Title: Predicting Wave Dynamics using Deep Learning with Multistep Integration Inspired Attention and Physics-Based Loss Decomposition Show Chinese title

Title: 利用具有多步积分引导注意力和基于物理的损失分解的深度学习预测波动态特性

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. Show Chinese abstract

Abstract: 本文提出了一种基于物理的深度学习框架，用于流体介质中波传播的数据驱动预测。 该方法被称为多步积分启发式注意机制（MI2A），结合了基于去噪的卷积自动编码器以减少潜在表示，以及具有长期短期记忆单元的基于注意力的循环神经网络以实现降维坐标的时间演化。 该架构从经典的线性多步方法中汲取灵感，以增强潜在时间积分中的稳定性和长时间准确性。 尽管混合神经结构在建模波动态方面效率很高，但自回归预测通常容易随着时间推移积累相位和幅度误差。 为了缓解MI2A框架中的这一问题，我们引入了一种新颖的损失分解策略，明确地将训练损失函数分为独立的相位和幅度分量。 我们通过两个以标准均方误差损失训练的标准基线降阶模型来评估MI2A的性能：一个序列到序列循环神经网络和一种使用Luong风格注意的变体。 为了证明MI2A模型的有效性，我们考虑了三个复杂性逐渐增加的基准波传播问题，即一维线性对流、非线性粘性Burgers方程和二维Saint-Venant浅水系统。 我们的结果显示，MI2A框架显著提高了长期预测的准确性和稳定性，准确保留了波幅和相位特性。 与标准长短期记忆和基于注意力的模型相比，基于MI2A的深度学习表现出更优越的泛化能力和时间精度，使其成为实时波建模的一个有前景的工具。