Related papers: Discrete Differential Principle for Continuous Smo…
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
We propose a novel method for forecasting the temporal evolution of probability distributions observed at discrete time points. Extending the Dynamic Probability Density Decomposition (DPDD), we embed distributional dynamics into…
We consider structure-preserving methods for conservative systems, which rigorously replicate the conservation property yielding better numerical solutions. There, corresponding to the skew-symmetry of the differential operator, that of…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
A recently developed numerical method for the calculation of derivatives of functions of general complex matrices, which can also be combined with implicit matrix function approximations such as Krylov-Ritz type algorithms, is presented. An…
In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…
Many processes in biology, chemistry, physics, medicine, and engineering are modeled by a system of differential equations. Such a system is usually characterized via unknown parameters and estimating their 'true' value is thus required. In…
This paper develops and implements a practical simulation-based method for estimating dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function under aperiodic…
We present a new fractional Taylor formula for singular functions whose Caputo fractional derivatives are of bounded variation. It bridges and ``interpolates" the usual Taylor formulas with two consecutive integer orders. This enables us to…
Recently, Differentiable Ray Tracing has been successfully applied in the field of wireless communications for learning radio materials or optimizing the transmitter orientation. However, in the frame of gradient based optimization,…
Due to the high complexity and technical requirements of industrial production processes, surface defects will inevitably appear, which seriously affects the quality of products. Although existing lightweight detection networks are highly…
This letter is concerned with solving continuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In the proposed smoothing method, we apply the TME method to approximate the transition density of the…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulas w.r.t. increments of the time are presented for…
Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power…
With the wide spread of deep learning and gradient descent inspired optimization algorithms, differentiable programming has gained traction. Nowadays it has found applications in many different areas as well, such as scientific computing,…
In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…