{"ID":2846439,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.01125","arxiv_id":"2511.01125","title":"One model to solve them all: 2BSDE families via neural operators","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2511.01125","url_pdf":"https://arxiv.org/pdf/2511.01125v1","authors":"[\"Takashi Furuya\",\"Anastasis Kratsios\",\"Dylan Possamaï\",\"Bogdan Raonić\"]","published":"2025-11-03T00:27:13Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.AP\",\"math.NA\",\"math.PR\",\"q-fin.CP\"]","methods":"[]","has_code":false}