Wavelet-based Loss for High-frequency Interface Dynamics
- URL: http://arxiv.org/abs/2209.02316v1
- Date: Tue, 6 Sep 2022 09:09:14 GMT
- Title: Wavelet-based Loss for High-frequency Interface Dynamics
- Authors: Lukas Prantl, Jan Bender, Tassilo Kugelstadt, Nils Thuerey
- Abstract summary: We present a new method based on a wavelet loss formulation, which remains transparent in terms of what is optimized.
We show that our method can successfully reconstruct high-frequency details in an illustrative synthetic test case.
We also evaluate the performance when applied to more complex surfaces based on physical simulations.
- Score: 30.246577036044332
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Generating highly detailed, complex data is a long-standing and frequently
considered problem in the machine learning field. However, developing
detail-aware generators remains an challenging and open problem. Generative
adversarial networks are the basis of many state-of-the-art methods. However,
they introduce a second network to be trained as a loss function, making the
interpretation of the learned functions much more difficult. As an alternative,
we present a new method based on a wavelet loss formulation, which remains
transparent in terms of what is optimized. The wavelet-based loss function is
used to overcome the limitations of conventional distance metrics, such as L1
or L2 distances, when it comes to generate data with high-frequency details. We
show that our method can successfully reconstruct high-frequency details in an
illustrative synthetic test case. Additionally, we evaluate the performance
when applied to more complex surfaces based on physical simulations. Taking a
roughly approximated simulation as input, our method infers corresponding
spatial details while taking into account how they evolve. We consider this
problem in terms of spatial and temporal frequencies, and leverage generative
networks trained with our wavelet loss to learn the desired spatio-temporal
signal for the surface dynamics. We test the capabilities of our method with a
set of synthetic wave function tests and complex 2D and 3D dynamics of
elasto-plastic materials.
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