Related papers: EqOD: Symmetry-Informed Stability Selection for PD…

Designing robust algorithms capable of training accurate neural networks on uncurated datasets from the web has been the subject of much research as it reduces the need for time consuming human labor. The focus of many previous research…

Outlier detection is an important topic in machine learning and has been used in a wide range of applications. Outliers are objects that are few in number and deviate from the majority of objects. As a result of these two properties, we…

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently,…

Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically requires prior knowledge of data types and symmetries,…

Pose estimation is a crucial problem in simultaneous localization and mapping (SLAM). However, developing a robust and consistent state estimator remains a significant challenge, as the traditional extended Kalman filter (EKF) struggles to…

This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…

We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…

Recent Semi-Supervised Object Detection (SS-OD) methods are mainly based on self-training, i.e., generating hard pseudo-labels by a teacher model on unlabeled data as supervisory signals. Although they achieved certain success, the limited…

We introduce Exponential Family Discriminant Analysis (EFDA), a unified generative framework that extends classical Linear Discriminant Analysis (LDA) beyond the Gaussian setting to any member of the exponential family. Under the assumption…

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…

Weakly-supervised object detection (WSOD) aims to train an object detector only requiring the image-level annotations. Recently, some works have managed to select the accurate boxes generated from a well-trained WSOD network to supervise a…

Accurately solving partial differential equations (PDEs) is essential across many scientific disciplines. However, high-fidelity solvers can be computationally prohibitive, motivating the development of reduced-order models (ROMs).…

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential…

System identification plays a crucial role in physics and machine learning for discovering governing equations directly from data. A powerful approach is the Sparse Identification of Nonlinear Dynamics (SINDy) method, which assumes that…

The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…

The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs) from data poses significant challenges, primarily in…

We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from a single trajectory of noisy observations. Identifying unknown differential equations from noisy…

While the mainstream research in anomaly detection has mainly followed the one-class classification, practical industrial environments often incur noisy training data due to annotation errors or lack of labels for new or refurbished…

We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs…