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Checkpointing Scheme
Checkpointing schemes are scientific computing algorithms used in solving time dependent adjoint equations, as well as reverse mode automatic differentiation.D. K. Pradhan and N. H. Vaidya, "Roll-forward checkpointing scheme: a novel fault-tolerant architecture," in IEEE Transactions on Computers, vol. 43, no. 10, pp. 1163-1174, Oct. 1994, doi: 10.1109/12.324542. References Bibliography * {{Cite book , last = Griewank , first = Andreas , title = Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation , publisher = SIAM Thailand ( ), historically known as Siam () and officially the Kingdom of Thailand, is a country in Southeast Asia, located at the centre of the Mainland Southeast Asia, Indochinese Peninsula, spanning , with a population of almost 70 mi ... , series = Frontiers in Applied Mathematics , volume = 19 , year = 2000 , isbn = 0-89871-451-6 Differential calculus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjoint Equation
An adjoint equation is a linear differential equation, usually derived from its primal equation using integration by parts. Gradient values with respect to a particular quantity of interest can be efficiently calculated by solving the adjoint equation. Methods based on solution of adjoint equations are used in wing shape optimization, Flow control (fluid), fluid flow control and uncertainty quantification. For example dX_t = a(X_t)dt + b(X_t)dW this is an Itō calculus, Itō stochastic differential equation. Now by using Euler scheme, we integrate the parts of this equation and get another equation, X_ = X_n + a \Delta t + \zeta b \sqrt, here \zeta is a random variable, later one is an adjoint equation. Example: Advection-Diffusion PDE Consider the following linear, scalar Convection–diffusion_equation, advection-diffusion equation for the primal solution u(\vec), in the domain \Omega with Dirichlet boundary conditions: : \begin \nabla \cdot \left(\vec u - \mu \nabla u \righ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automatic Differentiation
In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation, computational differentiation, auto-differentiation, or simply autodiff, is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.). By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program. Automatic differentiation is distinct from symbolic differentiation and numerical differentiation. Symbolic differentiation faces the difficulty of converting a computer program into a single mathematical expression and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Society For Industrial And Applied Mathematics
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics. SIAM is one of the four member organizations of the Joint Policy Board for Mathematics. Membership Membership is open to both individuals and organizations. By the end of its first full year of operation, SIAM had 130 memb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |