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Fourier Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural o…
Multipole Graph Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
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…
Kernel Analog Forecasting: Multiscale Test Problems
Dmitry Burov, Dimitrios Giannakis, Krithika Manohar +1
Data-driven prediction is becoming increasingly widespread as the volume of data available grows and as algorithmic development matches this growth. The nature of the predictions m…
Site characterization at downhole arrays by joint inversion of dispersion data and acceleration time series
Elnaz Seylabi, Andrew Stuart, Domniki Asimaki
We present a sequential data assimilation algorithm based on the ensemble Kalman inversion to estimate the near-surface shear wave velocity profile and damping when heterogeneous d…
Neural Operator: Graph Kernel Network for Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
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 Eu…