# Wavelet-based Loss for High-frequency Interface Dynamics

arXiv: https://arxiv.org/abs/2209.02316 · HTML: https://mlsanity.com/paper/2209.02316/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 57 references that are in the map.
- First posted on arXiv 6 Sep 2022.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Generating Images with Perceptual Similarity Metrics based on Deep Networks](https://mlsanity.com/paper/1602.02644/) (2016)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Temporal Generative Adversarial Nets with Singular Value Clipping](https://mlsanity.com/paper/1611.06624/) (2016)
- [Photorealistic Style Transfer via Wavelet Transforms](https://mlsanity.com/paper/1903.09760/) (2019)
- [Frame-Recurrent Video Super-Resolution](https://mlsanity.com/paper/1801.04590/) (2018)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Coherent Online Video Style Transfer](https://mlsanity.com/paper/1703.09211/) (2017)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Deep Dynamical Modeling and Control of Unsteady Fluid Flows](https://mlsanity.com/paper/1805.07472/) (2018)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [Multi-level Wavelet Convolutional Neural Networks](https://mlsanity.com/paper/1907.03128/) (2019)
- [Wavelet-Based Dual-Branch Network for Image Demoireing](https://mlsanity.com/paper/2007.07173/) (2020)
- [tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow](https://mlsanity.com/paper/1801.09710/) (2018)
- [Super-Resolution with Deep Convolutional Sufficient Statistics](https://mlsanity.com/paper/1511.05666/) (2015)
- [Multi-level Wavelet-based Generative Adversarial Network for Perceptual Quality Enhancement of Compressed Video](https://mlsanity.com/paper/2008.00499/) (2020)
- [Liquid Splash Modeling with Neural Networks](https://mlsanity.com/paper/1704.04456/) (2017)
- [Image Restoration by Estimating Frequency Distribution of Local Patches](https://mlsanity.com/paper/1805.09097/) (2018)
- [Lagrangian Neural Style Transfer for Fluids](https://mlsanity.com/paper/2005.00803/) (2020)

## Built on by (most cited first, 2 of 2)

- [Complex Wavelet Mutual Information Loss: A Multi-Scale Loss Function for Semantic Segmentation](https://mlsanity.com/paper/2502.00563/) (2025)
- [Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows](https://mlsanity.com/paper/2607.22280/) (2026)

## Abstract (arXiv)

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.