With the recent success of representation learning methods, which includes
deep learning as a special case, there has been considerable interest in
developing techniques that incorporate known physical constraints into the
learned representation. As one example, in many applications that involve a
signal propagating through physical media (e.g., optics, acoustics, fluid
dynamics, etc), it is known that the dynamics of the signal must satisfy
constraints imposed by the wave equation. Here we propose a matrix
factorization technique that decomposes such signals into a sum of components,
where each component is regularized to ensure that it {nearly} satisfies wave
equation constraints. Although our proposed formulation is non-convex, we prove
that our model can be efficiently solved to global optimality. Through this
line of work we establish theoretical connections between wave-informed
learning and filtering theory in signal processing. We further demonstrate the
application of this work on modal analysis problems commonly arising in
structural diagnostics and prognostics.

在最近的表示学习方法的成功的基础上，我们提出一种基于矩阵分解的技术，将信号分解为满足波动方程约束的组成部分，从而在波动方程约束下利用已知的物理约束进行学习，建立了波动信息学习与信号处理中的滤波理论之间的理论联系，并展示了该方法在结构诊断和预测中常见的模态分析问题上的应用。