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This content will become publicly available on January 1, 2025

Title: Wave Physics-Informed Matrix Factorizations
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.  more » « less
Award ID(s):
1747783
NSF-PAR ID:
10488296
Author(s) / Creator(s):
; ;
Publisher / Repository:
IEEE
Date Published:
Journal Name:
IEEE Transactions on Signal Processing
Volume:
72
ISSN:
1053-587X
Page Range / eLocation ID:
535 to 548
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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