Predicting Wave Dynamics using Deep Learning with Multistep Integration Inspired Attention and Physics-Based Loss Decomposition

• URL: http://arxiv.org/abs/2504.11433v1
• Date: Tue, 15 Apr 2025 17:47:20 GMT
• Title: Predicting Wave Dynamics using Deep Learning with Multistep Integration Inspired Attention and Physics-Based Loss Decomposition
• Authors: Indu Kant Deo, Rajeev K. Jaiman,
• Abstract summary: We present a physics-based deep learning framework for data-driven prediction of wave propagation in fluid media.<n>The proposed approach combines a denoising-based convolutional autoencoder for reduced latent representation with an attention-based recurrent neural network.<n>We show that the MI2A framework significantly improves the accuracy and stability of long-term predictions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we present a physics-based deep learning framework for data-driven prediction of wave propagation in fluid media. The proposed approach, termed Multistep Integration-Inspired Attention (MI2A), combines a denoising-based convolutional autoencoder for reduced latent representation with an attention-based recurrent neural network with long-short-term memory cells for time evolution of reduced coordinates. This proposed architecture draws inspiration from classical linear multistep methods to enhance stability and long-horizon accuracy in latent-time integration. Despite the efficiency of hybrid neural architectures in modeling wave dynamics, autoregressive predictions are often prone to accumulating phase and amplitude errors over time. To mitigate this issue within the MI2A framework, we introduce a novel loss decomposition strategy that explicitly separates the training loss function into distinct phase and amplitude components. We assess the performance of MI2A against two baseline reduced-order models trained with standard mean-squared error loss: a sequence-to-sequence recurrent neural network and a variant using Luong-style attention. To demonstrate the effectiveness of the MI2A model, we consider three benchmark wave propagation problems of increasing complexity, namely one-dimensional linear convection, the nonlinear viscous Burgers equation, and the two-dimensional Saint-Venant shallow water system. Our results demonstrate that the MI2A framework significantly improves the accuracy and stability of long-term predictions, accurately preserving wave amplitude and phase characteristics. Compared to the standard long-short term memory and attention-based models, MI2A-based deep learning exhibits superior generalization and temporal accuracy, making it a promising tool for real-time wave modeling.

Related papers

• Differential Machine Learning for Time Series Prediction [1.3812010983144802]
  We propose a novel approach that enhances neural network predictions through differential learning. We develop a differential long short-term memory (Diff-LSTM) network that uses a shared LSTM cell to simultaneously process both data streams.
  arXiv  Detail & Related papers  (2025-03-05T09:36:57Z)
• Oscillatory State-Space Models [61.923849241099184]
  We propose Lineary State-Space models (LinOSS) for efficiently learning on long sequences.<n>A stable discretization, integrated over time using fast associative parallel scans, yields the proposed state-space model.<n>We show that LinOSS is universal, i.e., it can approximate any continuous and causal operator mapping between time-varying functions.
  arXiv  Detail & Related papers  (2024-10-04T22:00:13Z)
• Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data [37.69303106863453]
  We propose a novel approach for phase-resolved wave surface reconstruction using neural networks. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids.
  arXiv  Detail & Related papers  (2023-05-18T12:30:26Z)
• Learning Controllable Adaptive Simulation for Multi-resolution Physics [86.8993558124143]
  We introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error.
  arXiv  Detail & Related papers  (2023-05-01T23:20:27Z)
• Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence [0.0]
  We investigate how an often overlooked processing step affects the quality of an emulator's predictions. We implement ML architectures from a class of methods called reservoir computing: (1) a form of spatial Vector Autoregression (N VAR), and (2) an Echo State Network (ESN) In all cases, subsampling the training data consistently leads to an increased bias at small scales that resembles numerical diffusion.
  arXiv  Detail & Related papers  (2023-04-28T21:34:53Z)
• Gait Recognition in the Wild with Multi-hop Temporal Switch [81.35245014397759]
  gait recognition in the wild is a more practical problem that has attracted the attention of the community of multimedia and computer vision. This paper presents a novel multi-hop temporal switch method to achieve effective temporal modeling of gait patterns in real-world scenes.
  arXiv  Detail & Related papers  (2022-09-01T10:46:09Z)
• Wave simulation in non-smooth media by PINN with quadratic neural network and PML condition [2.7651063843287718]
  The recently proposed physics-informed neural network (PINN) has achieved successful applications in solving a wide range of partial differential equations (PDEs) In this paper, we solve the acoustic and visco-acoustic scattered-field wave equation in the frequency domain with PINN instead of the wave equation to remove source perturbation. We show that PML and quadratic neurons improve the results as well as attenuation and discuss the reason for this improvement.
  arXiv  Detail & Related papers  (2022-08-16T13:29:01Z)
• An advanced spatio-temporal convolutional recurrent neural network for storm surge predictions [73.4962254843935]
  We study the capability of artificial neural network models to emulate storm surge based on the storm track/size/intensity history. This study presents a neural network model that can predict storm surge, informed by a database of synthetic storm simulations.
  arXiv  Detail & Related papers  (2022-04-18T23:42:18Z)
• Deep Residual Error and Bag-of-Tricks Learning for Gravitational Wave Surrogate Modeling [32.15071712355222]
  We show how to reduce the maximum mismatch for waveforms in a validation set by 13.4 times. The most significant improvement comes from the addition of a second network that models the residual error.
  arXiv  Detail & Related papers  (2022-03-16T07:12:42Z)
• Predicting Physics in Mesh-reduced Space with Temporal Attention [15.054026802351146]
  We propose a new method that captures long-term dependencies through a transformer-style temporal attention model. Our method outperforms a competitive GNN baseline on several complex fluid dynamics prediction tasks. We believe our approach paves the way to bringing the benefits of attention-based sequence models to solving high-dimensional complex physics tasks.
  arXiv  Detail & Related papers  (2022-01-22T18:32:54Z)
• Learning Wave Propagation with Attention-Based Convolutional Recurrent Autoencoder Net [0.0]
  We present an end-to-end attention-based convolutional recurrent autoencoder (AB-CRAN) network for data-driven modeling of wave propagation phenomena. We employ a denoising-based convolutional autoencoder from the full-order snapshots given by time-dependent hyperbolic partial differential equations for wave propagation. The attention-based sequence-to-sequence network increases the time-horizon of prediction by five times compared to the plain RNN-LSTM.
  arXiv  Detail & Related papers  (2022-01-17T20:51:59Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)
• Convolutional Tensor-Train LSTM for Spatio-temporal Learning [116.24172387469994]
  We propose a higher-order LSTM model that can efficiently learn long-term correlations in the video sequence. This is accomplished through a novel tensor train module that performs prediction by combining convolutional features across time. Our results achieve state-of-the-art performance-art in a wide range of applications and datasets.
  arXiv  Detail & Related papers  (2020-02-21T05:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.