相关论文: Periodic Adjoint Sensitivity Analysis

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…

Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a…

We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…

This paper considers an adaptive tracking control problem for stochastic regression systems with multi-threshold quantized observations. Different from the existing studies for periodic reference signals, the reference signal in this paper…

In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an…

We present basic results, known and new, on nontrivial solutions of periodic stationary nonlinear Schr\"odinger equations. We also sketch an application to nonlinear optics and discuss some open problems.

Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…

We present an optimization-based method for the joint estimation of system parameters and noise covariances of linear time-variant systems. Given measured data, this method maximizes the likelihood of the parameters. We solve the…

Performing sensitivity analysis for influence diagrams using the decision circuit framework is particularly convenient, since the partial derivatives with respect to every parameter are readily available [Bhattacharjya and Shachter, 2007;…

For the time-parallel Parareal method, there exists both numerical and analytical proof that it converges very well for diffusive problems like the heat equation. Many applications, however, do not lead to simple homogeneous diffusive…

This paper applies He's new amplitude-frequency relationship recently established by Ji-Huan He (Int J Appl Comput Math 3 1557-1560, 2017) to study periodic solutions of strongly nonlinear systems with odd nonlinearities. Some examples are…

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

One of the main features of interest in analysing the light curves of stars is the underlying periodic behaviour. The corresponding observations are a complex type of time series with unequally spaced time points and are sometimes…

Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be…

Nonlinear interference is modeled by a time-varying conditionally Gaussian channel. It is shown that approximating this channel with a time-invariant channel imposes considerable loss in the performance of channel decoding. An adaptive…

The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method…

Various issues concerned with the design and sensitivity of the Anderson bridge are discussed. We analyse the circuit using the tools of Network Analysis to determine the conditions under which the balance may be obtained with greater…

This paper proposes a wavelet-based method for analysing periodic autoregressive moving average (PARMA) time series. Even though Fourier analysis provides an effective method for analysing periodic time series, it requires the estimation of…

Using the spectral approach, we analyze the effective properties of a composite which deviates slightly from periodicity. We find that, when the inclusions are randomly displaced from their equilibrium positions, the sharp resonances seen…