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Normalizing flows are a class of generative models that enable exact likelihood evaluation. While these models have already found various applications in particle physics, normalizing flows are not flexible enough to model many of the…

High Energy Physics - Phenomenology · Physics 2022-09-07 Rob Verheyen

Machine learning methods have been extensively used to study the dynamics of complex fluid flows. One such algorithm, known as adaptive neural fuzzy inference system (ANFIS), can generate data-driven predictions for flow fields but has not…

Fluid Dynamics · Physics 2021-03-08 Zexia Zhang , Ajay B. Limaye , Ali Khosronejad

Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…

Machine Learning · Computer Science 2024-04-09 Kaiwen Zheng , Cheng Lu , Jianfei Chen , Jun Zhu

Current evaluation methods for autonomous driving prediction models rely heavily on simplistic metrics such as Average Displacement Error (ADE) and Final Displacement Error (FDE). While these metrics offer basic performance assessments,…

Robotics · Computer Science 2025-10-14 Feifei Liu , Haozhe Wang , Zejun Wei , Qirong Lu , Yiyang Wen , Xiaoyu Tang , Jingyan Jiang , Zhijian He

Trajectory prediction of aerial vehicles is a key requirement in applications ranging from missile guidance to UAV collision avoidance. While most prediction methods assume deterministic target motion, real-world targets often exhibit…

Robotics · Computer Science 2025-12-19 Marc Schneider , Renato Loureiro , Torbjørn Cunis , Walter Fichter

The task of detecting anomalous data patterns is as important in practical applications as challenging. In the context of spatial data, recognition of unexpected trajectories brings additional difficulties, such as high dimensionality and…

Ensuring the safety and reliability of Automated Driving Systems (ADS) remains a critical challenge, as traditional verification methods such as large-scale on-road testing are prohibitively costly and time-consuming.To address…

Software Engineering · Computer Science 2025-12-18 Ji Zhou , Yongqi Zhao , Yixian Hu , Hexuan Li , Zhengguo Gu , Nan Xu , Arno Eichberger

We propose two new evaluation metrics to assess realness of generated images based on normalizing flows: a simpler and efficient flow-based likelihood distance (FLD) and a more exact dual-flow based likelihood distance (D-FLD). Because…

Computer Vision and Pattern Recognition · Computer Science 2024-10-08 Pranav Jeevan , Neeraj Nixon , Amit Sethi

Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…

Machine Learning · Computer Science 2022-09-01 Chandramouli Shama Sastry , Andreas Lehrmann , Marcus Brubaker , Alexander Radovic

The widescale deployment of Autonomous Vehicles (AV) appears to be imminent despite many safety challenges that are yet to be resolved. It is well-known that there are no universally agreed Verification and Validation (VV) methodologies…

Robotics · Computer Science 2020-11-17 Dhanoop Karunakaran , Stewart Worrall , Eduardo Nebot

Microscopic traffic simulation provides a controllable, repeatable, and efficient testing environment for autonomous vehicles (AVs). To evaluate AVs' safety performance unbiasedly, the probability distributions of environment statistics in…

Systems and Control · Electrical Eng. & Systems 2022-07-05 Xintao Yan , Shuo Feng , Haowei Sun , Henry X. Liu

A Normalizing Flow computes a bijective mapping from an arbitrary distribution to a predefined (e.g. normal) distribution. Such a flow can be used to address different tasks, e.g. anomaly detection, once such a mapping has been learned. In…

Quantum Physics · Physics 2024-07-23 Bodo Rosenhahn , Christoph Hirche

Recent advances in deep learning have enabled the development of autonomous systems that use deep neural networks for perception. Formal verification of these systems is challenging due to the size and complexity of the perception DNNs as…

Machine Learning · Computer Science 2025-04-30 Christopher Watson , Rajeev Alur , Divya Gopinath , Ravi Mangal , Corina S. Pasareanu

Deep generative models complement Markov-chain-Monte-Carlo methods for efficiently sampling from high-dimensional distributions. Among these methods, explicit generators, such as Normalising Flows (NFs), in combination with the Metropolis…

Machine Learning · Computer Science 2024-05-29 Vikas Kanaujia , Mathias S. Scheurer , Vipul Arora

Tabular regression is a well-studied problem with numerous industrial applications, yet most existing approaches focus on point estimation, often leading to overconfident predictions. This issue is particularly critical in industrial…

Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. However, their invertibility constraint imposes limitations on data distributions that reside on…

Computer Vision and Pattern Recognition · Computer Science 2022-08-19 Janis Postels , Martin Danelljan , Luc Van Gool , Federico Tombari

We propose a stochastic prediction-control framework to promote safety in automated driving by directly controlling the joint state probability density functions (PDFs) subject to the vehicle dynamics via trajectory-level state feedback. To…

Systems and Control · Electrical Eng. & Systems 2020-11-10 Shadi Haddad , Kenneth F. Caluya , Abhishek Halder , Baljeet Singh

Generative adversarial networks (GANs) and normalizing flows are both approaches to density estimation that use deep neural networks to transform samples from an uninformative prior distribution to an approximation of the data distribution.…

Machine Learning · Computer Science 2021-12-15 Tianci Liu , Jeffrey Regier

With the rapid development of automated vehicles (AVs) in recent years, commercially available AVs are increasingly demonstrating high-level automation capabilities. However, most existing AV safety evaluation methods are primarily designed…

Robotics · Computer Science 2025-06-17 Hang Zhou , Chengyuan Ma , Shiyu Shen , Zhaohui Liang , Xiaopeng Li

Neural Scene Flow Prior (NSFP) and Fast Neural Scene Flow (FNSF) have shown remarkable adaptability in the context of large out-of-distribution autonomous driving. Despite their success, the underlying reasons for their astonishing…

Computer Vision and Pattern Recognition · Computer Science 2024-03-26 Dongrui Liu , Daqi Liu , Xueqian Li , Sihao Lin , Hongwei xie , Bing Wang , Xiaojun Chang , Lei Chu