasis Possamaï, Dylan Raonić, Bogdan Machine Learning Numerical Analysis Analysis of PDEs Probability Computational Finance We introduce a mild generative variant of the classical neural operator model, which leverages Kolmogorov--Arnold networks to solve infinite families of second-order backward stochastic differential equations ($2$BSDEs) on regular bounded Euclidean domains with random terminal time. Our first main result shows that the solution operator associated with a broad range of $2$BSDE families is approximable by appropriate neural operator models. We then identify a structured subclass of (infinite) families of $2$BSDEs whose neural operator approximation requires only a polynomial number of parameters in the reciprocal approximation rate, as opposed to the exponential requirement in general worst-case neural operator guarantees. |
| title | One model to solve them all: 2BSDE families via neural operators |
| topic | Machine Learning Numerical Analysis Analysis of PDEs Probability Computational Finance |
| url | https://arxiv.org/abs/2511.01125 |