Search Results for author: Roberto Molinaro

Found 9 papers, 4 papers with code

Poseidon: Efficient Foundation Models for PDEs

3 code implementations29 May 2024 Maximilian Herde, Bogdan Raonić, Tobias Rohner, Roger Käppeli, Roberto Molinaro, Emmanuel de Bézenac, Siddhartha Mishra

Moreover, Poseidon scales with respect to model and data size, both for pretraining and for downstream tasks.

Convolutional Neural Operators for robust and accurate learning of 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.

Operator learning PDE Surrogate Modeling

Neural Inverse Operators for Solving PDE Inverse Problems

no code implementations26 Jan 2023 Roberto Molinaro, Yunan Yang, Björn Engquist, Siddhartha Mishra

A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions.

Operator learning

wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws

no code implementations18 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.

Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs

no code implementations29 Jun 2020 Siddhartha Mishra, Roberto Molinaro

Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs.

Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs

no code implementations29 Jun 2020 Siddhartha Mishra, Roberto Molinaro

Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs.

A Multi-level procedure for enhancing accuracy of machine learning algorithms

1 code implementation20 Sep 2019 Kjetil O. Lye, Siddhartha Mishra, Roberto Molinaro

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations.

BIG-bench Machine Learning Uncertainty Quantification

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