Wave Physics-informed Matrix Factorizations
This work addresses the need for physically-informed learning in domains like optics and acoustics, offering a novel approach for modal analysis in structural diagnostics and prognostics.
The paper tackled the problem of incorporating wave equation constraints into representation learning for signals propagating through physical media, proposing a matrix factorization method that decomposes signals into components regularized to satisfy these constraints and proving it can be efficiently solved to global optimality.
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.