A Machine Learning Approach to Solve Partial Differential Equations

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Conference Proceeding


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Artificial intelligence (AI) techniques have advanced significantly and are now used to solve some of the most challenging scientific problems, such as Partial Differential Equation models in Computational Sciences. In our study, we explored the effectiveness of a specific deep-learning technique called Physics-Informed Neural Networks (PINNs) for solving partial differential equations. As part of our numerical experiment, we solved a one-dimensional Initial and Boundary Value Problem that consisted of Burgers' equation, a Dirichlet boundary condition, and an initial condition imposed at the initial time, using PINNs. We examined the effects of network structure, learning rate, batch size, and other factors that influenced the network output and characterized the tradeoff between training speed and solution quality. In addition, we solved the problem using a standard Finite Difference method. We then compared the performance of PINNs with the standard numerical method to gain deeper insights into the efficiency and accuracy of PINNs.


Presented at West Chester University Research & Creative Activity Day

First Place Winner

ML Approach to Differential Equations.pdf (1629 kB)
A Machine Learning Approach to Solve Partial Differential Equations PDF file

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