167 citations · 1.3k across the 78 of their papers we have counts for
7 papers · 1 filter
Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependencies
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. Inspired by the ability of these systems to express…
Physics Informed Neural Networks for Simulating Radiative Transfer
Siddhartha Mishra, Roberto Molinaro
We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing…
Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks
Kjetil O. Lye, Siddhartha Mishra, Deep Ray +1
We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimizat…
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs
Siddhartha Mishra, Roberto Molinaro
Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inv…
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs
Siddhartha Mishra, Roberto Molinaro
Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error…
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences
Siddhartha Mishra, T. Konstantin Rusch
We propose a deep supervised learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiment…