A parametric physics-informed deep learning approach for 6th-order bending analysis of MSGT microbeams
Engineering with Computers, cilt.42, sa.6, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 42 Sayı: 6
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s00366-026-02421-2
- Dergi Adı: Engineering with Computers
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, INSPEC, zbMATH, Engineering Source (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: MEMS, Microbeams, Modified Strain Gradient Theory (MSGT), Parametric solution, Physics-informed neural networks, Size-dependent bending analysis
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
This study investigates the size-dependent static bending behavior of Euler-Bernoulli microbeams with the modified strain gradient theory (MSGT). To address the numerical stiffness and computational bottleneck caused by the sixth-order governing differential equations, a novel Parametric Physics-Informed Neural Network (P-PINN) framework is established. The original higher-order equation is mathematically decoupled into a trio of dependent systems of second-order differential equations, which enhances the gradient flow and convergence stability. Unlike traditional networks limited to fixed parameters, the P-PINN incorporates the dimensionless internal length scale ratio as a continuous input, functioning as a surrogate model for the predetermined parametric manifold without retraining. A dynamic Neural Tangent Kernel (NTK) based adaptive loss weighting algorithm and a two-stage (Adam and L-BFGS) optimization strategy are employed to enforce complex higher-order boundary conditions. The framework is validated against analytical solutions across simply supported and two variations of clamped-free boundary conditions. The results demonstrate predictive accuracy with Mean Squared Errors strictly bounded between and, verifying the framework’s potential to be an alternative solution method.