Related papers: An Augmented Subspace Based Adaptive Proper Orthog…
In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and…
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of…
We consider integrated circuits with semiconductors modeled by modified nodal analysis and drift-diffusion equations. The drift-diffusion equations are discretized in space using mixed finite element method. This discretization yields a…
In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to…
A phase proper orthogonal decomposition (Phase POD) method is demonstrated, utilizing phase averaging for the decomposition of spatio-temporal behaviour of statistically non-stationary turbulent flows in an optimized manner. The proposed…
We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…
In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…
The modal decomposition techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have become a common method for analysing the spatio-temporal coherence of dynamical systems. In particular, these techniques…
Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…
Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a…
Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…
Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative…
In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only…
Partial differential equations (PDEs) are often dependent on input quantities which are inherently uncertain. To quantify this uncertainty, these PDEs must be solved over a large ensemble of parameters. Even for a single realization this…
We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension…
We demonstrate that accurate computation of the spectral proper orthogonal decomposition (SPOD) critically depends on the choice of frequency resolution. Using both artificially generated data and large-eddy simulation data of a turbulent…
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…
In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The…
This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the…