2026年暑期随机计算系列报告信息

报告人：李晓月教授（天津工业大学）

报告时间：2026年7月18日16：00-17：00

报告地点：正新楼106

题目：Numerical approximation to the invariant measure of McKean-Vlasov stochastic differential equations

摘要：Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with super-linear growth coefficients. The paper establishes the theory on the propagation of chaos in the $L^{q}$ sense. The optimal uniform-in-time strong convergence rate $1/2$-order of the numerical solutions is obtained for the interacting particle system. Furthermore, it is proved that the numerical solutions capture the long-term dynamical behaviors of MV-SDEs precisely, including moment boundedness, stability, and ergodicity. Moreover, a unique numerical invariant probability measure is yielded, which converges to the underlying invariant probability measure of MV-SDEs in the $L^2$-Wasserstein distance. Finally, several numerical experiments are carried out to support the main results.

报告人：邹永魁教授（av视频 ）

报告时间：2026年7月19日16：00-17：00

报告地点：正新楼106

题目：Weak convergence of a full discretization to stochastic Allen-Cahn equation driven by multiplicative noise

摘要：Stochastic Allen-Cahn equation provides a prototypical class of semilinear SPDEs with non-globally Lipschitz nonlinearities and arises in the modeling of phase transition phenomena under random perturbations. In this talk, I will discuss the weak convergence analysis of a fully discrete approximation for stochastic Allen-Cahn equation driven by multiplicative noise. The numerical scheme combines a drift-implicit Euler method in time with a spectral Galerkin approximation in space.

The main challenges stem from the non-globally Lipschitz drift and the presence of Nemytskii-type multiplicative noise. By establishing suitable regularity estimates for the associated Kolmogorov equations and developing techniques for handling trace terms involving stochastic integrals, we obtain weak convergence rates for the fully discrete scheme. The analysis provides a rigorous framework for weak error estimates of SPDEs with non-globally Lipschitz nonlinearities driven by multiplicative noise.

报告人：张凯教授（av视频 ）

报告时间：2026年7月20日16：00-17：00

报告地点：正新楼106

题目：Machine learning for inverse scattering problems

摘要：In this presentation, we consider artificial neural networks for inverse scattering problems. As a working model, we consider the inverse problem of recovering a scattering object from the (possibly) limited-aperture radar cross section (RCS) data collected corresponding to a single incident field. This nonlinear and ill-posed inverse problem is practically important and highly challenging due to the severe lack of information. From a geometrical and physical point of view, the low-frequency data should be able to resolve the unique identifiability issue, but meanwhile lose the resolution. On the other hand, the machine learning can be used to break through the resolution limit. By combining the two perspectives, we develop a fully connected neural network (FCNN) for the inverse problem.

Extensive numerical results show that the proposed method can produce stunning reconstructions. The proposed strategy can be extended to tackling other inverse scattering problems with limited measurement information.

报告人：吕俊良教授（av视频 ）

报告时间：2026年7月21日16：00-17：00

报告地点：正新楼106

题目：Neural Network-Based Solutions for Acoustic Wave Scattering and Inversion

摘要：In this talk, I will present our latest progress on both forward and inverse acoustic scattering problems. For scattering in unbounded domains, we have introduced a novel alternating-optimized SNN approach that achieves both high computational efficiency and strong accuracy. To address problems involving large wave numbers, we have proposed the Hankel neural network method. This method is capable of achieving an accuracy of 10^{-4} even at a wave number of 2000. Furthermore, we have developed a new machine learning framework that can tackle multi-body scattering problems without any prior knowledge of the number of scatterers.

报告人：周知教授（香港理工大学）

报告时间：2026年7月23日16：00-17：00

报告地点：正新楼106，腾讯会议：766578418

题目：Numerical Analysis for Parameter Identification in PDEs

摘要：Identifying parameters in partial differential equations (PDEs) represent a very broad class of applied inverse problems. Usually, these problems are addressed through optimization approaches, which are then discretized for practical numerical implementation using finite difference, finite element, or neural network approximations, with the latter often referred to as unsupervised learning in this context. A key challenge in this context is deriving a priori error estimates for the numerical reconstruction of the target parameter. In this talk, we present our recent work on establishing convergence rates for finite element methods in recovering a diffusion coefficient in an elliptic equation. This is achieved by carefully exploiting relevant stability results. Moreover, the approach can be extended to unsupervised learning methods using fully connected neural networks, as well as to multi-parameter identification problems with applications in hybrid physics imaging.

