Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data

• URL: http://arxiv.org/abs/2204.03216v2
• Date: Fri, 8 Apr 2022 18:45:52 GMT
• Title: Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data
• Authors: Shaowu Pan, Steven L. Brunton, J. Nathan Kutz
• Abstract summary: We propose a general framework called Neural Implicit Flow (NIF) that enables a mesh-agnostic, low-rank representation of large-scale, parametric, spatialtemporal data. NIF consists of two modified multilayer perceptrons (i) ShapeNet, which isolates and represents the spatial complexity (i) ShapeNet, which accounts for any other input measurements, including parametric dependencies, time, and sensor measurements. We demonstrate the utility of NIF for parametric surrogate modeling, enabling the interpretable representation and compression of complex spatial-temporal dynamics, efficient many-spatial-temporal generalization, and improved performance for sparse
• Score: 4.996878640124385
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace. Engineering applications for modeling, characterization, design, and control of such large-scale systems often rely on dimensionality reduction to make solutions computationally tractable in real-time. Common existing paradigms for dimensionality reduction include linear methods, such as the singular value decomposition (SVD), and nonlinear methods, such as variants of convolutional autoencoders (CAE). However, these encoding techniques lack the ability to efficiently represent the complexity associated with spatio-temporal data, which often requires variable geometry, non-uniform grid resolution, adaptive meshing, and/or parametric dependencies. To resolve these practical engineering challenges, we propose a general framework called Neural Implicit Flow (NIF) that enables a mesh-agnostic, low-rank representation of large-scale, parametric, spatial-temporal data. NIF consists of two modified multilayer perceptrons (MLPs): (i) ShapeNet, which isolates and represents the spatial complexity, and (ii) ParameterNet, which accounts for any other input complexity, including parametric dependencies, time, and sensor measurements. We demonstrate the utility of NIF for parametric surrogate modeling, enabling the interpretable representation and compression of complex spatio-temporal dynamics, efficient many-spatial-query tasks, and improved generalization performance for sparse reconstruction.

Related papers

• Shape-informed surrogate models based on signed distance function domain encoding [8.052704959617207]
  We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs) Our approach is based on the combination of two neural networks (NNs)
  arXiv  Detail & Related papers  (2024-09-19T01:47:04Z)
• 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)
• Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions [0.0]
  This work presents a data-driven, non-intrusive framework which combines ROM construction with reduced dynamics identification. The proposed approach leverages autoencoder neural networks with parametric sparse identification of nonlinear dynamics (SINDy) to construct a low-dimensional dynamical model. These aim at tracking the evolution of periodic steady-state responses as functions of system parameters, avoiding the computation of the transient phase, and allowing to detect instabilities and bifurcations.
  arXiv  Detail & Related papers  (2022-11-13T01:57:18Z)
• Non-linear Independent Dual System (NIDS) for Discretization-independent Surrogate Modeling over Complex Geometries [0.0]
  Non-linear independent dual system (NIDS) is a deep learning surrogate model for discretization-independent, continuous representation of PDE solutions. NIDS can be used for prediction over domains with complex, variable geometries and mesh topologies. Test cases include a vehicle problem with complex geometry and data scarcity, enabled by a training method.
  arXiv  Detail & Related papers  (2021-09-14T23:38:41Z)
• Adaptive Machine Learning for Time-Varying Systems: Low Dimensional Latent Space Tuning [91.3755431537592]
  We present a recently developed method of adaptive machine learning for time-varying systems. Our approach is to map very high (N>100k) dimensional inputs into the low dimensional (N2) latent space at the output of the encoder section of an encoder-decoder CNN. This method allows us to learn correlations within and to track their evolution in real time based on feedback without interrupts.
  arXiv  Detail & Related papers  (2021-07-13T16:05:28Z)
• ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks [86.37110868126548]
  In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Euler's discretization scheme. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations.
  arXiv  Detail & Related papers  (2021-02-16T04:07:13Z)
• Non-intrusive surrogate modeling for parametrized time-dependent PDEs using convolutional autoencoders [0.0]
  We present a non-intrusive surrogate modeling scheme based on machine learning for predictive modeling of complex, systems by parametrized timedependent PDEs. We use a convolutional autoencoder in conjunction with a feed forward neural network to establish a low-cost and accurate mapping from problem's parametric space to its solution space.
  arXiv  Detail & Related papers  (2021-01-14T11:34:58Z)
• Deep Cellular Recurrent Network for Efficient Analysis of Time-Series Data with Spatial Information [52.635997570873194]
  This work proposes a novel deep cellular recurrent neural network (DCRNN) architecture to process complex multi-dimensional time series data with spatial information. The proposed architecture achieves state-of-the-art performance while utilizing substantially less trainable parameters when compared to comparable methods in the literature.
  arXiv  Detail & Related papers  (2021-01-12T20:08:18Z)
• Large-scale Neural Solvers for Partial Differential Equations [48.7576911714538]
  Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. Recent numerical solvers require manual discretization of the underlying equation as well as sophisticated, tailored code for distributed computing. We examine the applicability of continuous, mesh-free neural solvers for partial differential equations, physics-informed neural networks (PINNs) We discuss the accuracy of GatedPINN with respect to analytical solutions -- as well as state-of-the-art numerical solvers, such as spectral solvers.
  arXiv  Detail & Related papers  (2020-09-08T13:26:51Z)
• Physics-aware registration based auto-encoder for convection dominated PDEs [6.85316573653194]
  We propose a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. We demonstrate the efficacy and interpretability of our approach to separate convection/advection from diffusion/scaling on various manufactured and physical systems.
  arXiv  Detail & Related papers  (2020-06-28T16:58:21Z)
• Dense Non-Rigid Structure from Motion: A Manifold Viewpoint [162.88686222340962]
  Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. We show that our approach significantly improves accuracy, scalability, and robustness against noise.
  arXiv  Detail & Related papers  (2020-06-15T09:15:54Z)

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.