Reduced order modeling with Barlow Twins self-supervised learning: Navigating the space between linear and nonlinear solution manifolds

• URL: http://arxiv.org/abs/2202.05460v1
• Date: Fri, 11 Feb 2022 05:41:33 GMT
• Title: Reduced order modeling with Barlow Twins self-supervised learning: Navigating the space between linear and nonlinear solution manifolds
• Authors: Teeratorn Kadeethum, Francesco Ballarin, Daniel O'Malley, Youngsoo Choi, Nikolaos Bouklas, Hongkyu Yoon
• Abstract summary: The proposed framework relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning. We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC-AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT-AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. Furthermore, this BT-AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.

Related papers

• Pushing the Limits of Large Language Model Quantization via the Linearity Theorem [71.3332971315821]
  We present a "line theoremarity" establishing a direct relationship between the layer-wise $ell$ reconstruction error and the model perplexity increase due to quantization. This insight enables two novel applications: (1) a simple data-free LLM quantization method using Hadamard rotations and MSE-optimal grids, dubbed HIGGS, and (2) an optimal solution to the problem of finding non-uniform per-layer quantization levels.
  arXiv  Detail & Related papers  (2024-11-26T15:35:44Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Exploiting Temporal Structures of Cyclostationary Signals for Data-Driven Single-Channel Source Separation [98.95383921866096]
  We study the problem of single-channel source separation (SCSS) We focus on cyclostationary signals, which are particularly suitable in a variety of application domains. We propose a deep learning approach using a U-Net architecture, which is competitive with the minimum MSE estimator.
  arXiv  Detail & Related papers  (2022-08-22T14:04:56Z)
• Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method [0.0]
  Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay. We implement the non-linear manifold method introduced by Carlberg et al [37] with hyper-reduction achieved through reduced over-collocation and teacher-student training of a reduced decoder. We test the methodology on a 2d non-linear conservation law and a 2d shallow water models, and compare the results obtained with a purely data-driven method for which the dynamics is evolved in time with a long-short term memory network
  arXiv  Detail & Related papers  (2022-03-01T11:16:50Z)
• Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs [0.0]
  We propose a strategy for learning nonlinear ROM operators using deep neural networks (DNNs) The resulting hyper-reduced order model enhanced by DNNs is referred to as Deep-HyROMnet. Numerical results show that Deep-HyROMnets are orders of magnitude faster than POD-GalerkinDEIMs, keeping the same level of accuracy.
  arXiv  Detail & Related papers  (2022-02-05T23:45:25Z)
• Cogradient Descent for Dependable Learning [64.02052988844301]
  We propose a dependable learning based on Cogradient Descent (CoGD) algorithm to address the bilinear optimization problem. CoGD is introduced to solve bilinear problems when one variable is with sparsity constraint. It can also be used to decompose the association of features and weights, which further generalizes our method to better train convolutional neural networks (CNNs)
  arXiv  Detail & Related papers  (2021-06-20T04:28:20Z)
• Learning Generative Prior with Latent Space Sparsity Constraints [25.213673771175692]
  It has been argued that the distribution of natural images do not lie in a single manifold but rather lie in a union of several submanifolds. We propose a sparsity-driven latent space sampling (SDLSS) framework and develop a proximal meta-learning (PML) algorithm to enforce sparsity in the latent space. The results demonstrate that for a higher degree of compression, the SDLSS method is more efficient than the state-of-the-art method.
  arXiv  Detail & Related papers  (2021-05-25T14:12:04Z)
• POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition [0.0]
  Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) In this paper we propose a possible way to avoid an expensive training stage of DL-ROMs, by (i) performing a prior dimensionality reduction through POD, and (ii) relying on a multi-fidelity pretraining stage. The proposed POD-DL-ROM is tested on several (both scalar and vector, linear and nonlinear) time-dependent parametrized PDEs.
  arXiv  Detail & Related papers  (2021-01-28T07:34:15Z)
• ePointDA: An End-to-End Simulation-to-Real Domain Adaptation Framework for LiDAR Point Cloud Segmentation [111.56730703473411]
  Training deep neural networks (DNNs) on LiDAR data requires large-scale point-wise annotations. Simulation-to-real domain adaptation (SRDA) trains a DNN using unlimited synthetic data with automatically generated labels. ePointDA consists of three modules: self-supervised dropout noise rendering, statistics-invariant and spatially-adaptive feature alignment, and transferable segmentation learning.
  arXiv  Detail & Related papers  (2020-09-07T23:46:08Z)
• An Online Method for A Class of Distributionally Robust Optimization with Non-Convex Objectives [54.29001037565384]
  We propose a practical online method for solving a class of online distributionally robust optimization (DRO) problems. Our studies demonstrate important applications in machine learning for improving the robustness of networks.
  arXiv  Detail & Related papers  (2020-06-17T20:19:25Z)
• A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs [0.0]
  We show how to construct a DL-ROM for both linear and nonlinear time-dependent parametrized PDEs. Numerical results indicate that DL-ROMs whose dimension is equal to the intrinsic dimensionality of the PDE solutions manifold are able to approximate the solution of parametrized PDEs.
  arXiv  Detail & Related papers  (2020-01-12T21:18:18Z)

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.