Corpus ID: 237513925

Non-linear Independent Dual System (NIDS) for Discretization-independent Surrogate Modeling over Complex Geometries

@article{Duvall2021NonlinearID,
  title={Non-linear Independent Dual System (NIDS) for Discretization-independent Surrogate Modeling over Complex Geometries},
  author={J. Michael Duvall and Karthik Duraisamy and Shaowu Pan},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.07018}
}
Numerical solution of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization routines, model-based control, or solution of large-scale inverse problems. Existing Convolutional Neural Network-based frameworks for surrogate modeling require lossy pixelization and data-preprocessing, which is not suitable for realistic engineering applications. Therefore, we propose non-linear independent dual system (NIDS), which is a deep learning… Expand
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References

SHOWING 1-10 OF 63 REFERENCES
Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems
TLDR
The idea of conditional parametrization is generalized – using trainable functions of input parameters to generate the weights of a neural network, and extend them in a flexible way to encode information critical to the numerical simulations. Expand
Convolutional Neural Networks for Steady Flow Approximation
TLDR
This work proposes a general and flexible approximation model for real-time prediction of non-uniform steady laminar flow in a 2D or 3D domain based on convolutional neural networks (CNNs), and shows that convolutionAL neural networks can estimate the velocity field two orders of magnitude faster than a GPU-accelerated CFD solver and four orders of order than a CPU-based CFDsolver at a cost of a low error rate. Expand
GMLS-Nets: A framework for learning from unstructured data
TLDR
GMLS is generalized by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares based on a rigorous approximation theory, and the architectures are suggested to be an attractive foundation for data-driven model development in scientific machine learning applications. Expand
Graph Convolutional Neural Networks for Body Force Prediction
TLDR
The GCNN method, using inductive convolutional layers and adaptive pooling, is able to predict this quantity with a validation above 0.98, and a Normalized Mean Squared Error below 0.01, without relying on spatial structure. Expand
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Abstract We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinearExpand
Generalizability of Convolutional Encoder–Decoder Networks for Aerodynamic Flow-Field Prediction Across Geometric and Physical-Fluidic Variations
The generalizability of a convolutional encoder–decoder based model in predicting aerodynamic flow field across various flow regimes and geometric variation is assessed. A rich master datasetExpand
Overfit Neural Networks as a Compact Shape Representation
TLDR
This work asks whether neural networks can serve as first-class implicit shape representations in computer graphics, and calls such overfit networks Neural Implicits, which have fixed storage profiles and memory layout, but afford far greater accuracy. Expand
Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation
TLDR
An integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics is provided, whereas free-form deformation is applied for geometry parametrisation and two different reduced-order models based on proper orthogonal decomposition are employed in order to speed-up the full-order simulations. Expand
Fourier Neural Operator for Parametric Partial Differential Equations
TLDR
This work forms a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture and shows state-of-the-art performance compared to existing neural network methodologies. Expand
DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation
TLDR
This work introduces DeepSDF, a learned continuous Signed Distance Function (SDF) representation of a class of shapes that enables high quality shape representation, interpolation and completion from partial and noisy 3D input data. Expand
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