Related papers: Sparse Equation Matching: A Derivative-Free Learni…

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

Sparsity is a central aspect of interpretability in machine learning. Typically, sparsity is measured in terms of the size of a model globally, such as the number of variables it uses. However, this notion of sparsity is not particularly…

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…

In this work, a data-driven modeling framework of switched dynamical systems under time-dependent switching is proposed. The learning technique utilized to model system dynamics is Extreme Learning Machine (ELM). First, a method is…

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…

Partial differential equations (PDEs) with multiple scales or those defined over sufficiently large domains arise in various areas of science and engineering and often present problems when approximating the solutions numerically. Machine…

Structural equation modeling (SEM) is a statistical method widely used in educational research to investigate relationships between variables. SEM models are typically constructed based on theoretical foundations and assessed through fit…

Pixel-level vision tasks, such as semantic segmentation, require extensive and high-quality annotated data, which is costly to obtain. Semi-supervised semantic segmentation (SSSS) has emerged as a solution to alleviate the labeling burden…

We present a probabilistic modeling and inference framework for discriminative analysis dictionary learning under a weak supervision setting. Dictionary learning approaches have been widely used for tasks such as low-level signal denoising…

Aggregative cooperative optimization problems arise in distributed decision-making settings where each agent's objective depends on its own decision as well as on an aggregate variable capturing global system behavior. Motivated by…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

Recent hybrid models combining Linear State Space Models (SSMs) with self-attention mechanisms have demonstrated impressive results across a range of sequence modeling tasks. However, current approaches apply attention modules statically…

Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…

The well-established modular autonomous driving system is decoupled into different standalone tasks, e.g. perception, prediction and planning, suffering from information loss and error accumulation across modules. In contrast, end-to-end…

Density estimation is a fundamental problem in statistical learning. This problem is especially challenging for complex high-dimensional data due to the curse of dimensionality. A promising solution to this problem is given here in an…

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…

Incremental learning of semantic segmentation has emerged as a promising strategy for visual scene interpretation in the open- world setting. However, it remains challenging to acquire novel classes in an online fashion for the segmentation…

Feature matching is a crucial task in the field of computer vision, which involves finding correspondences between images. Previous studies achieve remarkable performance using learning-based feature comparison. However, the pervasive…

Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…