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Related Concept Videos

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

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.
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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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Improving Translational Accuracy

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Related Experiment Videos

EMBEDDED NONLOCAL OPERATOR REGRESSION (ENOR): QUANTIFYING MODEL ERROR IN LEARNING NONLOCAL OPERATORS.

Yiming Fan1, Habib N Najm2, Yue Yu1

  • 1Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA.

International Journal for Uncertainty Quantification
|June 25, 2026
PubMed
Summary
This summary is machine-generated.

We introduce Embedded Nonlocal Operator Regression (ENOR), a novel framework for accurate long-term simulations. ENOR learns surrogate models and their errors, improving uncertainty quantification for material responses.

Keywords:
Bayesian InferenceModel ErrorNonlocal ModelUncertainty Quantification

Related Experiment Videos

Area of Science:

  • Computational mechanics
  • Materials science
  • Numerical analysis

Background:

  • Nonlocal integral operators are effective for multiscale modeling but introduce errors in long-term simulations.
  • These discrepancies can accumulate, compromising the reliability of homogenized material response predictions.

Purpose of the Study:

  • To develop a robust framework for learning nonlocal homogenized surrogate models and their associated structural errors.
  • To enable discrepancy-adaptive uncertainty quantification for improved long-term predictions.

Main Methods:

  • The proposed Embedded Nonlocal Operator Regression (ENOR) framework builds upon Nonlocal Operator Regression (NOR).
  • It incorporates an embedded model error term within the trainable kernel.
  • Bayesian inference and a multilevel delayed acceptance Markov chain Monte Carlo (MLDA-MCMC) method are used for efficient parameter estimation and uncertainty quantification.

Main Results:

  • ENOR successfully learns both the surrogate model and its structural error.
  • The framework provides discrepancy-adaptive uncertainty quantification for homogenized material responses.
  • Application to long-term wave propagation in a 1D bar demonstrated improved posterior predictive uncertainty estimation compared to additive noise models.

Conclusions:

  • ENOR offers a reliable approach to address discrepancies in nonlocal homogenization models.
  • The method enhances the accuracy and trustworthiness of predictions in long-term simulations.
  • This framework advances the development of robust computational homogenization techniques.