Search research articles

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...

Residuals and Least-Squares Property

Residuals and Least-Squares Property

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...

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

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

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...

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...

Bernoulli's Equation: Problem Solving

Bernoulli's Equation: Problem Solving

A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity...

Calibration Curves: Linear Least Squares

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...

You might also read

Related Articles

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

Sort by

Same author

Physics-Informed Neural Networks with Unknown Partial Differential Equations: An Application in Multivariate Time Series.

Entropy (Basel, Switzerland)·2025

Same author

Variational Bayesian Approximation (VBA): Implementation and Comparison of Different Optimization Algorithms.

Entropy (Basel, Switzerland)·2024

Same author

Dynamical system identification, model selection, and model uncertainty quantification by Bayesian inference.

Chaos (Woodbury, N.Y.)·2024

Same author

Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain.

Entropy (Basel, Switzerland)·2020

Same author

Clinical Relevance of the First Domomedicine Platform Securing Multidrug Chronotherapy Delivery in Metastatic Cancer Patients at Home: The inCASA European Project.

Journal of medical Internet research·2016

Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026

Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026

Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026

Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026

Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026

Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026

See all related articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Search research articles

Related Experiment Video

Updated: Oct 9, 2025

A Novel Experimental and Analytical Approach to the Multimodal Neural Decoding of Intent During Social Interaction in Freely-behaving Human Infants

A Novel Experimental and Analytical Approach to the Multimodal Neural Decoding of Intent During Social Interaction in Freely-behaving Human Infants

Published on: October 4, 2015

Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems.

Ali Mohammad-Djafari^1,2,3

¹Laboratoire des Signaux et Système, CNRS, CentraleSupélec-University Paris Saclay, 91192 Gif-sur-Yvette, France.

Entropy (Basel, Switzerland)

|December 24, 2021

Summary

This summary is machine-generated.

Machine learning (ML) offers practical solutions for inverse problems, complementing traditional regularization methods. This approach enhances computational efficiency and flexibility in complex data modeling for applications like image reconstruction.

Keywords:

Bayesian inference Gauss–Markov–Potts Variational Bayesian Approach (VBA)artificial intelligence inverse problems machine learning physics-informed ML regularization

More Related Videos

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Published on: November 2, 2012

Author Spotlight: UAV Remote Sensing for Efficient Invasive Plant Biomass Estimation

Author Spotlight: UAV Remote Sensing for Efficient Invasive Plant Biomass Estimation

Published on: February 9, 2024

Related Experiment Videos

Last Updated: Oct 9, 2025

A Novel Experimental and Analytical Approach to the Multimodal Neural Decoding of Intent During Social Interaction in Freely-behaving Human Infants

A Novel Experimental and Analytical Approach to the Multimodal Neural Decoding of Intent During Social Interaction in Freely-behaving Human Infants

Published on: October 4, 2015

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Published on: November 2, 2012

Author Spotlight: UAV Remote Sensing for Efficient Invasive Plant Biomass Estimation

Author Spotlight: UAV Remote Sensing for Efficient Invasive Plant Biomass Estimation

Published on: February 9, 2024

Area of Science:

Computational Mathematics
Applied Physics
Machine Learning

Background:

Classical inverse problem solutions rely on regularization theory, optimizing data-model matching and regularization terms.
Bayesian Maximum A Posteriori (MAP) interpretation links these terms to likelihood and prior probability models, offering flexibility but posing computational challenges.

Purpose of the Study:

To explore the synergy between machine learning (ML) and classical inversion techniques for solving inverse problems.
To demonstrate how ML methods can provide efficient and practical approximate solutions, overcoming computational burdens of traditional Bayesian approaches.

Main Methods:

Review of regularization theory and its Bayesian Maximum A Posteriori (MAP) interpretation.
Introduction of machine learning (ML) methods, including neural networks (NN), deep neural networks (DNN), and physics-informed neural networks (PINN).
Application of these methods to image denoising, image restoration, and computed tomography (CT) image reconstruction.

Main Results:

Machine learning methods, particularly neural networks, offer practical and computationally efficient approximate solutions to inverse problems.
The integration of ML with inversion techniques enhances the ability to handle complex data and model priors.
Demonstrated success in image denoising, restoration, and CT reconstruction highlights the cooperative potential.

Conclusions:

Machine learning provides a powerful toolkit for addressing the computational challenges in solving inverse problems.
The combination of ML and classical inversion methods opens new avenues for practical applications in image processing and reconstruction.
This tutorial highlights the growing importance of ML in scientific computing and data analysis.