相关论文: Second-order adjoint sensitivity analysis methodol…

We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…

This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic…

Under consideration are the construction and properties of some special class of second other tangent sets on using the technique of nonstandard analysis.

The nonlinear response of stochastic models obeying a master equation is calculated up to fifth-order in the external field thus extending the third-order results obtained earlier (G. Diezemann, Phys. Rev. E{\bf 85}, 051502 (2012)). For…

This work presents an optimization framework for tailoring the nonlinear dynamic response of lightly damped mechanical systems using Spectral Submanifold (SSM) reduction. We derive the SSM-based backbone curve and its sensitivity with…

In one calculation, adjoint sensitivity analysis provides the gradient of a quantity of interest with respect to all system's parameters. Conventionally, adjoint solvers need to be implemented by differentiating computational models, which…

In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…

We treat the optimal linear filtering problem for a sum of two second order uncorrelated generalized stochastic processes. This is an operator equation involving covariance operators. We study both the wide-sense stationary case and the…

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…

We develop a sensitivity function for the design of electron optics using an adjoint approach based on a form of reciprocity implicit in Hamilton's equations of motion. The sensitivity function, which is computed with a small number of…

A new class of methods is introduced for solving the Kohn-Sham equations of density functional theory, based on constructing a mapping dynamically between the Kohn-Sham system and an auxiliary system. The resulting auxiliary density…

Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…

In this work, we propose a generalized, second-order, nonstandard finite difference (NSFD) method for non-autonomous dynamical systems. The proposed method combines the NSFD framework with a new non-local approximation of the right-hand…

We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…

A suboptimal active disturbance rejection controller (S-ADRC) is proposed for second-order systems with unknown time-varying nonlinear dynamics. The output-feedback controller guarantees a global convergence to the vicinity of an optimal…

Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…

Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…

We present a new software system PETSc TSAdjoint for first-order and second-order adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative calculation in PETSc TSAdjoint is essentially a high-level…

This paper considers fault estimation in nonlinear fractional order systems in observer form. For this aim, a step by step second order sliding mode observer is used. By means of a fractional inequality, the stability of the observer…

We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are…