好色视频 学术报告[2025]158号

(高水平大学建设系列报告1259号)

报告题目：A derivative-free localized stochastic method for very high-dimensional semi-linear parabolic PDEs

报告人：苏必豪 副研究员（海南大学）

报告时间：2025年12月26日上午10:30-11:30

报告地点：汇文楼2433

报告内容：We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semi-linear parabolic PDEs. The efficiency of the proposed method is built upon four essential components: (i) a martingale formulation of the forward-backward stochastic differential equation (FBSDE); (ii) a small scale stochastic particle method for local linear regression (LLR); (iii) a decoupling strategy with a matrix-free solver for the weighted least-squares system used to compute ∇u; (iv) a Newton iteration for solving the univariate nonlinear system in u. Unlike traditional deterministic methods that rely on global information, this localized computational scheme not only provides explicit pointwise evaluations of u and ∇u but, more importantly, is naturally suited for parallelization across particles. In addition, the algorithm avoids the need for spatial meshes and global basis functions required by classical deterministic approaches, as well as the derivative-dependent and lengthy training procedures often encountered in machine learning. More importantly, we rigorously analyze the error bound of the proposed scheme, which is fully explicit in both the particle number M and the time step size Δt. Numerical results conducted for problem dimensions ranging from d=100 to d=10000 consistently verify the efficiency and accuracy of the proposed method. Remarkably, all computations are carried out efficiently on a standard personal computer, without requiring any specialized hardware. These results confirm that the proposed method is built upon a principled design that not only extends the practical solvability frontier of ultra-high dimensional PDEs but also maintains rigorous error control and ease of implementation.

报告人简历：苏必豪，2024年6月毕业于上海财经大学，现为海南大学数学与统计好色视频 副研究员，研究方向为PDE数值解、金融模型的数值方法，主要关注随机模拟算法，相关工作已发表于Mathematics of Computation, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing等期刊。

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邀请人：李婧超

好色视频

2025年12月25日