搜索结果: 1-15 共查到“偏微分方程 methods”相关记录16条 . 查询时间(0.063 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Machine learning methods for forward and inverse PDEs
正反向 偏微分方程 机器学习
2023/4/27
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep learning of multi-scale PDEs based on data generated from particle methods
粒子方法 数据 多尺度 偏微分方程 深度学习
2023/4/26
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiscale finite element methods: ideas and challenges
多尺度 有限元方法 思路 挑战
2023/5/6
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...
Correction Methods, Approximate Biases, and Inference for Misclassified Data
Misclassified Data Approximate Biases
2014/12/8
When categorical data are misplaced into the wrong category, we say the data is affected by misclassification. This is common for data collection. It is well-known that naive estimators of category pr...
Statistical Methods for Nonlinear Dynamic Models with Measurement Error Using the Ricker Model
measurement error ricker SIMEX
2014/12/8
In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are sub...
Duality methods for a class of quasilinear systems
Hodge Frobenius equations Hodge Backlund transformations nonlinear Hodge theory Aharmonic forms
2012/6/12
Duality methods are used to generate solutions to nonlinear Hodge systems and to reveal, via the Hodge-B\"acklund transformation, underlying symmetries among a variety of models in the physics literat...
Semi-classical states for the Nonlinear Schroinger Equation on saddle points of the potential via variational methods
Nonlinear Schrodinger Equation Semiclassical states Variational Methods
2011/9/22
Abstract: In this paper we study semiclassical states for the problem $$ -\eps^2 \Delta u + V(x) u = f(u) \qquad \hbox{in} \RN,$$ where $f(u)$ is a superlinear nonlinear term. Under our hypotheses on ...
Almgren-type monotonicity methods for the classification of behavior at corners of solutions to semilinear elliptic equations
Almgren monotonicity formula semilinear elliptic equations conical boundary points
2011/9/19
Abstract: A monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence...
Barrier methods for critical exponent problems in geometric analysis and mathematical physics
Nonlinear elliptic equations geometric analysis Yamabe problem general relativity
2011/8/23
Abstract: We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. Th...
Geometric methods for nonlinear many-body quantum systems
Geometric methods nonlinear many-body quantum systems
2010/12/6
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr¨odinger operators. In this paper we provide a formalism which also allows to study ...
A general framework for deriving integral preserving numerical methods for PDEs
general framework deriving integral preserving numerical methods PDEs
2010/12/8
A general procedure for constructing conservative numerical integra-tors for time dependent partial di erential equations is presented. In particular, linearly implicit methods preserving a time avera...
Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations
Markov chain Monte Carlo methods sequential Monte Carlo methods
2010/12/14
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equa-tions. The associated stochastic processes belong to the class of se...
Probabilistic methods for discrete nonlinear Schrödinger equations
Nonlinear Schrodinger equation invariant measure discrete breather exactly solvable model
2010/12/14
Using techniques from probability theory, we show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation (NLS) are exactly solvable in dimensions three and higher.A num...
Spectral Methods in PDE
Spectral Methods PDE
2010/11/30
This is to review some recent progress in PDE. The emphasis is on (energy)supercritical nonlinear Schr¨odinger equations. The methods are applicable to other nonlinear equations.
In this paper we consider continuous-time and discrete-time waveform relaxation methods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the conv...