ArticleScientific reports2022
Data-driven discovery of the governing equations of dynamical systems via moving horizon optimization.
Article in Scientific reports, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
What it found
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Who cites it
11 citing papers in PubMed.
- Encoding Cumulation to Learn Perturbative Nonlinear Oscillatory Dynamics.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- Data-driven discovery of digital twins in biomedical research.Briefings in bioinformatics · 2026Review
- High-order expansion of neural ordinary differential equation flows.Science advances · 2025Article
- Implicit Runge-Kutta based sparse identification of governing equations in biologically motivated systems.Scientific reports · 2025Article
- Discovering governing equations of biological systems through representation learning and sparse model discovery.NAR genomics and bioinformatics · 2025Article
- Effects of Surrogate Hybridization and Adaptive Sampling for Simulation-Based Optimization.Industrial & engineering chemistry research · 2025Article
- Derivative-Free Domain-Informed Data-Driven Discovery of Sparse Kinetic Models.Industrial & engineering chemistry research · 2025Article
- From biological data to oscillator models using SINDy.iScience · 2024Article
- A review of the application of artificial intelligence to nuclear reactors: Where we are and what's next.Heliyon · 2023Review
- Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion.Research (Washington, D.C.) · 2023Article
- Modeling of Hydrodynamic Cavitation Reactors: Reflections on Present Status and Path Forward.ACS engineering Au · 2022Review
Corrections and comments
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Authors and funding
2 authors.
Funding
Abstract
Discovering the governing laws underpinning physical and chemical phenomena entirely from data is a key step towards understanding and ultimately controlling systems in science and engineering. Noisy measurements and complex, highly nonlinear underlying dynamics hinder the identification of such governing laws. In this work, we introduce a machine learning framework rooted in moving horizon nonlinear optimization for identifying governing equations in the form of ordinary differential equations from noisy experimental data sets. Our approach evaluates sequential subsets of measurement data, and exploits statistical arguments to learn truly parsimonious governing equations from a large dictionary of basis functions. The proposed framework reduces gradient approximation errors by implicitly embedding an advanced numerical discretization scheme, which improves robustness to noise as well as to model stiffness. Canonical nonlinear dynamical system examples are used to demonstrate that our approach can accurately recover parsimonious governing laws under increasing levels of measurement noise, and outperform state of the art frameworks in the literature. Further, we consider a non-isothermal chemical reactor example to demonstrate that the proposed framework can cope with basis functions that have nonlinear (unknown) parameterizations.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.