Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport

• URL: http://arxiv.org/abs/2204.06684v1
• Date: Thu, 14 Apr 2022 01:01:24 GMT
• Title: Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
• Authors: Lu Lu, Raphael Pestourie, Steven G. Johnson, Giuseppe Romano
• Abstract summary: We develop a multifidelity neural operator based on a deep operator network (DeepONet) A multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport.
• Score: 2.512625172084287
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires a large amount of high-fidelity data, which is often difficult to obtain in real engineering problems. Here, we address this challenge by using multifidelity learning, i.e., learning from multifidelity datasets. We develop a multifidelity neural operator based on a deep operator network (DeepONet). A multifidelity DeepONet includes two standard DeepONets coupled by residual learning and input augmentation. Multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport. By combining a trained multifidelity DeepONet with genetic algorithm or topology optimization, we demonstrate a fast solver for the inverse design of BTE problems.

Related papers

• Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling [19.60087366873302]
  Multi-fidelity surrogate modeling aims to learn an accurate surrogate at the highest fidelity level. Deep learning approaches utilize neural network based encoders and decoders to improve scalability. We propose Multi-fidelity Residual Neural Processes (MFRNP), a novel multi-fidelity surrogate modeling framework.
  arXiv  Detail & Related papers  (2024-02-29T04:40:25Z)
• HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork [14.93012615797081]
  This study proposes HyperDeepONet, which uses the expressive power of the hypernetwork to enable the learning of a complex operator with a smaller set of parameters. We analyze the complexity of DeepONet and conclude that HyperDeepONet needs relatively lower complexity to obtain the desired accuracy for operator learning.
  arXiv  Detail & Related papers  (2023-12-26T08:28:46Z)
• Deep-Unfolding for Next-Generation Transceivers [49.338084953253755]
  The stringent performance requirements of future wireless networks are spurring studies on defining the next-generation multiple-input multiple-output (MIMO) transceivers. For the design of advanced transceivers in wireless communications, optimization approaches often leading to iterative algorithms have achieved great success. Deep learning, approximating the iterative algorithms with deep neural networks (DNNs) can significantly reduce the computational time. Deep-unfolding has emerged which incorporates the benefits of both deep learning and iterative algorithms, by unfolding the iterative algorithm into a layer-wise structure.
  arXiv  Detail & Related papers  (2023-05-15T02:13:41Z)
• Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis [94.64007376939735]
  We theoretically characterize the impact of connectivity patterns on the convergence of deep neural networks (DNNs) under gradient descent training. We show that by a simple filtration on "unpromising" connectivity patterns, we can trim down the number of models to evaluate.
  arXiv  Detail & Related papers  (2022-05-11T17:43:54Z)
• Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems [0.9999629695552196]
  We present a composite Deep Operator Network (DeepONet) for learning using two datasets with different levels of fidelity. We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland.
  arXiv  Detail & Related papers  (2022-04-19T23:19:05Z)
• MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problems [12.826754199680474]
  A new data-driven method for operator learning of differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse problems more effectively using limited data.
  arXiv  Detail & Related papers  (2022-04-07T03:53:49Z)
• Enhanced DeepONet for Modeling Partial Differential Operators Considering Multiple Input Functions [5.819397109258169]
  A deep network operator (DeepONet) was proposed to model the general non-linear continuous operators for partial differential equations (PDE) Existing DeepONet can only accept one input function, which limits its application. We propose new Enhanced DeepONet or EDeepONet high-level neural network structure, in which two input functions are represented by two branch sub-networks. Our numerical results on modeling two partial differential equation examples shows that the proposed enhanced DeepONet is about 7X-17X or about one order of magnitude more accurate than the fully connected neural network.
  arXiv  Detail & Related papers  (2022-02-17T23:58:23Z)
• Understanding Self-supervised Learning with Dual Deep Networks [74.92916579635336]
  We propose a novel framework to understand contrastive self-supervised learning (SSL) methods that employ dual pairs of deep ReLU networks. We prove that in each SGD update of SimCLR with various loss functions, the weights at each layer are updated by a emphcovariance operator. To further study what role the covariance operator plays and which features are learned in such a process, we model data generation and augmentation processes through a emphhierarchical latent tree model (HLTM)
  arXiv  Detail & Related papers  (2020-10-01T17:51:49Z)
• Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks [50.42141893913188]
  We study a distributed variable for large-scale AUC for a neural network as with a deep neural network. Our model requires a much less number of communication rounds and still a number of communication rounds in theory. Our experiments on several datasets show the effectiveness of our theory and also confirm our theory.
  arXiv  Detail & Related papers  (2020-05-05T18:08:23Z)
• Self-Organized Operational Neural Networks with Generative Neurons [87.32169414230822]
  ONNs are heterogenous networks with a generalized neuron model that can encapsulate any set of non-linear operators. We propose Self-organized ONNs (Self-ONNs) with generative neurons that have the ability to adapt (optimize) the nodal operator of each connection.
  arXiv  Detail & Related papers  (2020-04-24T14:37:56Z)
• Large-Scale Gradient-Free Deep Learning with Recursive Local Representation Alignment [84.57874289554839]
  Training deep neural networks on large-scale datasets requires significant hardware resources. Backpropagation, the workhorse for training these networks, is an inherently sequential process that is difficult to parallelize. We propose a neuro-biologically-plausible alternative to backprop that can be used to train deep networks.
  arXiv  Detail & Related papers  (2020-02-10T16:20:02Z)

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.