# Symbolic system identification

March 14, 2023 — September 22, 2024

Symbolic regression + system identification = symbolic system identification.

There is some nifty work in learning approximations to physics, like the *SINDy* method. The trick seems to be sparse regression plus interpretable features; so we might recover the equations of motion for a system from data, discover the laws of gravity from watching apples fall, that kind of thing. Brunton, Proctor, and Kutz (2016) is the canonical modern reference for this, although see Schmidt and Lipson (2009) for a primordial reference before autodifferentiation was a mainstream. It’s hard to imagine scaling this up to big things like large image sensor arrays and other such weakly structured input. I could be wrong.

## 1 Bayesian

Tricky! it seems to be that the sparse Bayes model selection problem is no easier when we mix symbolic regression in (Champneys and Rogers 2024; Fung, Fasel, and Juniper 2024; Hirsh, Barajas-Solano, and Kutz 2022; More et al. 2023).

## 2 Weak form in

Messenger et al. (2024):

The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the weak form can play a critical role. In particular, we highlight several recent advances in weak form versions of equation learning, parameter estimation, and coarse graining, which offer surprising noise robustness, accuracy, and computational efficiency.

## 3 Tools

## 4 References

*Proceedings of Mathematical and Scientific Machine Learning*.

*Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control*.

*Proceedings of the National Academy of Sciences*.

*Royal Society Open Science*.

*Physica D: Nonlinear Phenomena*.

*Science*.

*Advances in Neural Information Processing Systems*.