# Sparsifying priors for Bayesian uncertainty quantification in model discovery

@article{Hirsh2021SparsifyingPF, title={Sparsifying priors for Bayesian uncertainty quantification in model discovery}, author={Seth M. Hirsh and David A. Barajas-Solano and J. Nathan Kutz}, journal={Royal Society Open Science}, year={2021}, volume={9} }

We propose a probabilistic model discovery method for identifying ordinary differential equations governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy) framework, where models are expressed as sparse linear combinations of pre-specified candidate functions. Promoting parsimony through sparsity leads to interpretable models that generalize to unknown data. Instead of targeting point estimates of the SINDy coefficients…

## 16 Citations

### Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants

- Computer ScienceArXiv
- 2022

The Bayesian SINDy autoencoder achieves better physics discovery with lower data and fewer training epochs, along with valid uncertainty quantiﬁcation suggested by the experimental studies, and is applied to real video data.

### Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

- Computer ScienceProceedings of the Royal Society A
- 2022

This work leverages the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of the nonlinear dynamics (SINDy) algorithm and shows that ensemble statistics from E-Sindy can be exploited for active learning and improved model predictive control.

### Bayesian operator inference for data-driven reduced-order modeling

- Mathematics, Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2022

### A Toolkit for Data-Driven Discovery of Governing Equations in High-Noise Regimes

- Computer ScienceIEEE Access
- 2022

An extensive toolkit of methods for circumventing the deleterious effects of noise in the context of the SINDy framework, and a technique that uses linear dependencies among functionals to transform a discovered model into an equivalent form that is closest to the true model, enabling more accurate assessment of a discoveredmodel’s correctness.

### Approximating a Laplacian Prior for Joint State and Model Estimation within an UKF

- MathematicsArXiv
- 2022

: A major challenge in state estimation with model-based observers are low-quality models that lack of relevant dynamics. We address this issue by simultaneously estimating the system’s states and…

### Automated Learning of Interpretable Models with Quantified Uncertainty

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2023

### A Bayesian Approach for Data-Driven Dynamic Equation Discovery

- Computer ScienceJournal of Agricultural, Biological and Environmental Statistics
- 2022

A Bayesian data-driven approach to nonlinear dynamic equation discovery is presented, which can accommodate measurement noise and missing data, which are common in complex nonlinear systems, and accounts for model parameter uncertainty.

### Equation discovery from data: promise and pitfalls, from rabbits to Mars

- MathematicsNew Zealand Journal of Mathematics
- 2022

The problem of equation discovery seeks to reconstruct the underlying dynamics of a time-varying system from observations of the system, and moreover to do so in an instructive way such that we may…

### A Bayesian Approach for Spatio-Temporal Data-Driven Dynamic Equation Discovery

- Computer Science
- 2022

A Bayesian approach to data-driven discovery of non-linear spatio-temporal dynamic equations is developed that can accommodate measurement noise and missing data, both of which are common in real-world data, and accounts for parameter uncertainty.

### Data-driven discovery of governing equations for coarse-grained heterogeneous network dynamics

- Computer Science
- 2022

This work uses data-driven model discovery methods to determine the governing equations for the emergent behavior of heterogeneous networked dynamical systems whose collective behaviour approaches a limit cycle, and provides a numerical exploration of the dimension of collective network dynamics as a function of several network parameters.

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