Related papers: Reduced Order Modeling with Shallow Recurrent Deco…
Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial…
We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schr\"odinger equation in the spectral domain given boundary data at a few frequencies. The ROM is the Galerkin projection of the Schr\"odinger…
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…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
A new deep-learning-based reduced-order modeling (ROM) framework is proposed for application in subsurface flow simulation. The reduced-order model is based on an existing embed-to-control (E2C) framework and includes an auto-encoder, which…
We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…
We present CS-SHRED, a novel deep learning architecture that integrates Compressed Sensing (CS) into a Shallow Recurrent Decoder (SHRED) to reconstruct spatiotemporal dynamics from incomplete, compressed, or corrupted data. Our approach…
Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…
Suitable reduced order models (ROMs) are computationally efficient tools in characterizing key dynamical and statistical features of nature. In this paper, a systematic multiscale stochastic ROM framework is developed for complex systems…
A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…
Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…
A nonlinear-manifold reduced order model (NM-ROM) is a great way of incorporating underlying physics principles into a neural network-based data-driven approach. We combine NM-ROMs with domain decomposition (DD) for efficient computation.…
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…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…
We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a…
Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…
This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…