Summary of A Physics-informed Machine Learning Approach For Solving Distributed Order Fractional Differential Equations, by Alireza Afzal Aghaei
A Physics-Informed Machine Learning Approach for Solving Distributed Order Fractional Differential Equations
by Alireza Afzal Aghaei
First submitted to arxiv on: 5 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper introduces a novel methodology for solving distributed-order fractional differential equations using a physics-informed machine learning framework. By extending support vector regression (SVR) to approximate unknown solutions during training, the approach incorporates physical laws directly into the learning process. Gegenbauer orthogonal polynomials are employed as kernel functions, leveraging their fractional differentiation properties to streamline problem formulation. The optimization problem is addressed through quadratic programming or positive definite systems in its dual form. Numerical experiments on Caputo-based distributed-order fractional differential equations validate the effectiveness of the proposed approach. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper uses a special kind of machine learning to solve tricky math problems called fractional differential equations. It’s like trying to figure out what shape something will be if you know how it changes over time, but you don’t have all the details at once. The new method combines physics and computer science to make solving these problems more efficient. It uses special polynomials that help with this kind of math and shows it works by testing it on some examples. |
Keywords
» Artificial intelligence » Machine learning » Optimization » Regression
