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The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
Anomaly inspection plays an important role in industrial manufacture. Existing anomaly inspection methods are limited in their performance due to insufficient anomaly data. Although anomaly generation methods have been proposed to augment…
This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a…
Interpreting motion captured in image sequences is crucial for a wide range of computer vision applications. Typical estimation approaches include optical flow (OF), which approximates the apparent motion instantaneously in a scene, and…
Unsupervised learning of anomaly detection in high-dimensional data, such as images, is a challenging problem recently subject to intense research. Through careful modelling of the data distribution of normal samples, it is possible to…
With the rise of generative models, there is a growing interest in unifying all tasks within a generative framework. Anomaly detection methods also fall into this scope and utilize diffusion models to generate or reconstruct normal samples…
We investigate the occurrence of anomalous diffusive transport associated with acoustic wave fields propagating through highly-scattering periodic media. Previous studies had correlated the occurrence of anomalous diffusion to either the…
Skeleton-based video anomaly detection (SVAD) is a crucial task in computer vision. Accurately identifying abnormal patterns or events enables operators to promptly detect suspicious activities, thereby enhancing safety. Achieving this…
We highlight a few recent results on the effect of the diffusion process in deterministic area preserving maps with noncompact phase space, namely the standard map. In more detail, we focus on the anomalous diffusion arising due to the…
Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are mostly one-shot generative models that apply Gaussian diffusion in the…
Anomaly localization in images -- identifying regions that deviate from normal patterns -- is vital in applications such as medical diagnosis and industrial inspection. A recent trend is the use of image generation models in anomaly…
Understanding, predicting, and generating object motions and transformations is a core problem in artificial intelligence. Modeling sequences of evolving images may provide better representations and models of motion and may ultimately be…
Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics, requiring the computation of collision-free paths for multiple agents moving from their respective start to goal positions. Coordinating multiple agents in a shared…
Numerical transport models based on the advection-dispersion equation (ADE) are built on the assumption that sub-grid cell transport is Fickian such that dispersive spreading around the average velocity is symmetric and without significant…
Trajectory anomaly detection is essential for identifying unusual and unexpected movement patterns in applications ranging from intelligent transportation systems to urban safety and fraud prevention. Existing methods only consider limited…
The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However,…
In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…
Group anomaly detection is crucial in many network applications, but faces challenges due to diverse anomaly patterns. Motivated by the success of large language models (LLMs) in natural language processing, graph foundation models (GFMs)…
Heavy and light particles are commonly found in many natural phenomena and industrial processes, such as suspensions of bubbles, dust, and droplets in incompressible turbulent flows. Based on a recent machine learning approach using a…
We develop a mathematical framework allowing to study anomalous transport in homogeneous solids. The main tools characterizing the anomalous transport properties are spectral and diffusion exponents associated to the covariant Hamiltonians…