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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…