Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

126
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
126
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

100
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
100
Operon Model01:23

Operon Model

108
The operon model represents a fundamental mechanism of gene regulation in prokaryotes, enabling coordinated expression of genes involved in related metabolic or functional pathways. Operons consist of structural genes, a promoter, and an operator, with transcription regulated by repressors, activators, and small effector molecules.Structure and Function of OperonsAn operon is a cluster of structural genes transcribed together under the control of a single promoter. The promoter region...
108
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

3.3K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.3K
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

704
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
704
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

130
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
130

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The role of computational science in digital twins.

Nature computational science·2024
Same author

Digital twins in mechanical and aerospace engineering.

Nature computational science·2024
Same author

Learning physics-based reduced-order models from data using nonlinear manifolds.

Chaos (Woodbury, N.Y.)·2024
Same author

A probabilistic graphical model foundation for enabling predictive digital twins at scale.

Nature computational science·2024
Same author

Scaling digital twins from the artisanal to the industrial.

Nature computational science·2024
Same author

The imperative of physics-based modeling and inverse theory in computational science.

Nature computational science·2024
Same journal

Correction to: 'Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes' (2020), by Mingotti et al.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

A stable hothouse triggered by a tipping mechanism.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Global stability of the Atlantic overturning circulation: edge state, long transients and boundary crisis under CO2 forcing.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Morse index classification and landscape of Kuramoto system for Hebbian-based binary pattern recognition.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Interpretable and equation-free response theory for complex systems.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
See all related articles

Related Experiment Video

Updated: Sep 7, 2025

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.3K

Localized non-intrusive reduced-order modelling in the operator inference framework.

Rudy Geelen1, Karen Willcox1

  • 1Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 20, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces data-driven localized reduced models, adapting to local dynamics for efficient computation. This non-intrusive operator inference method accelerates simulations of complex systems like partial differential equations.

Keywords:
data clusteringlocalizationmodel reductionnonlinear partial differential equationsoperator inferenceproper orthogonal decomposition

More Related Videos

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression
06:50

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression

Published on: November 8, 2019

6.7K
Constructing and Visualizing Models using Mime-based Machine-learning Framework
06:19

Constructing and Visualizing Models using Mime-based Machine-learning Framework

Published on: July 22, 2025

597

Related Experiment Videos

Last Updated: Sep 7, 2025

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.3K
O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression
06:50

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression

Published on: November 8, 2019

6.7K
Constructing and Visualizing Models using Mime-based Machine-learning Framework
06:19

Constructing and Visualizing Models using Mime-based Machine-learning Framework

Published on: July 22, 2025

597

Area of Science:

  • Computational Science
  • Applied Mathematics
  • Data-Driven Modeling

Background:

  • Reduced models are crucial for simulating complex dynamical systems, but global approaches struggle with nonlinearities and parameter sensitivity.
  • Existing methods often require intrusive modifications to high-fidelity codes, limiting their applicability.
  • Nonlinear partial differential equations (PDEs) present significant computational challenges due to localized phenomena and parameter variations.

Purpose of the Study:

  • To develop a data-driven, non-intrusive method for learning localized reduced models.
  • To enable adaptive reduced-order modeling that efficiently captures local dynamics.
  • To improve the computational speed and accuracy of simulating complex physical systems.

Main Methods:

  • Employs multiple local approximation subspaces instead of a single global basis.
  • Utilizes operator inference to learn localized reduced operators from snapshot data in an offline phase.
  • Implements an online phase with adaptive selection of local bases based on the system's current state.

Main Results:

  • Demonstrates significant computational speedups for the Burgers' equation and Cahn-Hilliard equation.
  • Maintains good accuracy in reduced models by adapting to local dynamics.
  • The non-intrusive approach is shown to be portable and applicable to legacy or proprietary codes.

Conclusions:

  • Localized operator inference provides an efficient and accurate data-driven approach for reduced-order modeling.
  • The method's non-intrusive nature broadens its applicability across diverse scientific and engineering problems.
  • This technique offers a powerful tool for accelerating the simulation of nonlinear PDEs and complex dynamical systems.