2.1k citations · 2.9k across the 29 of their papers we have counts for
30 papers
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…
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…
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…
Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving
Varun Kumar, Somdatta Goswami, Katiana Kontolati +2
Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-ta…
Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning
Luis Mandl, Somdatta Goswami, Lena Lambers +1
The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks…
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…
DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networks
Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis +1
Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data. This property becomes…
Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators
Nikolas Borrel-Jensen, Somdatta Goswami, Allan P. Engsig-Karup +2
We address the challenge of sound propagation simulations in 3D virtual rooms with moving sources, which have applications in virtual/augmented reality, game audio, and spatial com…
Learning in latent spaces improves the predictive accuracy of deep neural operators
Katiana Kontolati, Somdatta Goswami, George Em Karniadakis +1
Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural opera…
Real-Time Prediction of Gas Flow Dynamics in Diesel Engines using a Deep Neural Operator Framework
Varun Kumar, Somdatta Goswami, Daniel J. Smith +1
We develop a data-driven deep neural operator framework to approximate multiple output states for a diesel engine and generate real-time predictions with reasonable accuracy. As em…
Developing a cost-effective emulator for groundwater flow modeling using deep neural operators
Maria Luisa Taccari, He Wang, Somdatta Goswami +3
Current groundwater models face a significant challenge in their implementation due to heavy computational burdens. To overcome this, our work proposes a cost-effective emulator th…
LNO: Laplace Neural Operator for Solving Differential Equations
Qianying Cao, Somdatta Goswami, George Em Karniadakis
We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-per…
Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks
Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis +1
Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced comput…
Learning stiff chemical kinetics using extended deep neural operators
Somdatta Goswami, Ameya D. Jagtap, Hessam Babaee +2
We utilize neural operators to learn the solution propagator for the challenging chemical kinetics equation. Specifically, we apply the deep operator network (DeepONet) along with…
Deep neural operators can predict the real-time response of floating offshore structures under irregular waves
Qianying Cao, Somdatta Goswami, Tapas Tripura +2
The use of neural operators in a digital twin model of an offshore floating structure can provide a paradigm shift in structural response prediction and health monitoring, providin…
On the Geometry Transferability of the Hybrid Iterative Numerical Solver for Differential Equations
Adar Kahana, Enrui Zhang, Somdatta Goswami +3
The discovery of fast numerical solvers prompted a clear and rapid shift towards iterative techniques in many applications, especially in computational mechanics, due to the increa…
Physics-Informed Deep Neural Operator Networks
Somdatta Goswami, Aniruddha Bora, Yue Yu +1
Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reac…
Variational energy based XPINNs for phase field analysis in brittle fracture
Ayan Chakraborty, Cosmin Anitescu, Somdatta Goswami +2
Modeling fracture is computationally expensive even in computational simulations of two-dimensional problems. Hence, scaling up the available approaches to be directly applied to l…
Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms
Somdatta Goswami, David S. Li, Bruno V. Rego +3
Thoracic aortic aneurysm (TAA) is a localized dilatation of the aorta resulting from compromised wall composition, structure, and function, which can lead to life-threatening disse…
Deep transfer operator learning for partial differential equations under conditional shift
Somdatta Goswami, Katiana Kontolati, Michael D. Shields +1
Transfer learning (TL) enables the transfer of knowledge gained in learning to perform one task (source) to a related but different task (target), hence addressing the expense of d…
Learning two-phase microstructure evolution using neural operators and autoencoder architectures
Vivek Oommen, Khemraj Shukla, Somdatta Goswami +2
Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and gener…
On the influence of over-parameterization in manifold based surrogates and deep neural operators
Katiana Kontolati, Somdatta Goswami, Michael D. Shields +1
Constructing accurate and generalizable approximators for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. In this work, we propose new deve…