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Found 10 papers, 7 papers with code
Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs
Existing work in scientific machine learning (SciML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical partial differential equation (PDE) solvers.
Learning About Structural Errors in Models of Complex Dynamical Systems
Complex dynamical systems are notoriously difficult to model because some degrees of freedom (e. g., small scales) may be computationally unresolvable or are incompletely understood, yet they are dynamically important.
Introduction To Gaussian Process Regression In Bayesian Inverse Problems, With New ResultsOn Experimental Design For Weighted Error Measures
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost of evaluating the data likelihood.
Neural Operator: Learning Maps Between Function Spaces
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets.
Learning Dissipative Dynamics in Chaotic Systems
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping.
Fourier Neural Operator for Parametric Partial Differential Equations
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces.
Multipole Graph Neural Operator for Parametric Partial Differential Equations
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks.
Kernel Analog Forecasting: Multiscale Test Problems
The nature of the predictions made, and the manner in which they should be interpreted, depends crucially on the extent to which the variables chosen for prediction are Markovian, or approximately Markovian.
Neural Operator: Graph Kernel Network for Partial Differential Equations
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces.
Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations
Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems.
