6 papers
Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces
Khemraj Shukla, George Em Karniadakis
Deep Operator Networks (DeepONets; arXiv:1910.03193) typically encode an input function through point values on a fixed discretization. Building on the Topological DeepONet framewo…
Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles
Khemraj Shukla, Zongren Zou, Theo Kaeufer +2
Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconst…
Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks
Anas Jnini, Elham Kiyani, Khemraj Shukla +5
Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing co…
Drug Release Modeling using Physics-Informed Neural Networks
Daanish Aleem Qureshi, Khemraj Shukla, Vikas Srivastava
Accurate modeling of drug release is essential for designing and developing controlled-release systems. Classical models (Fick, Higuchi, Peppas) rely on simplifying assumptions tha…
Neural Operator Modeling of Platelet Geometry and Stress in Shear Flow
Marco Laudato, Luca Manzari, Khemraj Shukla
Thrombosis involves processes spanning large-scale fluid flow to sub-cellular events such as platelet activation. Traditional CFD approaches often treat blood as a continuum, which…
High-Fidelity Description of Platelet Deformation Using a Neural Operator
Marco Laudato, Luca Manzari, Khemraj Shukla
The goal of this work is to investigate the capability of a neural operator (DeepONet) to accurately capture the complex deformation of a platelet's membrane under shear flow. The…