相关论文: Generalized Paraxial Ray Trace Procedure Derived f…
The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the…
An exact generalization of the Ramsey transition probability is derived to improve ultra-high precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The…
Traditional ultrasound simulators solve the wave equation to model pressure distribution fields, achieving high accuracy but requiring significant computational time and resources. To address this, ray tracing approaches have been…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…
Problem of sound propagation in the ocean is considered. A novel approach of K. Hegewisch and S. Tomsovic for statistical modelling of acoustic wavefields in the random ocean is examined. The approach is based on construction of a wavefield…
We derive a generalized deviation equation -- analogous to the well-known geodesic deviation equation -- for test bodies in General Relativity. Our result encompasses and generalizes previous extensions of the standard geodesic deviation…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
Classically, anisotropic surface wave tomography is treated as an optimisation problem where it proceeds through a linearised two-step approach. It involves the construction of 2D group or phase velocity maps for each considered period,…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of local instability which may lead to chaos is…
A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the…
This paper develops methodology for local sensitivity analysis based on directional derivatives associated with spatial processes. Formal gradient analysis for spatial processes was elaborated in previous papers, focusing on distribution…
Explicit neural representations such as 3D Gaussian Splatting (3DGS) enable high-fidelity and real-time novel view synthesis, yet optimize for alpha-composited optical appearance rather than ray-intersectable geometry. In contrast,…
We design statistical hypothesis tests for performing leak detection in water pipeline channels. By applying an appropriate model for signal propagation, we show that the detection problem becomes one of distinguishing signal from noise,…
We consider a parabolic equation driven by a nonlinear diffusive operator and we obtain a gradient estimate in the domain where the equation takes place. This estimate depends on the structural constants of the equation, on the geometry of…
In this paper, we present a new method for computing approximate geodesic distances. We introduce the wave method for approximating geodesic distances from a point on a manifold mesh. Our method involves the solution of two linear systems…
An adiabatic mode Helmholtz equation for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the crosswedge benchmark and proved an excellent…