Preprint Alert
Together with colleagues from Department of Mathematical Sciences, Indian Institute of Technology (IIT) (BHU) Varanasi and the University of Wuppertal they present:
“Alikhanov–XfPINNs: Adaptive Physics-Informed Learning for Nonlinear Fractional PDEs on Nonuniform Meshes”. Link: (PDF) Alikhanov-XfPINNs: Adaptive Physics-Informed Learning for Nonlinear Fractional PDEs on Nonuniform Meshes
This work introduces a new framework combining:
- adaptive physics-informed neural networks (PINNs)
- high-order fractional discretization
- nonuniform temporal meshes
- accelerated treatment of memory effects in fractional PDEs
Our goal is to bridge modern scientific machine learning with robust numerical analysis for challenging nonlinear fractional PDEs. This preprint represents a first step in a broader series of German–Indian cooperation activities in applied mathematics, scientific computing, and AI-enhanced PDE modeling.
