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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

88
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...
88
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

70
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
70
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

508
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
508
Pharmacokinetic Models: Comparison and Selection Criterion01:26

Pharmacokinetic Models: Comparison and Selection Criterion

115
Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.
115
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

7.7K
The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
7.7K
Analysis of Population Pharmacokinetic Data01:12

Analysis of Population Pharmacokinetic Data

321
Analysis of population pharmacokinetic data involves studying the behavior of drugs within diverse populations to understand their pharmacokinetic parameters. Traditional pharmacokinetic methods typically involve collecting samples from a few individuals and estimating these parameters. While these methods are commonly used, they have limitations in capturing the variability in drug response among individuals or heterogeneous populations. Population pharmacokinetics is employed to address these...
321

You might also read

Related Articles

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

Sort by
Same author

Generalization as the great leap in evolvability: insights from machine learning.

Evolution; international journal of organic evolution·2026
Same author

The Price Equation Reveals a Universal Force-Metric-Bias Law of Algorithmic Learning and Natural Selection.

Entropy (Basel, Switzerland)·2025
Same author

Circuit Design in Biology and Machine Learning. II. Anomaly Detection.

Entropy (Basel, Switzerland)·2025
Same author

How cancer arises: Genetics releases, plasticity creates, genetics stabilizes.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Circuit design in biology and machine learning. I. Random networks and dimensional reduction.

Evolution; international journal of organic evolution·2025
Same author

Natural selection at multiple scales.

Evolution; international journal of organic evolution·2025
Same journal

Double Parasitism by Two Cuckoo Gentes in a Daurian Redstart Nest.

Ecology and evolution·2026
Same journal

Size and Ecology of a Giant <i>Pavona clavus</i> Coral Colony in the Kingdom of Tonga.

Ecology and evolution·2026
Same journal

How to Account for Past Selection When Maternal Effects Are Cascading.

Ecology and evolution·2026
Same journal

Light and Pollination Limitation Alter Patterns of Fitness and Phenotypic Selection in <i>Sagittaria trifolia</i> L.: Insights From Sequential Inflorescences.

Ecology and evolution·2026
Same journal

Teaching Macrosystems Ecology Concepts With a Collaborative, Adaptable Education Module.

Ecology and evolution·2026
Same journal

Instance of a Heteroplasmic Mitogenome in Alvinocaridid Shrimp <i>Mirocaris fortunata</i> (Martin & Christiansen 1995) Found at the Moytirra Deep-Sea High-Temperature Hydrothermal Vent Field.

Ecology and evolution·2026
See all related articles

Related Experiment Video

Updated: Aug 6, 2025

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
20:24

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

16.6K

Optimizing differential equations to fit data and predict outcomes.

Steven A Frank1

  • 1Department of Ecology and Evolutionary Biology University of California Irvine California USA.

Ecology and Evolution
|March 23, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces advanced methods for fitting differential equation models to observed data, overcoming common challenges in ecological modeling. The research highlights how neural ordinary differential equations and Bayesian sampling improve model accuracy and prediction for dynamic systems.

Keywords:
Bayesian analysisJulia programming languageLangevin dynamicsartificial neural networksautomatic differentiationdifferential equation modelsecological and evolutionary dynamicsoptimization

More Related Videos

Procedure to Evaluate the Efficiency of Flocculants for the Removal of Dispersed Particles from Plant Extracts
10:37

Procedure to Evaluate the Efficiency of Flocculants for the Removal of Dispersed Particles from Plant Extracts

Published on: April 9, 2016

9.0K
An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

2.1K

Related Experiment Videos

Last Updated: Aug 6, 2025

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
20:24

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

16.6K
Procedure to Evaluate the Efficiency of Flocculants for the Removal of Dispersed Particles from Plant Extracts
10:37

Procedure to Evaluate the Efficiency of Flocculants for the Removal of Dispersed Particles from Plant Extracts

Published on: April 9, 2016

9.0K
An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

2.1K

Area of Science:

  • Dynamical systems analysis
  • Computational mathematics
  • Ecological modeling

Background:

  • Fitting differential equation models to observed data is crucial for understanding system dynamics.
  • Traditional methods face challenges in gradient computation and achieving good fits.
  • Recent advances in automatic differentiation offer new possibilities for dynamic system analysis.

Purpose of the Study:

  • To illustrate methods for overcoming common challenges in fitting differential equation models to real-world data.
  • To compare the performance of ordinary differential equations (ODEs) and neural ordinary differential equations (NODEs) in ecological modeling.
  • To analyze model prediction quality and identify underfitting/overfitting tendencies.

Main Methods:

  • Utilized classic ecological data (hare and lynx populations) for model fitting.
  • Employed ordinary differential equations (ODEs) and neural ordinary differential equations (NODEs).
  • Applied Bayesian-inspired preconditioned stochastic gradient Langevin dynamics (pSGLD) for posterior distribution analysis.

Main Results:

  • Demonstrated overcoming common fitting challenges with ODEs and NODEs.
  • Compared model fits across different parameter spaces and dimensions.
  • pSGLD analysis revealed tendencies for underfitting and overfitting in various models.

Conclusions:

  • Coupling fitted differential equation systems with pSGLD sampling offers a powerful approach to study optimization surfaces.
  • This methodology provides insights into the geometry of observed and model trajectories.
  • The study advances the understanding and application of differential equation modeling in complex systems.