7 papers
Towards Unified AI-Driven Fracture Mechanics: The Extended Deep Energy Method (XDEM)
Yizheng Wang, Yuzhou Lin, Somdatta Goswami +8
Physics-Informed Neural Networks (PINNs) have recently emerged as powerful tools for solving partial differential equations (PDEs), with the Deep Energy Method (DEM) proving especi…
Neural Hodge Corrective Solvers: A Hybrid Iterative-Neural Framework
Arjun Puthli, Somdatta Goswami, Souvik Chakraborty
We introduce the Neural Hodge Corrective Solver (NHCS), a hybrid iterative-neural framework for partial differential equations that embeds learned corrective operators within the D…
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…
Neural Chaos: A Spectral Stochastic Neural Operator
Bahador Bahmani, Ioannis G. Kevrekidis, Michael D. Shields
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties,…
Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazards
Somdatta Goswami, Dimitris G. Giovanis, Bowei Li +2
Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on…
A Resolution Independent Neural Operator
Bahador Bahmani, Somdatta Goswami, Ioannis G. Kevrekidis +1
The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture…