9 papers
Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines
Siavash Khodakarami, Vivek Oommen, Nazanin Ahmadi Daryakenari +2
Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed…
Importance of localized dilatation and distensibility in identifying determinants of thoracic aortic aneurysm with neural operators
David S. Li, Somdatta Goswami, Qianying Cao +4
Thoracic aortic aneurysms (TAAs) arise from diverse mechanical and mechanobiological disruptions to the aortic wall that increase the risk of dissection or rupture. Evidence links…
A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
Juan Diego Toscano, Daniel T. Chen, Vivek Oommen +2
Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these…
Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction
Vivek Oommen, Siavash Khodakarami, Aniruddha Bora +2
Neural operators are promising surrogates for dynamical systems but when trained with standard L2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that…
Equilibrium Conserving Neural Operators for Super-Resolution Learning
Vivek Oommen, Andreas E. Robertson, Daniel Diaz +5
Neural surrogate solvers can estimate solutions to partial differential equations in physical problems more efficiently than standard numerical methods, but require extensive high-…
Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems
Siavash Khodakarami, Vivek Oommen, Aniruddha Bora +1
Neural operators have emerged as powerful surrogates for modeling complex physical problems. However, they suffer from spectral bias making them oblivious to high-frequency modes,…