Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On physics-informed data-driven isotropic and anisotropic constitutive
  models through probabilistic machine learning and space-filling sampling   Data-driven constitutive modeling is an emerging field in computational solid
mechanics with the prospect of significantly relieving the computational costs
of hierarchical computational methods. Traditionally, these surrogates have
been trained using datasets which map strain inputs to stress outputs directly.
Data-driven constitutive models for elastic and inelastic materials have
commonly been developed based on artificial neural networks (ANNs), which
recently enabled the incorporation of physical laws in the construction of
these models. However, ANNs do not offer convergence guarantees and are reliant
on user-specified parameters. In contrast to ANNs, Gaussian process regression
(GPR) is based on nonparametric modeling principles as well as on fundamental
statistical knowledge and hence allows for strict convergence guarantees. GPR
however has the major disadvantage that it scales poorly as datasets get large.
In this work we present a physics-informed data-driven constitutive modeling
approach for isostropic and anisotropic materials based on probabilistic
machine learning that can be used in the big data context. The trained GPR
surrogates are able to respect physical principles such as material frame
indifference, material symmetry, thermodynamic consistency, stress-free
undeformed configuration, and the local balance of angular momentum.
Furthermore, this paper presents the first sampling approach that directly
generates space-filling points in the invariant space corresponding to bounded
domain of the gradient deformation tensor. Overall, the presented approach is
tested on synthetic data from isotropic and anisotropic constitutive laws and
shows surprising accuracy even far beyond the limits of the training domain,
indicating that the resulting surrogates can efficiently generalize as they
incorporate knowledge about the underlying physics.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin