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no code implementations • 3 Oct 2022 • Samuel Lanthaler, Roberto Molinaro, Patrik Hadorn, Siddhartha Mishra

A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities.

1 code implementation • 2 Oct 2022 • T. Konstantin Rusch, Benjamin P. Chamberlain, Michael W. Mahoney, Michael M. Bronstein, Siddhartha Mishra

We present Gradient Gating (G$^2$), a novel framework for improving the performance of Graph Neural Networks (GNNs).

Ranked #1 on Node Classification on snap-patents

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 • 30 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.

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 • 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.

2 code implementations • 16 Apr 2022 • Yizhong Wang, Swaroop Mishra, Pegah Alipoormolabashi, Yeganeh Kordi, Amirreza Mirzaei, Anjana Arunkumar, Arjun Ashok, Arut Selvan Dhanasekaran, Atharva Naik, David Stap, Eshaan Pathak, Giannis Karamanolakis, Haizhi Gary Lai, Ishan Purohit, Ishani Mondal, Jacob Anderson, Kirby Kuznia, Krima Doshi, Maitreya Patel, Kuntal Kumar Pal, Mehrad Moradshahi, Mihir Parmar, Mirali Purohit, Neeraj Varshney, Phani Rohitha Kaza, Pulkit Verma, Ravsehaj Singh Puri, Rushang Karia, Shailaja Keyur Sampat, Savan Doshi, Siddhartha Mishra, Sujan Reddy, Sumanta Patro, Tanay Dixit, Xudong Shen, Chitta Baral, Yejin Choi, Noah A. Smith, Hannaneh Hajishirzi, Daniel Khashabi

This large and diverse collection of tasks enables rigorous benchmarking of cross-task generalization under instructions -- training models to follow instructions on a subset of tasks and evaluating them on the remaining unseen ones.

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.

1 code implementation • 4 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.

1 code implementation • ICLR 2022 • T. Konstantin Rusch, Siddhartha Mishra, N. Benjamin Erichson, Michael W. Mahoney

We propose a novel method called Long Expressive Memory (LEM) for learning long-term sequential dependencies.

Ranked #1 on Time Series Classification on EigenWorms

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.

1 code implementation • ACL 2022 • Shib Sankar Dasgupta, Michael Boratko, Siddhartha Mishra, Shriya Atmakuri, Dhruvesh Patel, Xiang Lorraine Li, Andrew McCallum

In this work, we provide a fuzzy-set interpretation of box embeddings, and learn box representations of words using a set-theoretic training objective.

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.

1 code implementation • 9 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.

1 code implementation • ICLR 2021 • T. Konstantin Rusch, Siddhartha Mishra

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators.

1 code implementation • 25 Sep 2020 • Siddhartha Mishra, Roberto Molinaro

We propose a novel machine learning algorithm for simulating radiative transfer.

4 code implementations • 13 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.

1 code implementation • 29 Jun 2020 • Siddhartha Mishra, Roberto Molinaro

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

1 code implementation • 29 Jun 2020 • Siddhartha Mishra, Roberto Molinaro

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

1 code implementation • 26 May 2020 • Siddhartha Mishra, T. Konstantin Rusch

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

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.

1 code implementation • 20 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.

2 code implementations • 6 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

3 code implementations • 7 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.

no code implementations • 25 Jul 2018 • Siddhartha Mishra

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

1 code implementation • 30 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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