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

When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning dynamics that can differ from those seen in direct function…

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle…

In addition to accurate scene understanding through precise semantic segmentation of LiDAR point clouds, detecting out-of-distribution (OOD) objects, instances not encountered during training, is essential to prevent the incorrect…

Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under $\ell_1$ constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated…

The growing demand for oriented object detection (OOD) across various domains has driven significant research in this area. However, the high cost of dataset annotation remains a major concern. Current mainstream OOD algorithms can be…

This paper proposes a novel fault detection and isolation (FDI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the proposed…

Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized…

We present an error mitigation strategy composed of Echo Verification (EV) and Clifford Data Regression (CDR), the combination of which allows one to learn the effect of the quantum noise channel to extract error mitigated estimates for the…

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy…

This work introduces an efficient novel approach for epistemic uncertainty estimation for ensemble models for regression tasks using pairwise-distance estimators (PaiDEs). Utilizing the pairwise-distance between model components, these…

We consider the emphatic temporal-difference (TD) algorithm, ETD($\lambda$), for learning the value functions of stationary policies in a discounted, finite state and action Markov decision process. The ETD($\lambda$) algorithm was recently…

Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff…

Imbalanced datasets are a fundamental issue in industrial condition monitoring and fault classification pipelines, causing classical machine learning models to overfit the majority classes while failing to learn the minority fault patterns.…

The phenomenon of critical slowing down (CSD) has played a key role in the search for reliable precursors of catastrophic regime shifts. This is caused by its presence in a generic class of bifurcating dynamical systems. Simple time-series…

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

Despite the remarkable success, recent reconstruction-based anomaly detection (AD) methods via diffusion modeling still involve fine-grained noise-strength tuning and computationally expensive multi-step denoising, leading to a fundamental…

Outlier detection (OD), also known as anomaly detection, is a critical machine learning (ML) task with applications in fraud detection, network intrusion detection, clickstream analysis, recommendation systems, and social network…

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and…

In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…