相关论文: Gibbs Phenomenon Suppression in PDE-Based Statisti…
Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these spatiotemporal inverse problems, observed multivariate time series are used to infer parameters of physical or…
Dirichlet processes and their extensions have reached a great popularity in Bayesian nonparametric statistics. They have also been introduced for spatial and spatio-temporal data, as a tool to analyze and predict surfaces. A popular…
The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by…
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infiltration and solute transport in unsaturated porous media. The…
Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from the shortcut problem deeply rooted in auto-regressive prediction, causing…
This paper introduces a quadrature-free, non-intrusive approach to balanced truncation for both continuous-time and discrete-time systems. The method non-intrusively constructs reduced-order models using available transfer function samples…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
By means of an original approach, called "method of the moving frame", we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path dependent…
Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could…
Dependent generalized extreme value (dGEV) models have attracted much attention due to the dependency structure that often appears in real datasets. To construct a dGEV model, a natural approach is to assume that some parameters in the…
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…
In computed tomography, data consist of measurements of the attenuation of X-rays passing through an object. The goal is to reconstruct the linear attenuation coefficient of the object's interior. For each position of the X-ray source,…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
Modeling long-range dependencies in time series generation poses a fundamental trade-off between representational capacity and computational efficiency. Traditional temporal diffusion models suffer from local entanglement and the…
Partial differential equations are frequently solved using a global basis, such as the Fourier series, due to excellent convergence. However, convergence becomes impaired when discontinuities are present due to the Gibbs phenomenon,…
Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In…
It is well known that, in the context of General Relativity, some spacetimes, when described by a congruence of comoving observers, may consist in a distribution of a perfect (non-dissipative) fluid, whereas the same spacetime as seen by a…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Discharge of hazardous substances into the marine environment poses a substantial risk to both public health and the ecosystem. In such incidents, it is imperative to accurately estimate the release strength of the source and reconstruct…
One challenge in developing a statistical field theory of turbulence is the analysis of the functional equations that govern the complete statistics of the flow field. Simplified models of turbulence may help to develop such a statistical…