36 citations · 69 across the 14 of their papers we have counts for
10 papers · 1 filter
Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solvers
Andreas E. Robertson, Ashley T. Lenau, John D. Shimanek +5
Latent neural surrogate solvers, or latent dynamics models, accelerate simulations of time-dependent physical systems by evolving a compressed latent space rather than resolving fu…
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…
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,…
XAI4Extremes: An interpretable machine learning framework for understanding extreme-weather precursors under climate change
Jiawen Wei, Aniruddha Bora, Vivek Oommen +7
Extreme weather events are increasing in frequency and intensity due to climate change. This, in turn, is exacting a significant toll in communities worldwide. While prediction ski…
From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning
Juan Diego Toscano, Vivek Oommen, Alan John Varghese +4
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and…
Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling
Vivek Oommen, Aniruddha Bora, Zhen Zhang +1
We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer c…
RiemannONets: Interpretable Neural Operators for Riemann Problems
Ahmad Peyvan, Vivek Oommen, Ameya D. Jagtap +1
Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numeri…
Rethinking materials simulations: Blending direct numerical simulations with neural operators
Vivek Oommen, Khemraj Shukla, Saaketh Desai +2
Direct numerical simulations (DNS) are accurate but computationally expensive for predicting materials evolution across timescales, due to the complexity of the underlying evolutio…