Related papers: Weak-Form Latent Space Dynamics Identification

Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space…

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…

Formal verification provides a powerful framework for proving that dynamical systems satisfy their specifications. However, these techniques face scalability challenges in high-dimensional settings, as they often rely on state-space…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Latent spaces offer an efficient and effective means of summarizing data while implicitly preserving meta-information through relational encoding. We leverage these meta-embeddings to develop a modality-agnostic, unified encoder. Our method…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Instance segmentation is a fundamental research in computer vision, especially in autonomous driving. However, manual mask annotation for instance segmentation is quite time-consuming and costly. To address this problem, some prior works…

Learning suitable Whole slide images (WSIs) representations for efficient retrieval systems is a non-trivial task. The WSI embeddings obtained from current methods are in Euclidean space not ideal for efficient WSI retrieval. Furthermore,…

Latent representations are critical for the performance and robustness of machine learning models, as they encode the essential features of data in a compact and informative manner. However, in vision tasks, these representations are often…

Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…

Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the…

Deformable image registration (DIR) remains a fundamental yet challenging problem in medical image analysis, largely due to the prohibitively high-dimensional deformation space of dense displacement fields and the scarcity of voxel-level…

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…

Video anomaly detection under video-level labels is currently a challenging task. Previous works have made progresses on discriminating whether a video sequencecontains anomalies. However, most of them fail to accurately localize the…

In this paper, we study the numerical stability of reduced order models for convection-dominated stochastic systems in a relatively simple setting: a stochastic Burgers equation with linear multiplicative noise. Our preliminary results…

Most time series foundation models are pretrained by directly predicting future observations, which often yields weakly structured latent representations that capture surface noise rather than coherent and predictable temporal dynamics. In…

Biologically inspired algorithms for simultaneous localization and mapping (SLAM) such as RatSLAM have been shown to yield effective and robust robot navigation in both indoor and outdoor environments. One drawback however is the…

Despite weakly supervised object detection (WSOD) being a promising step toward evading strong instance-level annotations, its capability is confined to closed-set categories within a single training dataset. In this paper, we propose a…

Wireless signal strength based localization can enable robust localization for robots using inexpensive sensors. For this, a location-to-signal-strength map has to be learned for each access point in the environment. Due to the ubiquity of…

In this paper, we focus on learning a linear time-invariant (LTI) model with low-dimensional latent variables but high-dimensional observations. We provide an algorithm that recovers the high-dimensional features, i.e. column space of the…