# Harnessing Loss Decomposition for Long-Horizon Wave Predictions via Deep Neural Networks

arXiv: https://arxiv.org/abs/2412.02924 · HTML: https://mlsanity.com/paper/2412.02924/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 12 of 12)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems](https://mlsanity.com/paper/1808.01346/) (2018)
- [Prediction Error Meta Classification in Semantic Segmentation: Detection via Aggregated Dispersion Measures of Softmax Probabilities](https://mlsanity.com/paper/1811.00648/) (2018)
- [Understanding AdamW through Proximal Methods and Scale-Freeness](https://mlsanity.com/paper/2202.00089/) (2022)
- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [Reduced-order modeling for parameterized PDEs via implicit neural representations](https://mlsanity.com/paper/2311.16410/) (2023)
- [Predicting waves in fluids with deep neural network](https://mlsanity.com/paper/2201.06628/) (2022)
- [Continual Learning of Range-Dependent Transmission Loss for Underwater Acoustic using Conditional Convolutional Neural Net](https://mlsanity.com/paper/2404.08091/) (2024)

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

- [Predicting Wave Dynamics using Deep Learning with Multistep Integration Inspired Attention and Physics-Based Loss Decomposition](https://mlsanity.com/paper/2504.11433/) (2025)
- [When Do Autoregressive Sequence Models Forecast Physical Wavefields? A Controlled Study on Synthetic Seismograms](https://mlsanity.com/paper/2606.10868/) (2026)

## Abstract (arXiv)

Accurate prediction over long time horizons is crucial for modeling complex physical processes such as wave propagation. Although deep neural networks show promise for real-time forecasting, they often struggle with accumulating phase and amplitude errors as predictions extend over a long period. To address this issue, we propose a novel loss decomposition strategy that breaks down the loss into separate phase and amplitude components. This technique improves the long-term prediction accuracy of neural networks in wave propagation tasks by explicitly accounting for numerical errors, improving stability, and reducing error accumulation over extended forecasts.