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We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…

Machine Learning · Statistics 2019-10-03 Geoffrey Roeder , Paul K. Grant , Andrew Phillips , Neil Dalchau , Edward Meeds

Traditional monocular Visual-Inertial Odometry (VIO) systems struggle in low-texture environments where sparse visual features are insufficient for accurate pose estimation. To address this, dense Monocular Depth Estimation (MDE) has been…

Computer Vision and Pattern Recognition · Computer Science 2026-02-13 Arda Alniak , Sinan Kalkan , Mustafa Mert Ankarali , Afsar Saranli , Abdullah Aydin Alatan

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

Numerical Analysis · Mathematics 2025-06-18 Matteo Caldana , Jan S. Hesthaven

Calibrating chemical kinetics in a reaction-diffusion system is challenging because of complex dynamics governed by tightly coupled chemistry and transport, while experimental observations are often sparse and noisy. We propose a physics…

Computational Engineering, Finance, and Science · Computer Science 2026-03-31 Feixue Cai , Hua Zhou , Zhuyin Ren

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…

Machine Learning · Computer Science 2024-08-25 Defang Chen , Zhenyu Zhou , Can Wang , Chunhua Shen , Siwei Lyu

Collecting high quality data for object detection tasks is challenging due to the inherent subjectivity in labeling the boundaries of an object. This makes it difficult to not only collect consistent annotations across a dataset but also to…

Computer Vision and Pattern Recognition · Computer Science 2025-05-30 Darryl Hannan , Timothy Doster , Henry Kvinge , Adam Attarian , Yijing Watkins

Pre-trained vision foundation models have transformed many computer vision tasks. Despite their strong ability to learn discriminative and generalizable features crucial for out-of-distribution (OOD) detection, their impact on this task…

Computer Vision and Pattern Recognition · Computer Science 2025-10-14 Shizhen Zhao , Jiahui Liu , Xin Wen , Haoru Tan , Xiaojuan Qi

Irregularly sampled time series with missing values are often observed in multiple real-world applications such as healthcare, climate and astronomy. They pose a significant challenge to standard deep learning models that operate only on…

Machine Learning · Computer Science 2024-10-04 Christian Klötergens , Vijaya Krishna Yalavarthi , Maximilian Stubbemann , Lars Schmidt-Thieme

Amortized simulator-based inference offers a powerful framework for tackling Bayesian inference in computational fields such as engineering or neuroscience, increasingly leveraging modern generative methods like diffusion models to map…

Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of…

Numerical Analysis · Mathematics 2024-10-10 Colby Fronk , Linda Petzold

Expensive multi-objective optimization is a prevalent and crucial concern in many real-world scenarios, where sample-efficiency is vital due to the limited evaluations to recover the true Pareto front for decision making. Existing works…

Machine Learning · Computer Science 2026-02-03 Yiming Yao , Fei Liu , Liang Zhao , Xi Lin , Yilu Liu , Qingfu Zhang

Outlier detection (OD) is widely used in practice; but its effective deployment on new tasks is hindered by lack of labeled outliers, which makes algorithm and hyperparameter selection notoriously hard. Foundation models (FMs) have…

Machine Learning · Computer Science 2026-02-04 Xueying Ding , Haomin Wen , Simon Klütterman , Leman Akoglu

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

Machine Learning · Computer Science 2021-10-18 Lenart Treven , Philippe Wenk , Florian Dörfler , Andreas Krause

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Machine Learning · Computer Science 2025-02-11 Elisa Negrini , Yuxuan Liu , Liu Yang , Stanley J. Osher , Hayden Schaeffer

Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely…

Machine Learning · Computer Science 2025-09-15 Wenhao Mu , Zhi Cao , Mehmed Uludag , Alexander Rodríguez

Learning large scale nonlinear ordinary differential equation (ODE) systems from data is known to be computationally and statistically challenging. We present a framework together with the adaptive integral matching (AIM) algorithm for…

Statistics Theory · Mathematics 2017-10-27 Frederik Vissing Mikkelsen , Niels Richard Hansen

Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…

Machine Learning · Computer Science 2025-03-24 Qiyu Kang , Xuhao Li , Kai Zhao , Wenjun Cui , Yanan Zhao , Weihua Deng , Wee Peng Tay

Detecting unknown objects in semantic segmentation is crucial for safety-critical applications such as autonomous driving. Large vision foundation models, including DINOv2, InternImage, and CLIP, have advanced visual representation learning…

Computer Vision and Pattern Recognition · Computer Science 2025-10-06 Laith Nayal , Hadi Salloum , Ahmad Taha , Yaroslav Kholodov , Alexander Gasnikov

A concept of using Neural Ordinary Differential Equations(NODE) for Transfer Learning has been introduced. In this paper we use the EfficientNets to explore transfer learning on CIFAR-10 dataset. We use NODE for fine-tuning our model. Using…

Machine Learning · Computer Science 2020-01-22 Rajath S , Sumukh Aithal K , Natarajan Subramanyam

Deep neural networks (DNNs) remain challenged by distribution shifts in complex open-world domains like automated driving (AD): Robustness against yet unknown novel objects (semantic shift) or styles like lighting conditions (covariate…

Computer Vision and Pattern Recognition · Computer Science 2026-05-13 Mert Keser , Halil Ibrahim Orhan , Niki Amini-Naieni , Gesina Schwalbe , Alois Knoll , Matthias Rottmann