6 papers
Learning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs
Akshay Govind Srinivasan, Balaji Srinivasan
Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (P…
Exact Constraint Enforcement in Physics-Informed Extreme Learning Machines using Null-Space Projection Framework
Rishi Mishra, Smriti, Balaji Srinivasan +2
Physics-informed extreme learning machines (PIELMs) typically impose boundary and initial conditions through penalty terms, yielding only approximate satisfaction that is sensitive…
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…
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…
Eig-PIELM: A Mesh-Free Approach for Efficient Eigen-Analysis with Physics-Informed Extreme Learning Machines
Rishi Mishra, Smriti, Ganapathy Krishnamurthi +2
In this work, a novel Eig-PIELM framework is proposed that extends physics-informed extreme learning machine for an efficient and accurate solution of linear eigenvalue problems. T…