118 citations · 129 across the 12 of their papers we have counts for
5 papers · 1 filter
Deep vs. Shallow: Benchmarking Physics-Informed Neural Architectures on the Biharmonic Equation
Akshay Govind Srinivasan, Vikas Dwivedi, Balaji Srinivasan
Partial differential equation (PDE) solvers are fundamental to engineering simulation. Classical mesh-based approaches (finite difference/volume/element) are fast and accurate on h…
Towards Fast Option Pricing PDE Solvers Powered by PIELM
Akshay Govind Srinivasan, Anuj Jagannath Said, Sathwik Pentela +2
Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerge…
Gated X-TFC: Soft Domain Decomposition for Forward and Inverse Problems in Sharp-Gradient PDEs
Vikas Dwivedi, Enrico Schiassi, Monica Sigovan +1
Physics-informed neural networks (PINNs) and related methods struggle to resolve sharp gradients in singularly perturbed boundary value problems without resorting to some form of d…
Kernel-Adaptive PI-ELMs for Forward and Inverse Problems in PDEs with Sharp Gradients
Vikas Dwivedi, Balaji Srinivasan, Monica Sigovan +1
Physics-informed machine learning frameworks such as Physics-Informed Neural Networks (PINNs) and Physics-Informed Extreme Learning Machines (PI-ELMs) have shown great promise for…
Curriculum Learning-Driven PIELMs for Fluid Flow Simulations
Vikas Dwivedi, Bruno Sixou, Monica Sigovan
This paper presents two novel, physics-informed extreme learning machine (PIELM)-based algorithms for solving steady and unsteady nonlinear partial differential equations (PDEs) re…