报告人：徐英祥教授（东北师范大学）

报告时间：2026年7月24日16：00-17：00

报告地点：正新楼106

题目：Parallel algorithms for heat-viscoelastic structure interaction

摘要：In this talk we report our recent work on domain decomposition methods for heat-viscoelastic interaction problems. The optimized Schwarz waveform relaxation (OSWR) methods that decouple the coupled system are investigated, and the decoupled viscoelastic equation is solved using the OSWR and ParaDiag methods.

报告人：徐岩教授（中国科学技术大学）

报告时间：2026年7月25日16：00-17：00

报告地点：正新楼106

题目：Higher order implicit structure-preserving numerical schemes for nonlinear time-dependent problems

摘要：In this talk, we discuss local discontinuous Galerkin (LDG) method for solving the nonlinear time-dependent equations. The space discretization results in an extremely local, element based discretization, which is beneficial for adaptivity, parallel computing and maintaining high order accuracy on unstructured meshes. We also develop a novel semi-implicit time marching method. The method can be used in a large class of problems, especially for highly nonlinear ordinary differential equations (ODEs) without easily separating of stiff and non-stiff components, which is more general and efficient comparing with traditional semi-implicit methods. This time discretization method is intended to be combined with the method of lines, which provides a flexible framework to develop high order semi-implicit time marching methods for nonlinear partial differential equations (PDEs). Coupled with the LDG spatial discretization, the fully discrete schemes are all high order accurate in both space and time, and stable numerically with the time step proportional to the spatial mesh size. Using Lagrange multipliers the conditions imposed by the structure preserving limiters are directly coupled to a DG discretization combined with implicit time integration method. The structure preserving DG discretization is then reformulated as a Karush-Kuhn-Tucker (KKT) problem. We therefore develop an efficient active set semi-smooth Newton method that is suitable for the KKT formulation of time-implicit structure preserving DG discretizations. Convergence of this semi-smooth Newton method is proven using a specially designed quasi-directional derivative of the time-implicit structure preserving DG discretization. Numerical experiments are carried out to illustrate the accuracy and capability of the proposed method.

报告人：王雨顺教授（南京师范大学）

报告时间：2026年7月27日16：00-17：00

报告地点：正新楼106

题目：保能量算法构造的辅助变量法

摘要：报告首先以Camassa-Holm方程为例，给出了一种可以构造任意高阶保系统原始能量的Runge-Kutta方法。随后，讨论了一般梯度流系统保结构算法构造的辅助变量法，研究了扩展系统的结构性质。报告从保结构算法的角度讨论了能量二次化方法的机理，分析了其只能保修正能量的原因，并尝试利用扩展系统的结构构造保原始能量的算法。

报告人：曹婉容教授（东南大学）

报告时间：2026年7月28日16：00-17：00

报告地点：正新楼106

题目：Strong convergence of an explicit full-discrete scheme for stochastic Burgers equations driven by fractional-type noise

摘要：We investigate numerical approximations for the stochastic Burgers equation driven by an additive cylindrical fractional Brownian motion with Hurst parameter H\in( 1/2 , 1). To discretize the continuous problem in space, a spectral Galerkin method is employed,followed by the presentation of a nonlinear-tamed accelerated exponential Euler method to yield a fully discrete scheme. By showing the exponential integrability of the stochastic convolution of the fractional Brownian motion, we present the boundedness of moments of semidiscrete and full-discrete approximations. Building upon these results and the convergence of the fully discrete scheme in probability proved by a stopping time technique, we derive the strong convergence of the proposed scheme.

报告人：张磊教授（北京大学）

报告时间：2026年7月29日16：00-17：00

报告地点：正新楼106

题目：揭示复杂系统的多稳态：解景观的新进展

摘要：复杂系统（如液晶、凝聚态物质、无序体系等）内部通常拥有极为丰富的拓扑多稳态，这些状态往往蕴含着新奇的物理性质。解景观(Solution Landscape)提供了一张全景式的演化“地图”，它不仅包含了系统的所有局部极小点，还给出了连接这些极小点的各阶鞍点以及层次化的网络连接图。本次报告聚焦解景观理论与计算方法的最新进展，探讨其在破解物理难题中的重要作用：

•软物质多稳态：提出“双相关联序演化”策略，打破单相热力学演化约束，成功解锁向列相液晶中隐藏的拓扑多稳态（PRL, 136, 068101 (2026)）。

•无序体系复本对称破缺：首次绘制三维颗粒体系的能量景观图谱，在真实空间中证实了帕里西全阶复本对称破缺理论关于超度量性与自相似性的预言（PRL, 136, 198202 (2026)）。

