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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

Research in quantum machine learning has recently proliferated due to the potential of quantum computing to accelerate machine learning. An area of machine learning that has not yet been explored is neural ordinary differential equation…

Quantum Physics · Physics 2025-06-27 Nicholas S. DiBrita , Jason Han , Tirthak Patel

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Machine Learning · Computer Science 2025-10-20 Ziqian Li , Kang Liu , Yongcun Song , Hangrui Yue , Enrique Zuazua

Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…

Machine Learning · Computer Science 2026-05-27 Divyam Goel , Nithin Chalapathi , Sanjeev Raja , Aditi S. Krishnapriyan

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…

Systems and Control · Electrical Eng. & Systems 2020-11-30 Aaron Tuor , Jan Drgona , Draguna Vrabie

A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an…

Dynamical Systems · Mathematics 2018-05-23 Bernadett Ács , Gergely Szlobodnyik , Gábor Szederkényi

The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…

Dynamical Systems · Mathematics 2016-05-10 Meritxell Sáez , Carsten Wiuf , Elisenda Feliu

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

Machine Learning · Computer Science 2022-12-01 Zhilu Lai , Wei Liu , Xudong Jian , Kiran Bacsa , Limin Sun , Eleni Chatzi

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

Numerical Analysis · Mathematics 2019-07-31 Hyeontae Jo , Hwijae Son , Hyung Ju Hwang , Eunheui Kim

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability…

Molecular Networks · Quantitative Biology 2011-05-11 Gabor Szederkenyi , Katalin M. Hangos

Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…

Machine Learning · Computer Science 2022-10-17 Kazuki Irie , Francesco Faccio , Jürgen Schmidhuber

We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…

Machine Learning · Computer Science 2020-09-10 Victor M. Martinez Alvarez , Rareş Roşca , Cristian G. Fălcuţescu

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Machine Learning · Computer Science 2020-05-21 Mansura Habiba , Barak A. Pearlmutter

Inferring parameters of macro-kinetic growth models, typically represented by Ordinary Differential Equations (ODE), from the experimental data is a crucial step in bioprocess engineering. Conventionally, estimates of the parameters are…

Machine Learning · Computer Science 2023-12-07 Maxim Borisyak , Stefan Born , Peter Neubauer , Mariano Nicolas Cruz-Bournazou

We report a novel approach for the efficient computation of solutions of a broad class of large-scale systems of non-linear ordinary differential equations, describing aggregation kinetics. The method is based on a new take on the…

Numerical Analysis · Mathematics 2023-12-14 Dmitrii Lukashevich , Ivan Tyukin , Nikolay Brilliantov

Machine learning techniques applied to chemical reactions has a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to platforms for reaction planning. ML-based techniques can be of…

Chemical Physics · Physics 2021-01-12 M. Meuwly

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…

Machine Learning · Computer Science 2025-03-10 Jindou Jia , Zihan Yang , Meng Wang , Kexin Guo , Jianfei Yang , Xiang Yu , Lei Guo

We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs).…

Machine Learning · Computer Science 2022-06-22 Thomas Asikis , Lucas Böttcher , Nino Antulov-Fantulin

In many scientific fields, there is an interest in understanding the way in which complex chemical networks evolve. The chemical networks which researchers focus upon, have become increasingly complex and this has motivated the development…