Related papers: Weak-Form Latent Space Dynamics Identification
Numerical solving parameterised partial differential equations (P-PDEs) is highly practical yet computationally expensive, driving the development of reduced-order models (ROMs). Recently, methods that combine latent space identification…
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…
Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system…
Image instance segmentation is a fundamental research topic in autonomous driving, which is crucial for scene understanding and road safety. Advanced learning-based approaches often rely on the costly 2D mask annotations for training. In…
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In this…
The Weak form Estimation of Nonlinear Dynamics (WENDy) method is a recently proposed class of parameter estimation algorithms that exhibits notable noise robustness and computational efficiency. This work examines the coverage and bias…
Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery from undersampled…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
Most existing latent-space models for dynamical systems require fixing the latent dimension in advance, they rely on complex loss balancing to approximate linear dynamics, and they don't regularize the latent variables. We introduce RRAEDy,…
High-quality audio is essential in a wide range of applications, including online communication, virtual assistants, and the multimedia industry. However, degradation caused by noise, compression, and transmission artifacts remains a major…
Weakly-supervised object detection (WSOD) has emerged as an inspiring recent topic to avoid expensive instance-level object annotations. However, the bounding boxes of most existing WSOD methods are mainly determined by precomputed…
The Weak-form Estimation of Non-linear Dynamics (WENDy) framework is a recently developed approach for parameter estimation and inference of systems of ordinary differential equations (ODEs). Prior work demonstrated WENDy to be robust,…
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…
Efficient modeling of the Richtmyer-Meshkov instability (RMI) is essential to many engineering tasks, including high-speed combustion and drive and capsule geometry optimization in Inertial Confinement Fusion (ICF). In the latter, RMI…
Video restoration plays a pivotal role in revitalizing degraded video content by rectifying imperfections caused by various degradations introduced during capturing (sensor noise, motion blur, etc.), saving/sharing (compression, resizing,…
Weak supervision is a popular method for building machine learning models without relying on ground truth annotations. Instead, it generates probabilistic training labels by estimating the accuracies of multiple noisy labeling sources…
In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This…
Identifying governing partial differential equations (PDEs) from noisy spatiotemporal data remains challenging due to differentiation-induced noise amplification and ambiguity from overcomplete libraries. We propose a prior-informed…
The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in…
Modeling the dynamic behavior of deformable objects is crucial for creating realistic digital worlds. While conventional simulations produce high-quality motions, their computational costs are often prohibitive. Subspace simulation…