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Advanced deep learning-based approaches have been actively applied to forecast the spatiotemporal physical dynamics governed by partial differential equations (PDEs), which acts as a critical procedure in tackling many science and…

Machine Learning · Computer Science 2026-03-03 Siyang Li , Yize Chen , Yan Guo , Ming Huang , Hui Xiong

As traditional machine learning tools are increasingly applied to science and engineering applications, physics-informed methods have emerged as effective tools for endowing inferences with properties essential for physical realizability.…

Numerical Analysis · Mathematics 2020-12-23 Nathaniel Trask , Andy Huang , Xiaozhe Hu

This paper proposes the use of spectral element methods \citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system identification. This is achieved…

Neural and Evolutionary Computing · Computer Science 2020-01-20 Alessio Quaglino , Marco Gallieri , Jonathan Masci , Jan Koutník

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…

Machine Learning · Computer Science 2026-05-12 Mingtao Xia , Xiangting Li , Qijing Shen , Tom Chou

Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…

Robotics · Computer Science 2024-06-13 Thai Duong , Abdullah Altawaitan , Jason Stanley , Nikolay Atanasov

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is a necessary step to draw conclusions from these data, and it often becomes quite essential to construct dynamical models using these…

Machine Learning · Computer Science 2021-09-24 Pawan Goyal , Peter Benner

Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers. These solvers are computationally expensive, requiring the use of tiny step sizes for numerical stability and…

Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…

Machine Learning · Computer Science 2022-09-20 Lucas Böttcher , Thomas Asikis

We present a mathematical and computational framework for the problem of learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the…

Optimization and Control · Mathematics 2022-01-19 Amir Ali Ahmadi , Bachir El Khadir

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

While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…

Machine Learning · Statistics 2020-06-19 Horia Mania , Michael I. Jordan , Benjamin Recht

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…

Machine Learning · Computer Science 2023-11-14 Ilze Amanda Auzina , Çağatay Yıldız , Sara Magliacane , Matthias Bethge , Efstratios Gavves

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

Machine Learning · Computer Science 2025-03-27 C. Coelho , M. Fernanda P. Costa , L. L. Ferrás

Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…

Dynamical Systems · Mathematics 2023-01-18 Yuji Okamoto , Ryosuke Kojima

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

Machines of all kinds from vehicles to industrial equipment are increasingly instrumented with hundreds of sensors. Using such data to detect anomalous behaviour is critical for safety and efficient maintenance. However, anomalies occur…

Artificial Intelligence · Computer Science 2016-05-06 Mohit Yadav , Pankaj Malhotra , Lovekesh Vig , K Sriram , Gautam Shroff

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…

Computational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of Machine Learning (ML) to recover physical models from…

Machine Learning · Computer Science 2023-12-06 Simone Manti , Alessandro Lucantonio

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…

Modern robotics is gravitating toward increasingly collaborative human robot interaction. Tools such as acceleration policies can naturally support the realization of reactive, adaptive, and compliant robots. These tools require us to model…

Robotics · Computer Science 2017-10-09 Daniel Kappler , Franziska Meier , Nathan Ratliff , Stefan Schaal