相关论文: A DEIM driven reduced basis method for the diffuse…

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…

This paper enhances the Diffuse Interface Method (DIM) for simulating compressible multiphase flows across all Mach numbers by addressing the accuracy challenges posed at low Mach regimes. A correction to the Riemann solver is introduced,…

Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…

Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac…

We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full…

This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a…

In this paper, a multiscale flux basis algorithm is developed to efficiently solve a flow problem in fractured porous media. Here, we take into account a mixed-dimensional setting of the discrete fracture matrix model, where the fracture…

The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to…

We propose a domain-decomposition pore-network method (DD-PNM) for modeling single-phase Stokes flow in porous media. The method combines the accuracy of finite-element discretizations on body-fitted meshes within pore subdomains with a…

This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…

The Stokes system with constant viscosity can be cast into different formulations by exploiting the incompressibility constraint. For instance the strain in the weak formulation can be replaced by the gradient to decouple the velocity…

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…

The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order…

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…

In this paper a time dependent Stokes problem that is motivated by a standard sharp interface model for the fluid dynamics of two-phase flows is studied. This Stokes interface problem has discontinuous density and viscosity coefficients and…

Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…

We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with a mixed three-field formulation with weak stress symmetry. The fluid flow is modeled with a…

We present a physics-informed neural network (PINN) approach for the discovery of slow invariant manifolds (SIMs), for the most general class of fast/slow dynamical systems of ODEs. In contrast to other machine learning (ML) approaches that…

Encoder-decoder transformer models have achieved great success on various vision-language (VL) tasks, but they suffer from high inference latency. Typically, the decoder takes up most of the latency because of the auto-regressive decoding.…