# Learning governing physics from output only measurements

arXiv: https://arxiv.org/abs/2208.05609 · HTML: https://mlsanity.com/paper/2208.05609/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 50 references that are in the map.
- First posted on arXiv 11 Aug 2022.

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

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression](https://mlsanity.com/paper/2012.01937/) (2020)
- [Simulation free reliability analysis: A physics-informed deep learning based approach](https://mlsanity.com/paper/2005.01302/) (2020)
- [Bayesian equation selection on sparse data for discovery of stochastic dynamical systems](https://mlsanity.com/paper/2101.04437/) (2021)

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

- [Discovering stochastic partial differential equations from limited data using variational Bayes inference](https://mlsanity.com/paper/2306.15873/) (2023)

## Abstract (arXiv)

Extracting governing physics from data is a key challenge in many areas of science and technology. The existing techniques for equations discovery are dependent on both input and state measurements; however, in practice, we only have access to the output measurements only. We here propose a novel framework for learning governing physics of dynamical system from output only measurements; this essentially transfers the physics discovery problem from the deterministic to the stochastic domain. The proposed approach models the input as a stochastic process and blends concepts of stochastic calculus, sparse learning algorithms, and Bayesian statistics. In particular, we combine sparsity promoting spike and slab prior, Bayes law, and Euler Maruyama scheme to identify the governing physics from data. The resulting model is highly efficient and works with sparse, noisy, and incomplete output measurements. The efficacy and robustness of the proposed approach is illustrated on several numerical examples involving both complete and partial state measurements. The results obtained indicate the potential of the proposed approach in identifying governing physics from output only measurement.