We propose a very general framework for deriving rigorous bounds on the approximation
error for physics-informed neural networks (PINNs) and operator learning architectures such …

Although very successfully used in conventional machine learning, convolution based
neural network architectures--believed to be inconsistent in function space--have been …

A large class of hyperbolic and advection-dominated PDEs can have solutions with
discontinuities. This paper investigates, both theoretically and empirically, the operator …

Existing architectures for operator learning require that the number and locations of sensors
(where the input functions are evaluated) remain the same across all training and test …

Fourier Neural Operators (FNOs) have emerged as very popular machine learning
architectures for learning operators, particularly those arising in PDEs. However, as FNOs …

The computational efficiency of many neural operators, widely used for learning solutions of
PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the …

The computational efficiency of many neural operators, widely used for learning solutions of
PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations …

Physics-informed neural networks (PINNs) have been widely used for the robust and
accurate approximation of partial differential equations. In the present thesis, we provide …