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In these two talks, some results on derived representation type via topological and homological methods will be introduced: (1) Two geometric models for graded skew-gentle algebras will be introduced ...
We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kahler geometry such as Hormander's $\dbar$-L2 estimate with singular weight, Demailly's Calabi--Yau metho...
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...
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
A new class of high-order maximum principle preserving numerical methods is proposed for solving the semilinear Allen-Cahn equation. We start with the method consists of a $k$th-order multistep expone...
Nonconvex constrained optimization (NCO) has been one of the important research fields in optimization community. It has widely appeared in many application fields. However, challenges for solving NCO...
2023年2月25日,农学院智慧农业团队在《Science of The Total Environment》期刊发表了题为“Improving the spatial and temporal estimation of ecosystem respiration using multi-source data and machine learning methods in a rainfed ...
In this talk, we present the pointwise convergence of one-point large deviations rate functions (LDRFs) of the spatial finite difference method and further the fully discrete method based on the tempo...
One can elucidate integrability properties of ODEs by knowing the existence of second integrals. However, little is known about how they are preserved, if at all, under numerical methods. In this talk...
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...
近日,北京大学化学与分子工程学院彭海琳课题组、清华大学生命科学学院王宏伟课题组和北京大学工学院韦小丁课题组合作在《自然-方法学》 (Nature Methods)发表了题为“Uniform thin ice on ultraflat graphene for high-resolution cryo-EM”的研究论文,报道了新型超平整石墨烯电镜载网,破解了高分辨冷冻电镜表征中均匀薄冰的制备难题。
Multiscale phenomena significantly impact on the computation and modeling for scientific and engineering problems. Multiscale finite element methods are used to build reduced order computational model...
In this talk, we first consider convex optimization whose smooth components have a locally Lipschitz continuous gradient and propose a first-order method for finding an epsilon-KKT solution. We then c...
In this work, we propose and analyze domain decomposition methods to decouple the large system arisen from the discretization of dual-porosity-Stokes model. Robin boundary conditions are used to decou...

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