Automatic adjoint differentiation for gradient descent and model calibration

In this work, we discuss the Automatic Adjoint Differentiation (AAD) for functions of the form G=12∑m1(Eyi−Ci)2, which often appear in the calibration of stochastic models. We demonstrate that it allows a perfect SIMDa parallelization and provides its relative computational cost. In addition, we demonstrate that this theoretical result is in concordance with numerical experiments. a Single Input Multiple Data.publishe

AAD: breaking the primal barrier

In this article we present a new approach for automatic adjoint differentiation (AAD) with a special focus on computations where derivatives ∂F(X) ∂X are required for multiple instances of vectors X. In practice, the presented approach is able to calculate all the differentials faster than the primal (original) C++ program for F.publishe

Global solution of the initial value problem for the focusing Davey-Stewartson II system

We consider the two dimensional focusing Davey-Stewartson II system and construct the global solution of the Cauchy problem for a dense in $L^2(\mathbb C)$ set of initial data. We do not assume that the initial data is small. So, the solutions may have singularities. We show that the blow-up may occur only on a real analytic variety and the variety is bounded in each strip $t \leq T$