  Stochastic differential equation (SDE in short) solvers find numerous
applications across various fields. However, in practical simulations, we
usually resort to using Ito-Taylor series-based methods like the Euler-Maruyama
method. These methods often suffer from the limitation of fixed time scales and
recalculations for different Brownian motions, which lead to computational
inefficiency, especially in generative and sampling models. To address these
issues, we propose a novel approach: learning a mapping between the solution of
SDE and corresponding Brownian motion. This mapping exhibits versatility across
different scales and requires minimal paths for training. Specifically, we
employ the DeepONet method to learn a nonlinear mapping. And we also assess the
efficiency of this method through simulations conducted at varying time scales.
Additionally, we evaluate its generalization performance to verify its good
versatility in different scenarios.
