# Wave-Informed Matrix Factorization with Global Optimality Guarantees

arXiv: https://arxiv.org/abs/2107.09144 · HTML: https://mlsanity.com/paper/2107.09144/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 19 Jul 2021.

## Builds on (most cited first, 17 of 17)

- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [Matrix Completion has No Spurious Local Minimum](https://mlsanity.com/paper/1605.07272/) (2016)
- [Global Optimality of Local Search for Low Rank Matrix Recovery](https://mlsanity.com/paper/1605.07221/) (2016)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [Global optimization of Lipschitz functions](https://mlsanity.com/paper/1703.02628/) (2017)
- [Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach](https://mlsanity.com/paper/1609.03240/) (2016)
- [HybridNet: Integrating Model-based and Data-driven Learning to Predict Evolution of Dynamical Systems](https://mlsanity.com/paper/1806.07439/) (2018)
- [Structured Low-Rank Matrix Factorization: Global Optimality, Algorithms, and Applications](https://mlsanity.com/paper/1708.07850/) (2017)
- [Unsupervised Representation Learning of Structured Radio Communication Signals](https://mlsanity.com/paper/1604.07078/) (2016)
- [Convex relaxations of structured matrix factorizations](https://mlsanity.com/paper/1309.3117/) (2013)
- [Opening the black box of deep learning](https://mlsanity.com/paper/1805.08355/) (2018)
- [Enabling Simulation-Based Optimization Through Machine Learning: A Case Study on Antenna Design](https://mlsanity.com/paper/1908.11225/) (2019)

## Built on by (most cited first, 1 of 1)

- [Wave Physics-informed Matrix Factorizations](https://mlsanity.com/paper/2312.13584/) (2023)

## Abstract (arXiv)

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can 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 satisfies wave equation constraints. Although our proposed formulation is non-convex, we prove that our model can be efficiently solved to global optimality in polynomial time. We demonstrate the benefits of our work by applications in structural health monitoring, where prior work has attempted to solve this problem using sparse dictionary learning approaches that do not come with any theoretical guarantees regarding convergence to global optimality and employ heuristics to capture desired physical constraints.