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Scalable h-adaptive probabilistic solver for time-independent and time-dependent systems
Akshay Thakur, Sawan Kumar, Matthew Zahr +1
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discreti…
A Bayesian Approach for Discovering Time- Delayed Differential Equation from Data
Debangshu Chowdhury, Souvik Chakraborty
Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlyi…
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…
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…