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In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate model from the…

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…

High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…

We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…

Convection-dominated problems are known for their slow Kolmogorov $n$-width decays and are challenging for model order reduction (MOR). In this work, we propose a hybrid surrogate modeling approach and a non-intrusive variant that overcome…

Representation learning for high-dimensional, complex physical systems aims to identify a low-dimensional intrinsic latent space, which is crucial for reduced-order modeling and modal analysis. To overcome the well-known Kolmogorov barrier,…

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of $\mathrm{CO_2}$ sequestration). Here, we present a non-intrusive reduced order model of natural…

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

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…

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…

This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…

Recent learning approaches that implicitly represent surface geometry using coordinate-based neural representations have shown impressive results in the problem of multi-view 3D reconstruction. The effectiveness of these techniques is,…

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…