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One model to solve them all: 2BSDE families via neural operators

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Listed:
  • Takashi Furuya
  • Anastasis Kratsios
  • Dylan Possamai
  • Bogdan Raoni'c

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.

Suggested Citation

  • Takashi Furuya & Anastasis Kratsios & Dylan Possamai & Bogdan Raoni'c, 2025. "One model to solve them all: 2BSDE families via neural operators," Papers 2511.01125, arXiv.org.
    • Handle: RePEc:arx:papers:2511.01125
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    References listed on IDEAS

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    1. Maximilien Germain & Mathieu Lauri`ere & Huy^en Pham & Xavier Warin, 2021. "DeepSets and their derivative networks for solving symmetric PDEs," Papers 2103.00838, arXiv.org, revised Jan 2022.
    2. Anastasis Kratsios & Ariel Neufeld & Philipp Schmocker, 2025. "Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programs," Papers 2508.14995, arXiv.org.
    3. Maximilien Germain & Mathieu Laurière & Huyên Pham & Xavier Warin, 2022. "DeepSets and their derivative networks for solving symmetric PDEs ," Post-Print hal-03154116, HAL.
    4. Dena Firoozi & Anastasis Kratsios & Xuwei Yang, 2025. "Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operators," Papers 2510.20017, arXiv.org.
    5. Luca Galimberti & Anastasis Kratsios & Giulia Livieri, 2022. "Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis," Papers 2210.13300, arXiv.org, revised Apr 2025.
    6. Nikolas Nüsken & Lorenz Richter, 2021. "Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space," Partial Differential Equations and Applications, Springer, vol. 2(4), pages 1-48, August.
    7. Huyên Pham & Xavier Warin & Maximilien Germain, 2021. "Neural networks-based backward scheme for fully nonlinear PDEs," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-24, February.
    8. William Lefebvre & Grégoire Loeper & Huyên Pham, 2023. "Differential learning methods for solving fully nonlinear PDEs," Digital Finance, Springer, vol. 5(1), pages 183-229, March.
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