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

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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...
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A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth
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ADMM-Based Algorithm for Training Fault Tolerant RBF Networks and Selecting Centers.

Hao Wang, Ruibin Feng, Zi-Fa Han

    IEEE Transactions on Neural Networks and Learning Systems
    |August 18, 2017
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    Summary

    This study introduces a novel fault-tolerant algorithm for training Radial Basis Function (RBF) networks, simultaneously selecting RBF centers and improving network performance in the presence of faults.

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    Area of Science:

    • Machine Learning
    • Artificial Intelligence
    • Computational Science

    Background:

    • Selecting appropriate Radial Basis Function (RBF) centers is crucial for RBF network training.
    • Existing center selection algorithms often fail in fault-tolerant scenarios.
    • There is a need for robust methods that can handle faults during RBF network training.

    Purpose of the Study:

    • To develop a fault-tolerant algorithm for RBF network training.
    • To achieve simultaneous RBF center selection and network training.
    • To enhance the robustness of RBF networks against potential faults.

    Main Methods:

    • Utilizing all training input vectors as initial RBF centers.
    • Incorporating an L1-norm term into the objective function for sparsity and center selection.
    • Formulating the problem as a constrained optimization task due to the non-differentiable L1-norm.
    • Applying the alternating direction method of multipliers (ADMM) framework to solve the optimization problem.

    Main Results:

    • The proposed algorithm effectively performs RBF center selection during the training phase.
    • The L1-norm regularization successfully drives unimportant weights to zero, facilitating center selection.
    • The ADMM-based approach provides a convergent solution for the constrained optimization problem.
    • Simulation results demonstrate the superiority of the proposed method over existing algorithms.

    Conclusions:

    • The developed fault-tolerant algorithm offers an effective approach for simultaneous RBF center selection and network training.
    • This method enhances the robustness of RBF networks, particularly in fault-prone environments.
    • The proposed technique represents a significant advancement in RBF network training methodologies.