报告人：吴树林教授（东北师范大学）

报告时间：2026年7月30日16：00-17：00

报告地点：正新楼106

题目：时间并行计算

摘要：时间并行(Parallel-in-Time,简称PinT)计算是最近30年发源于欧美国家的一个研究方向，相关算法和已有算法（例如混合精度算法、Krylov子空间加速、多重网格、区域分解等等）进行技术性融合能极大提高复杂动力系统整体求解速度，在科学与工程计算领域引起大量研究和广泛应用。在加速方面的实际应用价值是推动PinT研究持续发展的核心因素。本报告我们主要介绍PinT算法如何与已有的优秀算法进行技术性融合。

报告人：王晚生教授（上海师范大学）

报告时间：2026年7月31日16：00-17：00

报告地点：正新楼106

题目：Deep learning numerical methods for high-dimensional nonlinear PIDEs and FBSDEJs based on the probabilistic representation of solutions

摘要：We propose deep learning algorithms for solving high-dimensional parabolic integro-differential equations (PIDEs) and high-dimensional forward-backward stochastic differential equations with jumps (FBSDEJs), where the jump-diffusion process is derived by a Brownian motion and an independent compensated Poisson random measure. In the novel algorithm for coupled FBSDEJs, a pair of deep neural networks for the approximations of the gradient and the integral kernel is introduced in a crucial way based on the deep FBSDE method. For FBSDEJs with small-to-moderate jump sizes and moderate jump intensities we propose the novel FBSJNN framework in which a single neural network to approximate the PIDE solution is used , while leveraging Taylor expansion to eliminate the need for a separate approximation of the non-local integral term. For both the deep learning algorithms, we derive the error estimates by exploring the error bound of Euler time discretization and the simulation error of deep learning algorithm. For the former, it is also shown that the approximation error converges to zero given the universal approximation capability of neural networks. several numerical examples are provided to show the efficiency of these proposed algorithms.

报告人：刘伟教授（江苏师范大学）

报告时间：2026年8月1日16：00-17：00

报告地点：正新楼106

题目：Variational Framework for SPDE: Old and New

摘要：In this talk we mainly present some recent progress on the variational framework for SPDE，especially on the regularization effect by noise.

报告时间：2026年8月2日16：00-17：00

报告地点：正新楼106，腾讯会议：176424931

题目：高维Boltzman分布抽样

摘要：高维Boltzman分布是统计力学系统平衡态，也是机器学习训练的目标分布。它的随机抽样目的在于克服维数灾难。我将在此报告中回顾几种经典的随机算法：Metropolis-Hasting，吉布斯抽样与随机梯度下降法；介绍一些相关的已知结果与未知问题。

报告人：孔令华教授（江西师范大学）

报告时间：2026年8月3日16：00-17：00

报告地点：正新楼106

题目：Efficient Energy-preserving Numerical Methods for Three-dimensional Deterministic and Stochastic Maxwell Equations

摘要：This talk will give some efficient numerical method for three-dimensional deterministic and stochastic Maxwell equations. It needs to solve a large scale of algebraic system at every marching time step by general unconditionally stable scheme. To get over the obstacle, it employs the splitting method to reduce the 3D problem to 1D problems which greatly decreases the scale of the algebraic systems. The energy-preserving property is paid special attention. Some theoretical results of the new schemes, such as convergence, are discussed. Lastly, numerical results are reported to illustrate the validness of the new schemes.

报告人：武海军教授（南京大学）

报告时间：2026年8月4日16：00-17：00

报告地点：正新楼106

题目：Preasymptotic analyses of FEM and CIP-FEM for the Helmholtz equation with large wave number

摘要：

报告人：赵卫东教授（山东大学）

报告时间：2026年8月5日16：00-17：00

报告地点：正新楼106

题目：Staged PINN for Inverse Problems of Variable Coefficients of PDEs

摘要：In this talk, we consider deep learning methods for inverse problems of piecewise-continuous variable coefficients of partial differential equations (PDEs). We use two different neural networks: the solution and coefficient networks, and decomposes the complex training process into three stages according to all the information at hand. The solution network learns an initial approximation of the PDE solution in the first stage. Based on this approximation, the coefficient network estimates the unknown coefficients in the second stage. With the two networks learned in the first two stages, in the third stage, the two networks are trained together on newly constructed training sets. Our numerical tests show that the three staged physical informed neural networks (PINN) are effective and accurate for solving PDE inverse problems of various types of variable coefficients, including polynomial, trigonometric, exponential, space-time dependent, and piecewise-continuous functions.

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