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We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…

Machine Learning · Computer Science 2023-07-25 Sören Becker , Michal Klein , Alexander Neitz , Giambattista Parascandolo , Niki Kilbertus

We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…

Machine Learning · Computer Science 2021-07-14 Gabriel Kronberger , Lukas Kammerer , Michael Kommenda

We introduce ODEFormer, the first transformer able to infer multidimensional ordinary differential equation (ODE) systems in symbolic form from the observation of a single solution trajectory. We perform extensive evaluations on two…

Machine Learning · Computer Science 2023-10-10 Stéphane d'Ascoli , Sören Becker , Alexander Mathis , Philippe Schwaller , Niki Kilbertus

Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and…

Machine Learning · Computer Science 2026-02-10 Maximilian Mauel , Johannes R. Hübers , David Berghaus , Patrick Seifner , Ramses J. Sanchez

Symbolic regression, i.e. predicting a function from the observation of its values, is well-known to be a challenging task. In this paper, we train Transformers to infer the function or recurrence relation underlying sequences of integers…

Machine Learning · Computer Science 2022-06-29 Stéphane d'Ascoli , Pierre-Alexandre Kamienny , Guillaume Lample , François Charton

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Machine Learning · Computer Science 2020-10-19 Daehoon Gwak , Gyuhyeon Sim , Michael Poli , Stefano Massaroli , Jaegul Choo , Edward Choi

Natural laws are often described through differential equations yet finding a differential equation that describes the governing law underlying observed data is a challenging and still mostly manual task. In this paper we make a step…

Machine Learning · Computer Science 2022-11-08 Sören Becker , Michal Klein , Alexander Neitz , Giambattista Parascandolo , Niki Kilbertus

Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and…

Machine Learning · Computer Science 2021-07-16 Juliane Weilbach , Sebastian Gerwinn , Christian Weilbach , Melih Kandemir

Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…

Optimization and Control · Mathematics 2021-03-11 Xing Qiu , Tao Xu , Babak Soltanalizadeh , Hulin Wu

Offline imitation from observations aims to solve MDPs where only task-specific expert states and task-agnostic non-expert state-action pairs are available. Offline imitation is useful in real-world scenarios where arbitrary interactions…

Machine Learning · Computer Science 2023-11-03 Kai Yan , Alexander G. Schwing , Yu-Xiong Wang

Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging,…

Machine Learning · Computer Science 2025-10-15 Maximilian Mauel , Manuel Hinz , Patrick Seifner , David Berghaus , Ramses J. Sanchez

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…

Methodology · Statistics 2023-09-01 Itai Dattner , Shota Gugushvili , Oleksandr Laskorunskyi

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…

Machine Learning · Computer Science 2025-03-12 Xin Li , Chengli Zhao , Xue Zhang , Xiaojun Duan

Uncovering the underlying ordinary differential equations (ODEs) that govern dynamic systems is crucial for advancing our understanding of complex phenomena. Traditional symbolic regression methods often struggle to capture the temporal…

Machine Learning · Computer Science 2025-06-24 Yang Chang , Kuang-Da Wang , Ping-Chun Hsieh , Cheng-Kuan Lin , Wen-Chih Peng

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

Computation · Statistics 2025-06-30 Mohan Wu , Martin Lysy

Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations,…

Molecular Networks · Quantitative Biology 2023-02-14 Samuel W. K. Wong , Shihao Yang , S. C. Kou

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

Machine Learning · Statistics 2022-06-20 Paidamoyo Chapfuwa , Sherri Rose , Lawrence Carin , Edward Meeds , Ricardo Henao

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…

Methodology · Statistics 2023-10-25 Mingwei Xu , Samuel W. K. Wong , Peijun Sang

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…

Mathematical Software · Computer Science 2017-07-17 Andrea Vandin

Learning-enabled control systems increasingly rely on multiple sensing modalities (e.g., vision, audio, language, etc.) for perception and decision support. A key challenge is that multi-modal sensor training dynamics are often imbalanced:…

Machine Learning · Computer Science 2026-04-01 Heshan Fernando , Quan Xiao , Parikshit Ram , Yi Zhou , Horst Samulowitz , Nathalie Baracaldo , Tianyi Chen
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