118 citations · 129 across the 12 of their papers we have counts for
12 papers
Meta-Learned Basis Adaptation for Parametric Linear PDEs
Vikas Dwivedi, Monica Sigovan, Bruno Sixou
We propose a hybrid physics-informed framework for solving families of parametric linear partial differential equations (PDEs) by combining a meta-learned predictor with a least-sq…
Soft Partition-based KAPI-ELM for Multi-Scale PDEs
Vikas Dwivedi, Monica Sigovan, Bruno Sixou
Physics-informed machine learning holds great promise for solving differential equations, yet existing methods struggle with highly oscillatory, multiscale, or singularly perturbed…
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…
Global versus Local: Evaluating AlexNet Architectures for Tropical Cyclone Intensity Estimation
Vikas Dwivedi
Given the destructive impacts of tropical cyclones, it is critical to have a reliable system for cyclone intensity detection. Various techniques are available for this purpose, eac…
PICS in Pics: Physics Informed Contour Selection for Rapid Image Segmentation
Vikas Dwivedi, Balaji Srinivasan, Ganapathy Krishnamurthi
Effective training of deep image segmentation models is challenging due to the need for abundant, high-quality annotations. Generating annotations is laborious and time-consuming f…
Numerical Approximation in CFD Problems Using Physics Informed Machine Learning
Siddharth Rout, Vikas Dwivedi, Balaji Srinivasan
The thesis focuses on various techniques to find an alternate approximation method that could be universally used for a wide range of CFD problems but with low computational cost a…
Distributed physics informed neural network for data-efficient solution to partial differential equations
Vikas Dwivedi, Nishant Parashar, Balaji Srinivasan
The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and valida…
Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations
Vikas Dwivedi, Balaji Srinivasan
There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Netwo…