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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：mcGP: mesh-clustered Gaussian process emulator for partial differential equation systems
mcGP 偏微分方程组 网格聚类 高斯过程 仿真器
2023/4/18
Partial differential equations (PDEs) have become an essential tool for modeling complex physical systems. Such equations are typically solved numerically via mesh-based methods, such as the finite el...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method
2015/7/8
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method Theory Insights
2015/6/17
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Nesterov’s accelerated scheme convex optimization first-order methods differential equation restarting
2015/6/17
We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can ...
ON UNIQUENESS OF SOLUTION OF A n-TH ORDER DIFFERENTIAL EQUATION IN CONFORMAL GEOMETRY
ON UNIQUENESS OF SOLUTION A n-TH ORDER DIFFERENTIAL EQUATION CONFORMAL GEOMETRY
2014/4/3
In this paper, we prove an uniqueness theorem for a n-th order elliptic equation on the standard n-sphere Sn. The problem arises naturally from the point of view of conformal geometry. The method we u...
A posteriori error analysis for a continuous space-time finite element method for a hyperbolic integro-differential equation
integro-differential equation continuous Galerkin finite element method convolution kernel stability a posteriori estimate
2012/5/9
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error repres...
Weighted pseudo almost periodic solutions of a fractional neutral functional differential equation
Weighted pseudo almost periodic solutions fractional neutral functional differential equations Existence Banach contraction mapping theorem
2011/10/11
In this paper, by applying the properties of weighted pseudoalmost periodic functions and Banach contraction mapping theorem, a set of sufficient conditions for the existence of weighted pseudo almost...
On the Boundary Value Problem with the Operator in Boundary Conditions for the Operator-Differential Equation of the Third Order
boundary-value problem operator-differential equation Hilbert space self-adjoined operator regular solvability
2011/9/20
Abstract: In this paper the boundary value problem for one class of the operator-differential equations of the third order on a semi-axis, where one of the boundary conditions is perturbed by some lin...
A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >1/2
Linear stochastic differential equation Fractional Brownian motion Stochastic calculus Ito formula
2011/9/15
Abstract: Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u...
Differential equation approximations of stochastic network processes: an operator semigroup approach
dynamic network birth-and-death process one-parameter operator semigroup
2011/9/6
Abstract: The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmo...
A global Monte-Carlo method for fitting parameters of differential equation models
global Monte-Carlo method fitting parameters Quantitative Methods
2011/10/8
Abstract: Finding the parameter values of differential equation models from data is an important part of the modelling process. Large models and sparse data often make the parameters very difficult to...
Nonparametric model reconstruction for stochastic differential equation from discretely observed time-series data
Nonparametric model reconstruction stochastic differential equation discretely observed time-series data
2011/8/2
Abstract: We develop a scheme for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from a time-series data. There is no need to have any prior knowledg...
Finite difference approximations for the first-order hyperbolic partial differential equation with point-wise delay
hyperbolic partial differential equation differential difference equation
2011/1/18
Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equa...
A Fuchsian matrix differential equation for Selberg correlation integrals
Fuchsian matrix differential equation Selberg correlation integrals
2010/11/12
We characterize averages of $\prod_{l=1}^N|x - t_l|^{\alpha - 1}$ with respect to the Selberg density, further contrained so that $t_l \in [0,x]$ $(l=1,...,q)$ and $t_l \in [x,1]$ $(l=q+1,...,N)$, in...
A period differential equation for a family of $K3$ surfaces and the Hilbert modular orbifold for the field $\mathbb{Q}(\sqrt{5})$
K3 surfaces Hilbert modular orbifolds period maps period di erential equations toric varieties
2010/12/14
In this article we study the period map for a family of K3 surfaces which is given by the anticanon-ial divisor of a toric variety. We determine the period di erential equation and its monodromy group...