Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Indu Kant Deo, Rajeev Jaiman

TL;DR

Problem: long-horizon wave forecasts suffer from accumulating phase and amplitude errors in autoregressive neural models. Approach: introduce a loss-decomposition framework that separates amplitude (dissipation) and phase (dispersion) errors into $\tau_{DISS}$ and $\tau_{DISP}$ and optimize a combined loss with weights $\alpha$ and $\beta$; the method is applied to an AB-CRAN trained on linear advection data with a denoising decoder. Contributions: first explicit phase–amplitude loss decomposition for wave-propagation networks; demonstration of improved phase fidelity and longer forecast horizons; detailed hyperparameter tuning via Ray Tune ASHA. Significance: enhances stability and physical reliability of long-term neural forecasts and is readily extensible to other physical domains like fluid dynamics and climate modeling.

Abstract

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.

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

TL;DR

Problem: long-horizon wave forecasts suffer from accumulating phase and amplitude errors in autoregressive neural models. Approach: introduce a loss-decomposition framework that separates amplitude (dissipation) and phase (dispersion) errors into and and optimize a combined loss with weights and ; the method is applied to an AB-CRAN trained on linear advection data with a denoising decoder. Contributions: first explicit phase–amplitude loss decomposition for wave-propagation networks; demonstration of improved phase fidelity and longer forecast horizons; detailed hyperparameter tuning via Ray Tune ASHA. Significance: enhances stability and physical reliability of long-term neural forecasts and is readily extensible to other physical domains like fluid dynamics and climate modeling.

Abstract

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.

Paper Structure

This paper contains 8 sections, 6 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Linear advection equation
  4. Attention-based Convolution Recurrent Autoencoder Network
  5. Loss decomposition
  6. Training
  7. Results
  8. Conclusion

Figures (4)

  • Figure 1: Schematic of dataset generation. Linear convection simulations were generated for parameter wave speed. Amplitude data were extracted and arranged into a training snapshot matrix.
  • Figure 2: Illustration of attention-based convolutional recurrent autoencoder architecture.
  • Figure 3: Linear convection problem: Exact solution (left), AB-CRAN solution with n = 2 (center) and error $e = |\hat{u} - u|$ (right) for the testing parameter $\mu_{test}$ = 1.0125 in the space-time domain.
  • Figure 4: Accuracy assessment for wave prediction: (a) Comparison of MSE-based loss and Loss-decomposition-based training prediction for $t^*$= 0.036, 0.392 (b) Error vs. time-horizon plot comparing MSE-based and loss-decomposition-based training predictions, with a time-horizon of 10 time-steps