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Valinejad, Ali, Momeni, Hamid, AllahBakhsh, Yazdani Cherati. (1405). A deep learning approach for data-driven solutions and parameter identification to Schrodinger-Hirota equations with conformable derivative. پژوهشنامه مدیریت اجرایی, (), -. doi: 10.22080/cjms.2026.30837.1790
Ali Valinejad; Hamid Momeni; Yazdani Cherati AllahBakhsh. "A deep learning approach for data-driven solutions and parameter identification to Schrodinger-Hirota equations with conformable derivative". پژوهشنامه مدیریت اجرایی, , , 1405, -. doi: 10.22080/cjms.2026.30837.1790
Valinejad, Ali, Momeni, Hamid, AllahBakhsh, Yazdani Cherati. (1405). 'A deep learning approach for data-driven solutions and parameter identification to Schrodinger-Hirota equations with conformable derivative', پژوهشنامه مدیریت اجرایی, (), pp. -. doi: 10.22080/cjms.2026.30837.1790
Valinejad, Ali, Momeni, Hamid, AllahBakhsh, Yazdani Cherati. A deep learning approach for data-driven solutions and parameter identification to Schrodinger-Hirota equations with conformable derivative. پژوهشنامه مدیریت اجرایی, 1405; (): -. doi: 10.22080/cjms.2026.30837.1790

A deep learning approach for data-driven solutions and parameter identification to Schrodinger-Hirota equations with conformable derivative

Caspian Journal of Mathematical Sciences
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 فروردین 1405
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2026.30837.1790
نویسندگان
Ali Valinejad1؛ Hamid Momeni2؛ Yazdani Cherati AllahBakhsh* 2
1Department of Computer Sciences, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran
2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
تاریخ دریافت: 28 آذر 1404،  تاریخ بازنگری: 19 اسفند 1404،  تاریخ پذیرش: 26 اسفند 1404 
چکیده
In this paper, a deep learning framework based on physics-informed neural networks (PINNs) is introduced for data-driven solution approximation and parameter identification of non-linear conformable time-fractional Schrödinger-Hirota equations. PINNs methods rely on automatic differentiation to encode physical knowledge into the training phase. This technique can not be used directly for equations with fractional operators, and additional techniques are needed to handle such operators. The capability of the conformable fractional derivatives enables us to embed these operators using the automatic differentiation into the training phase of PINNs models. The introduced framework leverages the residual-based attention scheme to encode the physical laws into the model training effectively. The initial conditions are imposed as hard constraints. A two-phase optimization scheme based on the Adam and L-BFGS optimizer is introduced. A variety of solitary wave solutions, including anti-kink soliton, solitary wave, bright soliton, and w-shaped periodic wave soliton, are simulated, and the related dynamics are discussed. An inverse problem solving for the model equation is performed in which we aim to estimate the true value of the fractional order of the conformable operator and the third-order dispersion term. Numerical experiments confirm that the proposed approach accurately captures soliton dynamics with conformable fractional derivatives.
کلیدواژه‌ها
Deep learning؛ Physics-informed neural networks؛ Soliton dynamics؛ Non-linear conformable time-fractional equations
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تعداد مشاهده مقاله: 19


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