Numerical Solution of Differential Equations Using Deep Neural Networks

Şahin N., Sümer D.

37th National Mathematics Symposium, Antalya, Türkiye, 1 - 04 Eylül 2025, ss.38, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Antalya
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.38
  • Ankara Yıldırım Beyazıt Üniversitesi Adresli: Evet

Özet

Many differential equations that model real-world problems are highly complex; even when an analytical solution exists, finding it can be extremely challenging. Therefore, the ability to approximate solutions to differential equations is crucial. The use of deep neural networks has become increasingly widespread in recent years; this study examines a method utilizing neural networks and compares its performance with that of a numerical method.

Given that accuracy and efficiency are paramount when solving differential equations, the approach involves using a neural network tasked with learning the local truncation error (LTE) of a numerical method to enhance accuracy. This LTE is intended to serve as a correction term to reduce the error incurred by the numerical method during the solution process. Additionally, the use of adaptive step sizes is planned to lower computational costs and improve efficiency.