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Physics-Informed Neural Operator for Learning Partial Differential Equations
Zongyi Li, Hongkai Zheng, Nikola Kovachki +5
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric…
U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow
Gege Wen, Zongyi Li, Kamyar Azizzadenesheli +2
Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a…
Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems
Sahin Lale, Kamyar Azizzadenesheli, Babak Hassibi +1
Autoregressive exogenous (ARX) systems are the general class of input-output dynamical systems used for modeling stochastic linear dynamical systems (LDS) including partially obser…
Neural Operator: Learning Maps Between Function Spaces
Nikola Kovachki, Zongyi Li, Burigede Liu +4
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of n…
Seismic wave propagation and inversion with Neural Operators
Yan Yang, Angela F. Gao, Jorge C. Castellanos +3
Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of res…
Learning Dissipative Dynamics in Chaotic Systems
Zongyi Li, Miguel Liu-Schiaffini, Nikola Kovachki +5
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many…