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Towards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanics
Sawan Kumar, Rajdip Nayek, Souvik Chakraborty
The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently han…
Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured grid
Subhankar Sarkar, Souvik Chakraborty
Scientific machine learning has seen significant progress with the emergence of operator learning. However, existing methods encounter difficulties when applied to problems on unst…
Discovering governing equation in structural dynamics from acceleration-only measurements
Calvin Alvares, Souvik Chakraborty
Over the past few years, equation discovery has gained popularity in different fields of science and engineering. However, existing equation discovery algorithms rely on the availa…
Neural Operator induced Gaussian Process framework for probabilistic solution of parametric partial differential equations
Sawan Kumar, Rajdip Nayek, Souvik Chakraborty
The study of neural operators has paved the way for the development of efficient approaches for solving partial differential equations (PDEs) compared with traditional methods. How…
MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation
Akshay Thakur, Souvik Chakraborty
We propose a neural operator framework, termed mixture density nonlinear manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages an amalgamation of the point…