Technology Category
Machine Learning: Deep Generative Models & AutoencodersComputer Vision: Low Level & Physics-based VisionPlanning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
Predicting Wave Dynamics using Deep Learning with Multistep Integration Inspired Attention and Physics-Based Loss Decomposition
🤖 AI Summary
Existing deep learning models for long-term, data-driven prediction of wave propagation in fluid media suffer from accumulating phase and amplitude errors over autoregressive steps, leading to prediction instability. To address this, we propose a physics-informed deep learning framework featuring: (i) a multi-step integration-inspired attention mechanism (MI2A) that enhances numerical stability of temporal integration in latent space; and (ii) a phase–amplitude decoupled physics-based loss decomposition strategy, jointly leveraging a denoising convolutional autoencoder and an LSTM-RNN to explicitly enforce wave physics constraints. Evaluated on three canonical benchmarks—1D linear advection, nonlinear Burgers equation, and 2D shallow water equations—the method significantly improves long-term prediction accuracy and generalization, effectively suppresses error accumulation, and precisely preserves both waveform phase and amplitude characteristics.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Predicting wave dynamics using deep learning with physics-based loss
Reducing phase and amplitude errors in autoregressive wave predictions
Improving long-term accuracy in wave propagation modeling
Innovation
Methods, ideas, or system contributions that make the work stand out.
Multistep Integration-Inspired Attention for stability
Physics-based loss decomposition for phase accuracy
Hybrid neural architecture for wave dynamics
🔎 Similar Papers
No similar papers found.
