相关论文: Data-driven model reduction for stochastic Burgers…

Reduced-order modeling lies at the interface of numerical analysis and data-driven scientific computing, providing principled ways to compress high-fidelity simulations in science and engineering. We propose a training framework that…

A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with…

In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…

We introduce a very weak space-time variational formulation for the wave equation, prove its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability. Then, we introduce a tensor product-style space-time…

The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerically these equations can be extremely demanding. Several…

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

We propose in this paper a Proper Generalized Decomposition (PGD) approach for the solution of problems in linear elastodynamics. The novelty of the work lies in the development of weak formulations of the PGD problems based on the…

Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This…

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…

In this work we propose a unified Fourier Spectral Transformer network that integrates the strengths of classical spectral methods and attention based neural architectures. By transforming the original PDEs into spectral ordinary…

A significant advancement in nonlinear projection-based model order reduction (PMOR) is presented through a highly effective methodology. This methodology employs Gaussian process regression (GPR) and radial basis function (RBF)…

We present a finite element method for the incompressible Navier--Stokes problem that is locally conservative, energy-stable and pressure-robust on time-dependent domains. To achieve this, the space--time formulation of the Navier--Stokes…

The accuracy of solving partial differential equations (PDEs) on coarse grids is greatly affected by the choice of discretization schemes. In this work, we propose to learn time integration schemes based on neural networks which satisfy…

We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for…

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge…

We introduce and analyze various Regularized Combined Field Integral Equations (CFIER) formulations of time-harmonic Navier equations in media with piece-wise constant material properties. These formulations can be derived systematically…

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…

Because the Navier-Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this…

We propose a factor network autoregressive (FNAR) model for time series with complex network structures. The coefficients of the model reflect many different types of connections between economic agents ("multilayer network"), which are…

In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…