相关论文: Second-order adjoint sensitivity analysis methodol…
Neural Ordinary Differential Equations (NODEs) are a new class of models that transform data continuously through infinite-depth architectures. The continuous nature of NODEs has made them particularly suitable for learning the dynamics of…
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
This paper deals with the problem of estimating second-order parameter sensitivities for stochastic reaction networks, where the reaction dynamics is modeled as a continuous time Markov chain over a discrete state space. Estimation of such…
Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
In this paper, a concurrent learning based adaptive observer is developed for a class of second-order nonlinear time-invariant systems with uncertain dynamics. The developed technique results in simultaneous online state and parameter…
We study the second order response functions of a colloidal particle being subjected to an anharmonic potential. Contrary to typical response measurements which require an external perturbation, here we experimentally confirm a recently…
Stochastic models for chemical reaction networks are increasingly popular in systems and synthetic biology. These models formulate the reaction dynamics as Continuous-Time Markov Chains (CTMCs) whose propensities are parameterized by a…
We present a new first-principle theory for the calculation of the macroscopic second-order susceptibility chi^(2), based on the Time-Dependent Density-Functional Theory approach. Our method allows to include straightforwardly the many-body…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Many optimization problems in electrical engineering consider a large number of design parameters. A sensitivity analysis identifies the design parameters with the strongest influence on the problem of interest. This paper introduces the…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
Gradients can be employed for sensitivity analysis. Here, we leverage the advantages of the Loss Landscape to comprehend which independent variables impact the dependent variable. We seek to grasp the loss landscape by utilizing first,…
This paper provides an analytical methodology to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) system. The hybrid ODE system is characterized by discontinuities…
The linear and nonlinear dynamical susceptibilities of a two level system are calculated as it undergoes a transition to a decoherent state. Analogously to the Glover-Tinkham-Ferrell sum rule of superconductivity, spectral weight in the…