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Ecological Momentary Assessment (EMA) studies enable the collection of high-frequency self-reports of suicidal thoughts and behaviors (STBs) via smartphones. Latent stochastic differential equations (SDEs) are a promising model class for…

Machine Learning · Statistics 2026-05-26 Malinda Lu , Yue-Jane Liu , Matthew K. Nock , Yaniv Yacoby

We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a…

Mathematical Software · Computer Science 2023-12-19 Oren Bassik , Yosef Berman , Soo Go , Hoon Hong , Ilia Ilmer , Alexey Ovchinnikov , Chris Rackauckas , Pedro Soto , Chee Yap

Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…

Machine Learning · Computer Science 2026-05-21 Jianhong Chen , Naichen Shi , Xubo Yue

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

Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…

Methodology · Statistics 2017-11-08 Philipp Frank , Theo Steininger , Torsten A. Enßlin

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

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

A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…

Data Analysis, Statistics and Probability · Physics 2016-11-25 Daniel Peavoy , Christian L. E. Franzke , Gareth O. Roberts

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

Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…

Dynamical Systems · Mathematics 2025-02-04 David Sabin-Miller , Daniel M. Abrams

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\bm\theta$ of physical significance…

Statistics Theory · Mathematics 2014-11-05 Prithwish Bhaumik , Subhashis Ghosal

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

Machine Learning · Statistics 2019-10-28 Batuhan Güler , Alexis Laignelet , Panos Parpas

The hazard function represents one of the main quantities of interest in the analysis of survival data. We propose a general approach for parametrically modelling the dynamics of the hazard function using systems of autonomous ordinary…

Methodology · Statistics 2024-07-19 J. A. Christen , F. J. Rubio

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

Machine Learning · Computer Science 2022-03-04 Hanshu Yan , Jiawei Du , Vincent Y. F. Tan , Jiashi Feng

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by timescale separation,…

Dynamical Systems · Mathematics 2026-02-27 Manu Jayadharan , Christina Catlett , Arthur N. Montanari , Niall M. Mangan

In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon,…

Machine Learning · Computer Science 2023-12-15 Karthik Elamvazhuthi , Samet Oymak , Fabio Pasqualetti

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

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

Machine Learning · Computer Science 2023-05-23 Katharina Ott , Michael Tiemann , Philipp Hennig

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

We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…

Optimization and Control · Mathematics 2025-06-16 M. Fernández de Dios , Ángel M. González-Rueda , Julio R. Banga , Julio González-Díaz , David R. Penas