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In many fields of application, dynamic processes that evolve through time are well described by systems of ordinary differential equations (ODEs). The analytical solution of the ODEs is often not available and different methods have been…

Methodology · Statistics 2017-07-19 Saverio Ranciati , Cinzia Viroli , Ernst Wit

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Computer Vision and Pattern Recognition · Computer Science 2024-08-26 Defang Chen , Zhenyu Zhou , Jian-Ping Mei , Chunhua Shen , Chun Chen , Can Wang

We demonstrate the use of symbolic regression in deriving analytical formulas, which are needed at various stages of a typical experimental analysis in collider phenomenology. As a first application, we consider kinematic variables like the…

High Energy Physics - Phenomenology · Physics 2023-03-29 Zhongtian Dong , Kyoungchul Kong , Konstantin T. Matchev , Katia Matcheva

We present a falsification framework that integrates learned surrogate dynamics with optimal control to efficiently generate counterexamples for cyber-physical systems specified in signal temporal logic (STL). The unknown system dynamics…

Systems and Control · Electrical Eng. & Systems 2026-02-03 Lasse Kötz , Jonas Sjöberg , Knut Åkesson

Many existing motion prediction approaches rely on symbolic perception outputs to generate agent trajectories, such as bounding boxes, road graph information and traffic lights. This symbolic representation is a high-level abstraction of…

Computer Vision and Pattern Recognition · Computer Science 2024-05-01 Norman Mu , Jingwei Ji , Zhenpei Yang , Nate Harada , Haotian Tang , Kan Chen , Charles R. Qi , Runzhou Ge , Kratarth Goel , Zoey Yang , Scott Ettinger , Rami Al-Rfou , Dragomir Anguelov , Yin Zhou

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…

Machine Learning · Computer Science 2022-08-16 Peter Y. Lu , Joan Ariño , Marin Soljačić

To be fully useful for public health practice, models for epidemic response must be able to do more than predict -- it is also important to incorporate the mechanisms underlying transmission dynamics to enable policymakers and practitioners…

Quantitative Methods · Quantitative Biology 2025-05-26 Jiale Tan , Marisa C. Eisenberg

Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs). In the context of machine learning, differentiable solvers are central for Neural ODEs…

Machine Learning · Computer Science 2021-07-06 Weiming Zhi , Tin Lai , Lionel Ott , Edwin V. Bonilla , Fabio Ramos

Masked image modeling (MIM) has been recognized as a strong self-supervised pre-training approach in the vision domain. However, the mechanism and properties of the learned representations by such a scheme, as well as how to further enhance…

Computer Vision and Pattern Recognition · Computer Science 2024-04-10 Kevin Zhang , Zhiqiang Shen

Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…

Methodology · Statistics 2025-07-10 Maren Hackenberg , Astrid Pechmann , Clemens Kreutz , Janbernd Kirschner , Harald Binder

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

Machine Learning · Computer Science 2022-03-16 Aowabin Rahman , Ján Drgoňa , Aaron Tuor , Jan Strube

Existing methods enhance the training of detection transformers by incorporating an auxiliary one-to-many assignment. In this work, we treat the model as a multi-task framework, simultaneously performing one-to-one and one-to-many…

Computer Vision and Pattern Recognition · Computer Science 2025-06-27 Chang-Bin Zhang , Yujie Zhong , Kai Han

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

Machine Learning · Computer Science 2019-12-06 Philippe Wenk , Gabriele Abbati , Michael A Osborne , Bernhard Schölkopf , Andreas Krause , Stefan Bauer

Deep Symbolic Optimization (DSO) is a novel computational framework that enables symbolic optimization for scientific discovery, particularly in applications involving the search for intricate symbolic structures. One notable example is…

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor…

Machine Learning · Computer Science 2023-02-09 Valerii Iakovlev , Cagatay Yildiz , Markus Heinonen , Harri Lähdesmäki

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

Numerical Analysis · Mathematics 2020-06-04 Junyu Liu , Zichao Long , Ranran Wang , Jie Sun , Bin Dong

Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…

Dynamical Systems · Mathematics 2026-05-07 Nibodh Boddupalli , Timothy Matchen , Jeff Moehlis

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…

Machine Learning · Computer Science 2021-10-28 Ricky T. Q. Chen , Brandon Amos , Maximilian Nickel

We present MILO (Metric for Image- and Latent-space Optimization), a lightweight, multiscale, perceptual metric for full-reference image quality assessment (FR-IQA). MILO is trained using pseudo-MOS (Mean Opinion Score) supervision, in…

Computer Vision and Pattern Recognition · Computer Science 2025-09-03 Uğur Çoğalan , Mojtaba Bemana , Karol Myszkowski , Hans-Peter Seidel , Colin Groth

We present a noise guided trajectory based system identification method for inferring the dynamical structure from observation generated by stochastic differential equations. Our method can handle various kinds of noise, including the case…

Numerical Analysis · Mathematics 2024-03-06 Ziheng Guo , Igor Cialenco , Ming Zhong