Divergence-free neural operators for stress field modeling in polycrystalline materials
The purpose of the current work is the development and comparison of Fourier neural operators (FNOs) for surrogate modeling of the quasi-static mechanical response of polycrystalline materials. Three types of such FNOs are considered here: a physics-guided FNO (PgFNO), a physics-informed FNO (PiFNO)...
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Main Authors | , , , , , |
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Format | Journal Article |
Language | English |
Published |
27.08.2024
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Subjects | |
Online Access | Get full text |
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Summary: | The purpose of the current work is the development and comparison of Fourier
neural operators (FNOs) for surrogate modeling of the quasi-static mechanical
response of polycrystalline materials. Three types of such FNOs are considered
here: a physics-guided FNO (PgFNO), a physics-informed FNO (PiFNO), and a
physics-encoded FNO (PeFNO). These are trained and compared with the help of
stress field data from a reference model for heterogeneous elastic materials
with a periodic grain microstructure. Whereas PgFNO training is based solely on
these data, that of the PiFNO and PeFNO is in addition constrained by the
requirement that stress fields satisfy mechanical equilibrium, i.e., be
divergence-free. The difference between the PiFNO and PeFNO lies in how this
constraint is taken into account; in the PiFNO, it is included in the loss
function, whereas in the PeFNO, it is "encoded" in the operator architecture.
In the current work, this encoding is based on a stress potential and Fourier
transforms. As a result, only the training of the PiFNO is constrained by
mechanical equilibrium; in contrast, mechanical equilibrium constrains both the
training and output of the PeFNO. Due in particular to this, stress fields
calculated by the trained PeFNO are significantly more accurate than those
calculated by the trained PiFNO in the example cases considered. |
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DOI: | 10.48550/arxiv.2408.15408 |