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The talk proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations-Variable Coefficient Physics-Informed Neural N...
The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields o...
本报告介绍我们近期的两项工作。(1) 求解PDE的PINN方法在处理时间发展方程时往往遇到难以收敛的困难。我们发展了时间方向的预训练PINN方法及自适应步长方法,解决了收敛性困难,使PDE求解精度能够得到系统性提高。我们在一系列时间发展方程上获得了比文献报道更精确的训练结果。(2) 辐射调源问题是一个典型的反问题,要求调整辐射输运方程的边条件(源),使解满足特定设计目标。我们针对辐射输运方程的时序...
We extend the concept of self-consistency for the Fokker-Planck equation (FPE) [Shen et al., 2022] to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of par...
In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow,surface diffusion flow, Willmore flow, etc., which arise from materials science...
Solving multi-scale PDEs is difficult in high-dimensional and/or convection-dominant cases. The interacting particle methods (IPM) are shown to outperform solving PDEs directly. Examples include compu...
Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose major difficulties for the computer simulation of multiscale PDE models in areas such as reser...
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first re...
Mathematical theory of continuum mechanics gives rise to important classes of nonlinear partial differential equations, such as the celebrated Euler and Navier-Stokes equations for both compressible a...
This conference is organized jointly by Nankai University and University of Bielefeld (Germany).  We would like to attract to the conference experts working on different aspects of PDEs on manifo...
The objective of the conference is to discuss recent advances and open problems in the field of partial differential equations and related topics.
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nystro ¨m’s method for discretization, and combine it with s...
We will have two main characters in these notes: the maximum principle and the sliding method. The latter has a twin, the moving plane method–they are often so indistinguishable that we will count the...
Sobolev spaces Hγ(M), γ ∈ R, M ⊂ Rd M-bounded Def If n ∈ N, then Hn - all generalized functions with derivatives up to n-th order belong to L2(M); kuk 2Hn = P |α | ≤n R M |Dαu| 2dx
Differential equations posed over immersed manifolds are of particular importance in studying geophysical flows; for instance, ocean and atmosphere simulations crucially rely on the capability ...

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