Search Results for author: Siddhartha Mishra

Found 27 papers, 16 papers with code

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.

Error analysis for deep neural network approximations of parametric hyperbolic conservation laws

no code implementations15 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.

Agnostic Physics-Driven Deep Learning

no code implementations30 May 2022 Benjamin Scellier, Siddhartha Mishra, Yoshua Bengio, Yann Ollivier

This work establishes that a physical system can perform statistical learning without gradient computations, via an Agnostic Equilibrium Propagation (Aeqprop) procedure that combines energy minimization, homeostatic control, and nudging towards the correct response.

Generic bounds on the approximation error for physics-informed (and) operator learning

no code implementations23 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.

Operator learning

Variable-Input Deep Operator Networks

no code implementations23 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.

Operator learning

Error estimates for physics informed neural networks approximating the Navier-Stokes equations

no code implementations17 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.

Graph-Coupled Oscillator Networks

1 code implementation4 Feb 2022 T. Konstantin Rusch, Benjamin P. Chamberlain, James Rowbottom, Siddhartha Mishra, Michael M. Bronstein

This demonstrates that the proposed framework mitigates the oversmoothing problem.

Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs

no code implementations28 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.

On the approximation of functions by tanh neural networks

no code implementations18 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.

UnICORNN: A recurrent model for learning very long time dependencies

1 code implementation9 Mar 2021 T. Konstantin Rusch, Siddhartha Mishra

The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem.

Sentiment Analysis Sequential Image Classification +1

Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks

4 code implementations13 Aug 2020 Kjetil O. Lye, Siddhartha Mishra, Deep Ray, Praveen Chandrasekhar

We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimization problems.

Active Learning Model Optimization

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

1 code implementation29 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

1 code implementation29 Jun 2020 Siddhartha Mishra, Roberto Molinaro

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

Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences

1 code implementation26 May 2020 Siddhartha Mishra, T. Konstantin Rusch

We propose a deep supervised learning algorithm based on low-discrepancy sequences as the training set.

On the approximation of rough functions with deep neural networks

no code implementations13 Dec 2019 Tim De Ryck, Siddhartha Mishra, Deep Ray

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

Data Compression

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

Statistical solutions of hyperbolic systems of conservation laws: numerical approximation

2 code implementations6 Jun 2019 Ulrik Skre Fjordholm, Kjetil Lye, Siddhartha Mishra, Franziska Weber

Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system of conservation laws.

Numerical Analysis Fluid Dynamics 35L65, 65M08, 65C05, 65C30

Deep learning observables in computational fluid dynamics

3 code implementations7 Mar 2019 Kjetil O. Lye, Siddhartha Mishra, Deep Ray

Under the assumption that the underlying neural networks generalize well, we prove that the deep learning MC and QMC algorithms are guaranteed to be faster than the baseline (quasi-) Monte Carlo methods.

A machine learning framework for data driven acceleration of computations of differential equations

no code implementations25 Jul 2018 Siddhartha Mishra

We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs.

BIG-bench Machine Learning

Numerical approximation of statistical solutions of scalar conservation laws

1 code implementation30 Oct 2017 Ulrik Skre Fjordholm, Kjetil Lye, Siddhartha Mishra

We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws.

Numerical Analysis 35L65, 65M08, 65C05, 65C30

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