Numerical Methods

Solving Plane Fracture Mechanics Problems Using Physics-Informed Neural Networks (PINNs)

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Solving Plane Fracture Mechanics Problems Using Physics-Informed Neural Networks (PINNs)

Physics-Informed Neural Networks (PINNs) is a numerical simulation method that combines neural networks with material constitutive models (PDEs). PINNs can be used to solve fracture mechanics problems without the need for discretizing the mesh. When using PINNs to solve fracture mechanics problems, it is usually necessary to embed the physical equations and initial/boundary conditions as … Read more

Comprehensive Summary of Optimization Algorithms in Machine Learning

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Comprehensive Summary of Optimization Algorithms in Machine Learning

Introduction For almost all machine learning algorithms, whether supervised learning, unsupervised learning, or reinforcement learning, they ultimately boil down to solving optimization problems. Therefore, optimization methods play a central role in the derivation and implementation of machine learning algorithms. In this article, I will provide a comprehensive summary of the optimization algorithms used in machine … Read more

A Comprehensive Guide to Optimization Algorithms in Machine Learning

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A Comprehensive Guide to Optimization Algorithms in Machine Learning

Introduction For almost all machine learning algorithms, whether supervised learning, unsupervised learning, or reinforcement learning, the final goal generally boils down to solving an optimization problem. Therefore, optimization methods occupy a central position in the derivation and implementation of machine learning algorithms. In this article, the author will provide a comprehensive summary of the optimization … Read more