4 papers · 1 filter
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…
From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems
Sawan Kumar, Tapas Tripura, Rajdip Nayek +1
Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed…
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…
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…