Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear Independent Dual System (NIDS) for Discretization-independent
  Surrogate Modeling over Complex Geometries   Numerical solutions 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 surrogate model for
discretization-independent, continuous representation of PDE solutions, and can
be used for prediction over domains with complex, variable geometries and mesh
topologies. NIDS leverages implicit neural representations to develop a
non-linear mapping between problem parameters and spatial coordinates to state
predictions by combining evaluations of a case-wise parameter network and a
point-wise spatial network in a linear output layer. The input features of the
spatial network include physical coordinates augmented by a minimum distance
function evaluation to implicitly encode the problem geometry. The form of the
overall output layer induces a dual system, where each term in the map is
non-linear and independent. Further, we propose a minimum distance
function-driven weighted sum of NIDS models using a shared parameter network to
enforce boundary conditions by construction under certain restrictions. The
framework is applied to predict solutions around complex,
parametrically-defined geometries on non-parametrically-defined meshes with
solutions obtained many orders of magnitude faster than the full order models.
Test cases include a vehicle aerodynamics problem with complex geometry and
data scarcity, enabled by a training method in which more cases are gradually
added as training progresses.

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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex