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Found 11 papers, 2 papers with code
An operator preconditioning perspective on training in physics-informed machine learning
In this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize residuals connected to partial differential equations (PDEs).
Convolutional Neural Operators for robust and accurate learning of PDEs
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs.
wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws
Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation.
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks.
Variable-Input Deep Operator Networks
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 samples, significantly restricting the range of their applicability.
Generic bounds on the approximation error for physics-informed (and) operator learning
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 as DeepONets and FNOs as well as for physics-informed operator learning.
Error estimates for physics informed neural networks approximating the Navier-Stokes equations
We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks.
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs
Moreover, we prove that the size of the PINNs and the number of training samples only grow polynomially with the underlying dimension, enabling PINNs to overcome the curse of dimensionality in this context.
On the approximation of functions by tanh neural networks
We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic tangent activation function.
Change Point Detection in Time Series Data using Autoencoders with a Time-Invariant Representation
Detectable change points include abrupt changes in the slope, mean, variance, autocorrelation function and frequency spectrum.
On the approximation of rough functions with deep neural networks
Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions.
