ترجمه فارسی مقاله یک شبکه عصبی کارآمد مبتنی بر موجک و مبتنی بر فیزیک برای مشکلات تکین آشفته

• کتاب صدها نکته فارسی (خودمونی) – نسخه PDF — زبان ساده و کاربردی
  مشاهده نمونه نسخه نکات ساده
• کتاب صدها نکته رسمی فارسی – نسخه PDF — نگارش استاندارد و علمی
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• کتاب صدها پرسش و پاسخ تشریحی – نسخه PDF
  — هر سؤال همراه با پاسخ کامل برای درک عمیق مفاهیم
  مشاهده نمونه نسخه پرسش و پاسخ
• کتاب پرسش و پاسخ چهارگزینه‌ای – نسخه یادگیری سریع
  — پاسخ‌ها بلافاصله بعد از سؤال برای مرور سریع
  مشاهده نمونه نسخه کوییز سریع
• کتاب پرسش و پاسخ چهارگزینه‌ای – نسخه خودآزمایی
  — پاسخ‌ها در انتهای بخش‌ها برای سنجش واقعی یادگیری
  مشاهده نمونه نسخه آزمونی

🎯 این بسته یک دورهٔ آموزشی کامل و چندلایه است؛ شامل ویدیوهای آموزشی، کتاب‌ها، تمرین‌ها و خودآزمایی.

چکیده

Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics as differential equations to address complex problems, including ones that may involve limited data availability. However, tackling solutions of differential equations with oscillations or singular perturbations and shock-like structures becomes challenging for PINNs. Considering these challenges, we designed an efficient wavelet-based PINNs (W-PINNs) model to solve singularly perturbed differential equations. Here, we represent the solution in wavelet space using a family of smooth-compactly supported wavelets. This framework represents the solution of a differential equation with significantly fewer degrees of freedom while still retaining in capturing, identifying, and analyzing the local structure of complex physical phenomena. The architecture allows the training process to search for a solution within wavelet space, making the process faster and more accurate. The proposed model does not rely on automatic differentiations for derivatives involved in differential equations and does not require any prior information regarding the behavior of the solution, such as the location of abrupt features. Thus, through a strategic fusion of wavelets with PINNs, W-PINNs excel at capturing localized nonlinear information, making them well-suited for problems showing abrupt behavior in certain regions, such as singularly perturbed problems. The efficiency and accuracy of the proposed neural network model are demonstrated in various test problems, i.e., highly singularly perturbed nonlinear differential equations, the FitzHugh-Nagumo (FHN), and Predator-prey interaction models. The proposed design model exhibits impressive comparisons with traditional PINNs and the recently developed wavelet-based PINNs, which use wavelets as an activation function for solving nonlinear differential equations.

چکیده به فارسی (ترجمه ماشینی)