Parallel-in-Time Solutions with Random Projection Neural Networks

• URL: http://arxiv.org/abs/2408.09756v1
• Date: Mon, 19 Aug 2024 07:32:41 GMT
• Title: Parallel-in-Time Solutions with Random Projection Neural Networks
• Authors: Marta M. Betcke, Lisa Maria Kreusser, Davide Murari,
• Abstract summary: This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator. We provide a theoretical analysis of the convergence properties of the proposed algorithm and show its effectiveness for several examples, including Lorenz and Burgers' equations.
• Score: 0.07282584715927627
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator. We provide a theoretical analysis of the convergence properties of the proposed algorithm and show its effectiveness for several examples, including Lorenz and Burgers' equations. In our numerical simulations, we further specialize the underpinning neural architecture to Random Projection Neural Networks (RPNNs), a 2-layer neural network where the first layer weights are drawn at random rather than optimized. This restriction substantially increases the efficiency of fitting RPNN's weights in comparison to a standard feedforward network without negatively impacting the accuracy, as demonstrated in the SIR system example.

Related papers

• Concurrent Training and Layer Pruning of Deep Neural Networks [0.0]
  We propose an algorithm capable of identifying and eliminating irrelevant layers of a neural network during the early stages of training. We employ a structure using residual connections around nonlinear network sections that allow the flow of information through the network once a nonlinear section is pruned.
  arXiv  Detail & Related papers  (2024-06-06T23:19:57Z)
• Parallel Proportional Fusion of Spiking Quantum Neural Network for Optimizing Image Classification [10.069224006497162]
  We introduce a novel architecture termed Parallel Proportional Fusion of Quantum and Spiking Neural Networks (PPF-QSNN) The proposed PPF-QSNN outperforms both the existing spiking neural network and the serial quantum neural network across metrics such as accuracy, loss, and robustness. This study lays the groundwork for the advancement and application of quantum advantage in artificial intelligent computations.
  arXiv  Detail & Related papers  (2024-04-01T10:35:35Z)
• Simple initialization and parametrization of sinusoidal networks via their kernel bandwidth [92.25666446274188]
  sinusoidal neural networks with activations have been proposed as an alternative to networks with traditional activation functions. We first propose a simplified version of such sinusoidal neural networks, which allows both for easier practical implementation and simpler theoretical analysis. We then analyze the behavior of these networks from the neural tangent kernel perspective and demonstrate that their kernel approximates a low-pass filter with an adjustable bandwidth.
  arXiv  Detail & Related papers  (2022-11-26T07:41:48Z)
• Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach [64.23331120621118]
  This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks. We introduce a related embedded network and show that the embedded network can be used to provide an $ell_infty$-norm box over-approximation of the reachable sets of the original network. We apply our algorithms to train implicit neural networks on the MNIST dataset and compare the robustness of our models with the models trained via existing approaches in the literature.
  arXiv  Detail & Related papers  (2022-08-08T03:13:24Z)
• Acceleration techniques for optimization over trained neural network ensembles [1.0323063834827415]
  We study optimization problems where the objective function is modeled through feedforward neural networks with rectified linear unit activation. We present a mixed-integer linear program based on existing popular big-$M$ formulations for optimizing over a single neural network.
  arXiv  Detail & Related papers  (2021-12-13T20:50:54Z)
• Training Sparse Neural Network by Constraining Synaptic Weight on Unit Lp Sphere [2.429910016019183]
  constraining the synaptic weights on unit Lp-sphere enables the flexibly control of the sparsity with p. Our approach is validated by experiments on benchmark datasets covering a wide range of domains.
  arXiv  Detail & Related papers  (2021-03-30T01:02:31Z)
• LocalDrop: A Hybrid Regularization for Deep Neural Networks [98.30782118441158]
  We propose a new approach for the regularization of neural networks by the local Rademacher complexity called LocalDrop. A new regularization function for both fully-connected networks (FCNs) and convolutional neural networks (CNNs) has been developed based on the proposed upper bound of the local Rademacher complexity.
  arXiv  Detail & Related papers  (2021-03-01T03:10:11Z)
• SPINN: Sparse, Physics-based, and Interpretable Neural Networks for PDEs [0.0]
  We introduce a class of Sparse, Physics-based, and Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations. By reinterpreting a traditional meshless representation of solutions of PDEs as a special sparse deep neural network, we develop a class of sparse neural network architectures that are interpretable.
  arXiv  Detail & Related papers  (2021-02-25T17:45:50Z)
• Connecting Weighted Automata, Tensor Networks and Recurrent Neural Networks through Spectral Learning [58.14930566993063]
  We present connections between three models used in different research fields: weighted finite automata(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks. We introduce the first provable learning algorithm for linear 2-RNN defined over sequences of continuous vectors input.
  arXiv  Detail & Related papers  (2020-10-19T15:28:00Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Parallelization Techniques for Verifying Neural Networks [52.917845265248744]
  We introduce an algorithm based on the verification problem in an iterative manner and explore two partitioning strategies. We also introduce a highly parallelizable pre-processing algorithm that uses the neuron activation phases to simplify the neural network verification problems.
  arXiv  Detail & Related papers  (2020-04-17T20:21:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.