Facts and issues of neural networks for numerical simulation
Résumé
Deep learning and artificial intelligence (AI) have transformed computer science, becoming the main method for addressing various problems, from partial differential equations to molecular discovery. Traditional numerical simulation techniques use finite differences to solve equations, but are computationally costly, often taking hours to days on powerful machines. Simulations need to be restarted for shape changes, making the process inefficient. Artificial neural networks now enable accurate simulations quickly and inexpensively. This paper reviews recent developments in neural networks, their advantages, disadvantages, and unresolved issues, often demonstrated through partial differential equations.
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