1 code implementation • 3 Oct 2023 • Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen
Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data.
1 code implementation • 9 Aug 2023 • Nikolas Borrel-Jensen, Somdatta Goswami, Allan P. Engsig-Karup, George Em Karniadakis, Cheol-Ho Jeong
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 computing.
1 code implementation • 15 Apr 2023 • Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, Michael D. Shields
Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems.
no code implementations • 2 Apr 2023 • Varun Kumar, Somdatta Goswami, Daniel J. Smith, George Em Karniadakis
As an alternative to physics based models, we develop an operator-based regression model (DeepONet) to learn the relevant output states for a mean-value gas flow engine model using the engine operating conditions as input variables.
no code implementations • 19 Mar 2023 • Qianying Cao, Somdatta Goswami, George Em Karniadakis
Herein, we demonstrate the superior approximation accuracy of a single Laplace layer in LNO over four Fourier modules in FNO in approximating the solutions of three ODEs (Duffing oscillator, driven gravity pendulum, and Lorenz system) and three PDEs (Euler-Bernoulli beam, diffusion equation, and reaction-diffusion system).
no code implementations • 3 Mar 2023 • Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen
Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly from observational data.
1 code implementation • 23 Feb 2023 • Somdatta Goswami, Ameya D. Jagtap, Hessam Babaee, Bryan T. Susi, George Em Karniadakis
Specifically, to train the DeepONet for the syngas model, we solve the skeletal kinetic model for different initial conditions.
no code implementations • 8 Jul 2022 • Somdatta Goswami, Aniruddha Bora, Yue Yu, George Em Karniadakis
Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e. g., in an advection-diffusion-reaction partial differential equation, or simply as a black box, e. g., a system-of-systems.
no code implementations • 8 May 2022 • Somdatta Goswami, David S. Li, Bruno V. Rego, Marcos Latorre, Jay D. Humphrey, George Em Karniadakis
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 dissection or rupture.
1 code implementation • 20 Apr 2022 • Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis
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 data acquisition and labeling, potential computational power limitations, and dataset distribution mismatches.
no code implementations • 11 Apr 2022 • Vivek Oommen, Khemraj Shukla, Somdatta Goswami, Remi Dingreville, George Em Karniadakis
We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space.
1 code implementation • 9 Mar 2022 • Katiana Kontolati, Somdatta Goswami, Michael D. Shields, George Em Karniadakis
In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics.
no code implementations • 16 Aug 2021 • Somdatta Goswami, Minglang Yin, Yue Yu, George Karniadakis
We propose a physics-informed variational formulation of DeepONet (V-DeepONet) for brittle fracture analysis.
1 code implementation • 27 Aug 2019 • Esteban Samaniego, Cosmin Anitescu, Somdatta Goswami, Vien Minh Nguyen-Thanh, Hongwei Guo, Khader Hamdia, Timon Rabczuk, Xiaoying Zhuang
In this contribution, we explore Deep Neural Networks (DNNs) as an option for approximation.
no code implementations • 4 Jul 2019 • Somdatta Goswami, Cosmin Anitescu, Souvik Chakraborty, Timon Rabczuk
While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy of the system.