Related papers: Sparse POD Mode Selection and Manifold Dimensional…

The functional and structural representation of the brain as a complex network is marked by the fact that the comparison of noisy and intrinsically correlated high-dimensional structures between experimental conditions or groups shuns…

The intricacy of 3D surfaces often results cutting-edge point cloud denoising (PCD) models in surface degradation including remnant noise, wrongly-removed geometric details. Although using multi-scale patches to encode the geometry of a…

In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems. This notion is based on causal dependence in the…

Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a…

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…

In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

In post--layout circuit simulation, efficient model order reduction (MOR) for many--port resistor--capacitor (RC) circuits remains a crucial issue. The current mainstream MOR methods for such circuits include high--order moment matching…

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

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…

Recently, deep learning has made remarkable strides, especially with generative modeling, such as large language models and probabilistic diffusion models. However, training these models often involves significant computational resources,…

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…

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…

This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse…

Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and…

Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

This paper presents the novel idea of generating object proposals by leveraging temporal information for video object detection. The feature aggregation in modern region-based video object detectors heavily relies on learned proposals…

Block orthogonal sparse superposition (BOSS) code is a class of joint coded modulation methods, which can closely achieve the finite-blocklength capacity with a low-complexity decoder at a few coding rates under Gaussian channels. However,…