no code implementations • 9 Oct 2023 • Tim De Ryck, Florent Bonnet, Siddhartha Mishra, Emmanuel de Bézenac

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).

2 code implementations • NeurIPS 2023 • Bogdan Raonić, Roberto Molinaro, Tim De Ryck, Tobias Rohner, Francesca Bartolucci, Rima Alaifari, Siddhartha Mishra, Emmanuel de Bézenac

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.

no code implementations • 18 Jul 2022 • Tim De Ryck, Siddhartha Mishra, Roberto Molinaro

Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation.

no code implementations • 15 Jul 2022 • Tim De Ryck, Siddhartha Mishra

We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks.

no code implementations • 23 May 2022 • Michael Prasthofer, Tim De Ryck, Siddhartha Mishra

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.

no code implementations • 23 May 2022 • Tim De Ryck, Siddhartha Mishra

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.

no code implementations • 17 Mar 2022 • Tim De Ryck, Ameya D. Jagtap, Siddhartha Mishra

We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks.

no code implementations • 28 Jun 2021 • Tim De Ryck, Siddhartha Mishra

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.

no code implementations • 18 Apr 2021 • Tim De Ryck, Samuel Lanthaler, Siddhartha Mishra

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.

2 code implementations • 21 Aug 2020 • Tim De Ryck, Maarten De Vos, Alexander Bertrand

Detectable change points include abrupt changes in the slope, mean, variance, autocorrelation function and frequency spectrum.

no code implementations • 13 Dec 2019 • Tim De Ryck, Siddhartha Mishra, Deep Ray

Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions.

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