Related papers: Learning POD of Complex Dynamics Using Heavy-ball …

We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity…

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…

Dimension reduction is a fundamental tool for analyzing high-dimensional data in supervised learning. Traditional methods for estimating intrinsic order often prioritize model-specific structural assumptions over predictive utility. This…

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While…

This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique…

Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems…

In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…

The manipulation of deformable linear objects (DLOs) via model-based control requires an accurate and computationally efficient dynamics model. Yet, data-driven DLO dynamics models require large training data sets while their predictions…

Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast…

Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode…

Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. In this paper, we employ contraction theory to improve the robustness of neural ODEs (NODEs). A dynamical…

The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by…

Understanding intraventricular hemodynamics requires compact and physically interpretable representations of the underlying flow structures, as characteristic flow patterns are closely associated with cardiovascular conditions and can…

Proper orthogonal decomposition (POD) is often employed in developing reduced-order models (ROM) in fluid flows for design, control, and optimization. Contrary to the usual practice where velocity field is the focus, we apply the POD…

Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

Reduced-order models (ROMs) provide a powerful means of synthesizing dynamic walking gaits on legged robots. Yet this approach lacks the formal guarantees enjoyed by methods that utilize the full-order model (FOM) for gait synthesis, e.g.,…

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…

In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Building on the structure of Fourier Neural Operators (FNO),…

Accurate modeling of the complex dynamics of fluid flows is a fundamental challenge in computational physics and engineering. This study presents an innovative integration of High-Order Singular Value Decomposition (HOSVD) with Long…