24 citations · 58 across the 7 of their papers we have counts for
7 papers
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…
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…
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…
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…
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…