PUBLICATIONS & PREPRINTS

1. C. Xenophontos, Aayushman Raina, A simple shallow neural network for emulating the solution to singularly perturbed problems, arXiv preprint arXiv:2609.05180, 2026.

DOI: doi.org/10.48550/arXiv.2609.05180 

2. S. Badireddi, Aayushman Raina, S. Natesan, Enhanced PINN approaches for Biharmonic singular perturbation problems with clamped boundary conditions , Indian Journal of Pure and Applied Mathematics, 2026 (In Press).

3. Aayushman Raina, S. Natesan, S. Toprakseven, A weak Galerkin mixed finite element method for singularly perturbed biharmonic problems on a layer-adapted mesh in 2D, Advances in Computational Mathematics, 46 (2026).

DOI: doi.org/10.1007/s10444-026-10314-7 

4. Aayushman Raina, S. Natesan, A Physics‐Informed Neural Network Framework for Tumor‐Immune Interactions, Metastatic Invasion, and Haptotaxis Systems , Mathematical Methods in the Applied Sciences, 2025.

DOI: doi.org/10.1002/mma.70355 

5. Aayushman Raina, S. Natesan, A weak Galerkin finite element method for singularly perturbed 2D elliptic boundary-value problems of reaction-diffusion type with exponentially graded mesh , International Journal of Computer Mathematics, 2025.

DOI: doi.org/10.1080/00207160.2025.2556462 

6. P. Boro, Aayushman Raina, S. Natesan, A Parameter-Driven Physics-Informed Neural Network Framework for Solving Two-Parameter Singular Perturbation Problems Involving Boundary Layers, Advances in Computational Science and Engineering, 5 (2025): pp. 72-102.

DOI: doi.org/10.3934/acse.2025019 

7. Aayushman Raina, S. Badireddi, S. Natesan, Application of PINN to Obtain Solution of Boundary Layer Problems Arising in Fluid Dynamics, Mathematical Foundations of Computing, 10 (2026): pp. 89-108.

DOI: www.aimsciences.org/article/doi/10.3934/mfc.2025024 

8. Aayushman Raina, S. Natesan, S. Toprakseven, An Efficient Operator Splitting Weak Galerkin Method for Singularly Perturbed 2D Parabolic PDEs , Numerical Algorithms, 2025.

DOI: doi.org/10.1007/s11075-025-02152-3 

9. Aayushman Raina, S. Natesan, A Weak Galerkin Finite Element method for Fourth order Parabolic Singularly Perturbed Problems on layer adapted Shishkin mesh, Applied Numerical Mathematics, 207 (2025), pp.~520--533.

DOI: https://doi.org/10.1016/j.apnum.2024.09.019 

10. Aayushman Raina, S. Natesan, S. Toprakseven, Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems, Mathematics and Computers in Simulation, 229 (2025), pp.~203--221.

DOI: doi.org/10.1016/j.matcom.2024.09.017 

11. Aayushman Raina, S. Natesan, S. Toprakseven, A Novel ADI-Weak Galerkin Method for Singularly Perturbed Two-Parameter 2D Parabolic PDEs, Numerical Methods for Partial Differential Equations, 41 (2025), p.~e23169.

DOI: doi.org/10.1002/num.23169