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We present two new accurate and efficient method to compute the formal solution of the polarized radiative transfer equation. In this work, the source function and the absorption matrix are approximated using quadratic and cubic Bezier…
Deep learning inspired by differential equations is a recent research trend and has marked the state of the art performance for many machine learning tasks. Among them, time-series modeling with neural controlled differential equations…
This paper focuses on the approximation of continuous functions on the unit sphere by spherical polynomials of degree $n$ via hyperinterpolation. Hyperinterpolation of degree $n$ is a discrete approximation of the $L^2$-orthogonal…
In this paper, we suggest two ways of calculating interpolation models for unconstrained smooth nonlinear optimization when Hessian-vector products are available. The main idea is to interpolate the objective function using a quadratic on a…
A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals.…
Spatiotemporal modulation approaches have been often employed as alternatives for producing optical non-reciprocity without magneto-optic materials. Unidirectional inter-modal scattering, enabled by either acousto-optic or electro-optic…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
Based on the understandings regarding linear upwind schemes with flux splitting to achieve free-stream preservation (Q. Li, etc. Commun. Comput. Phys., 22 (2017) 64-94), a series of WENO interpolation-based and upwind-biased nonlinear…
The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode…
We present a numerical implementation, based on Wannier interpolation, of a Kubo-Greenwood formalism for computing the spatially dispersive optical conductivity in crystals at first order in the wave vector of light. This approach is more…
In video super-resolution, it is common to use a frame-wise alignment to support the propagation of information over time. The role of alignment is well-studied for low-level enhancement in video, but existing works overlook a critical step…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…
This paper deals with Hermite osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
In this paper we propose projection methods based on spline quasi-interpolating projectors of degree $d$ and class $C^{d-1}$ on a bounded interval for the numerical solution of nonlinear integral equations. We prove that they have high…
Linear approximation approaches suffer from Gibbs oscillations when approximating functions with singularities. ENO-SR resolution is a local approach avoiding oscillations and with a full order of accuracy, but a loss of regularity of the…
The marriage of recurrent neural networks and neural ordinary differential networks (ODE-RNN) is effective in modeling irregularly-observed sequences. While ODE produces the smooth hidden states between observation intervals, the RNN will…
We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured…
This paper is concerned with high-order numerical methods for hyperbolic systems of balance laws. Such methods are typically based on high-order piecewise polynomial reconstructions (interpolations) of the computed discrete quantities.…