相关论文: A non-intrusive reduced basis EKI for time-fractio…

Ensemble Kalman inversion (EKI) is a technique for the numerical solution of inverse problems. A great advantage of the EKI's ensemble approach is that derivatives are not required in its implementation. But theoretically speaking, EKI's…

We propose enforcing constraints on Model-Based Diffusion by introducing emerging barrier functions inspired by interior point methods. We demonstrate that the standard Model-Based Diffusion algorithm can lead to catastrophic performance…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

In this work, we introduce a self-adaptive implicit-explicit (IMEX) time integration scheme, named IMEX-RB, for the numerical integration of systems of ordinary differential equations (ODEs), arising from spatial discretizations of partial…

In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order…

Continuous latent time series models are prevalent in Bayesian modeling; examples include the Kalman filter, dynamic collaborative filtering, or dynamic topic models. These models often benefit from structured, non mean field variational…

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…

Bayesian experimental design (BED) for complex physical systems is often limited by the nested inference required to estimate the expected information gain (EIG) or its gradients. Each outer sample induces a different posterior, creating a…

Integer-order calculus often falls short in capturing the long-range dependencies and memory effects found in many real-world processes. Fractional calculus addresses these gaps via fractional-order integrals and derivatives, but…

A proper orthogonal decomposition-based B-splines B\'ezier elements method (POD-BSBEM) is proposed as a non-intrusive reduced-order model for uncertainty propagation analysis for stochastic time-dependent problems. The method uses a…

Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…

The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for the purpose of inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates…

In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The…

This paper presents a new technique for developing reduced-order models (ROMs) for nonlinear radiative transfer problems in high-energy density physics. The proper orthogonal decomposition (POD) of photon intensities is applied to obtain…

Sampling from Boltzmann distributions, particularly those tied to high dimensional and complex energy functions, poses a significant challenge in many fields. In this work, we present the Energy-Based Diffusion Generator (EDG), a novel…

Diffusion generative modeling has become a promising approach for learning robotic manipulation tasks from stochastic human demonstrations. In this paper, we present Diffusion-EDFs, a novel SE(3)-equivariant diffusion-based approach for…

This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…

A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…

Hyper-reduction methods have gained increasing attention for their potential to accelerate reduced order models for nonlinear systems, yet their comparative accuracy and computational efficiency are not well understood. Motivated by this…

The Fisher-KPP partial differential equation has been employed in science to model various biological, chemical, and thermal phenomena. Time fractional extensions of Fisher's equation have also appeared in the literature, aiming to model…