相关论文: Solving time-dependent parametric PDEs by multicla…

For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…

Trajectory-wise data-driven reduced order models (ROMs) tend to be sensitive to training data, and thus lack robustness. We propose to construct a robust stochastic ROM closure (S-ROM) from data consisting of multiple trajectories from…

Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to…

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…

We present a model predictive control (MPC) framework for linear switched evolution equations arising from a parabolic partial differential equation (PDE). First-order optimality conditions for the resulting finite-horizon optimal control…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…

It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are…

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…

A space-time-parameters structure of parametric parabolic PDEs motivates the application of tensor methods to define reduced order models (ROMs). Within a tensor-based ROM framework, the matrix SVD - a traditional dimension reduction…

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…

This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the computational cost using traditional numerical schemes can be…

In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval…

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the…

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…