English
Related papers

Related papers: A Self-Adaptive Penalty Method for Integrating Pri…

200 papers

Conservation of energy is at the core of many physical phenomena and dynamical systems. There have been a significant number of works in the past few years aimed at predicting the trajectory of motion of dynamical systems using neural…

Machine Learning · Computer Science 2022-08-05 Yi Heng Lim , Muhammad Firmansyah Kasim

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…

Machine Learning · Computer Science 2024-02-16 Alistair White , Niki Kilbertus , Maximilian Gelbrecht , Niklas Boers

Neural Ordinary Differential Equations (Neural ODEs) construct the continuous dynamics of hidden units using ordinary differential equations specified by a neural network, demonstrating promising results on many tasks. However, Neural ODEs…

Computer Vision and Pattern Recognition · Computer Science 2024-01-11 Haoyu Chu , Shikui Wei , Qiming Lu , Yao Zhao

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…

Machine Learning · Computer Science 2025-01-16 Grant Norman , Jacqueline Wentz , Hemanth Kolla , Kurt Maute , Alireza Doostan

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

Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time…

Machine Learning · Computer Science 2025-08-05 Haoran Li , Muhao Guo , Yang Weng , Hanghang Tong

Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit…

Machine Learning · Computer Science 2023-10-24 Achkan Salehi , Steffen Rühl , Stephane Doncieux

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

Machine Learning · Computer Science 2021-11-02 Mansura Habiba , Barak A. Pearlmutter

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

Poverty is a complex dynamic challenge that cannot be adequately captured using predefined differential equations. Nowadays, artificial machine learning (ML) methods have demonstrated significant potential in modelling real-world dynamical…

Dynamical Systems · Mathematics 2026-04-02 Sandeep Kumar Samota , Snehashish Chakraverty , Narayan Sethi

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

Machine Learning · Computer Science 2025-05-28 Avik Pal , Alan Edelman , Christopher Rackauckas

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Machine Learning · Computer Science 2022-10-12 Andrzej Dulny , Andreas Hotho , Anna Krause

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

Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…

Machine Learning · Computer Science 2024-09-24 Jaouad Dabounou

There has been a significant focus on modelling emotion ambiguity in recent years, with advancements made in representing emotions as distributions to capture ambiguity. However, there has been comparatively less effort devoted to the…

Artificial Intelligence · Computer Science 2024-08-01 Jingyao Wu , Ting Dang , Vidhyasaharan Sethu , Eliathamby Ambikairajah

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Machine Learning · Computer Science 2019-11-22 Jonathan B. Freund , Jonathan F. MacArt , Justin Sirignano

The iterative search process of evolutionary algorithms (EAs) encapsulates optimization knowledge within historical populations and fitness evaluations. Effective utilization of this knowledge is crucial for facilitating knowledge transfer…

Neural and Evolutionary Computing · Computer Science 2026-04-22 Chao Wang , Lingling Li , Licheng Jiao , Jiaxuan Zhao , Fang Liu , Shuyuan Yang

Causal inference in continuous-time sequential decision problems is challenged by hidden confounders. We show that, in latent state-space models with time-varying interventions, observability of the latent dynamics from observed data is…

Machine Learning · Computer Science 2026-05-14 Jennifer Wendland , Nicolas Freitag , Maik Kschischo

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

The penalization method is a popular technique to provide particle swarm optimizers with the ability to handle constraints. The downside is the need of penalization coefficients whose settings are problem-specific. While adaptive…

Neural and Evolutionary Computing · Computer Science 2021-01-28 Mauro S. Innocente , Johann Sienz