# Discovery of Physics and Characterization of Microstructure from Data with Bayesian Hidden Physics Models

arXiv: https://arxiv.org/abs/2103.07502 · HTML: https://mlsanity.com/paper/2103.07502/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 12 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)
- [Bayesian Hidden Physics Models: Uncertainty Quantification for Discovery of Nonlinear Partial Differential Operators from Data](https://mlsanity.com/paper/2006.04228/) (2020)

## Abstract (arXiv)

There has been a surge in the interest of using machine learning techniques to assist in the scientific process of formulating knowledge to explain observational data. We demonstrate the use of Bayesian Hidden Physics Models to first uncover the physics governing the propagation of acoustic impulses in metallic specimens using data obtained from a pristine sample. We then use the learned physics to characterize the microstructure of a separate specimen with a surface-breaking crack flaw. Remarkably, we find that the physics learned from the first specimen allows us to understand the backscattering observed in the latter sample, a qualitative feature that is wholly absent from the specimen from which the physics were inferred. The backscattering is explained through inhomogeneities of a latent spatial field that can be recognized as the speed of sound in the media.