Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems

Rafael Anderka, Marc Peter Deisenroth, So Takao
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:50-76, 2024.

Abstract

Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state estimation, however can have difficulty learning the parameters accurately. On the other hand, machine learning based approaches can naturally learn the state and parameters, but their applicability can be limited, or produce uncertainties that are hard to interpret. Inspired by the Integrated Nested Laplace Approximation (INLA) method in spatial statistics, we propose an alternative approach to DA based on iteratively linearising the dynamical model. This produces a Gaussian Markov random field at each iteration, enabling one to use INLA to infer the state and parameters. Our approach can be used for arbitrary nonlinear systems, while retaining interpretability, and is furthermore demonstrated to outperform existing methods on the DA task. By providing a more nuanced approach to handling nonlinear PDE priors, our methodology offers improved accuracy and robustness in predictions, especially where data sparsity is prevalent.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-anderka24a, title = {Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems}, author = {Anderka, Rafael and Deisenroth, Marc Peter and Takao, So}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {50--76}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/anderka24a/anderka24a.pdf}, url = {https://proceedings.mlr.press/v244/anderka24a.html}, abstract = {Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state estimation, however can have difficulty learning the parameters accurately. On the other hand, machine learning based approaches can naturally learn the state and parameters, but their applicability can be limited, or produce uncertainties that are hard to interpret. Inspired by the Integrated Nested Laplace Approximation (INLA) method in spatial statistics, we propose an alternative approach to DA based on iteratively linearising the dynamical model. This produces a Gaussian Markov random field at each iteration, enabling one to use INLA to infer the state and parameters. Our approach can be used for arbitrary nonlinear systems, while retaining interpretability, and is furthermore demonstrated to outperform existing methods on the DA task. By providing a more nuanced approach to handling nonlinear PDE priors, our methodology offers improved accuracy and robustness in predictions, especially where data sparsity is prevalent.} }
Endnote
%0 Conference Paper %T Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems %A Rafael Anderka %A Marc Peter Deisenroth %A So Takao %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-anderka24a %I PMLR %P 50--76 %U https://proceedings.mlr.press/v244/anderka24a.html %V 244 %X Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state estimation, however can have difficulty learning the parameters accurately. On the other hand, machine learning based approaches can naturally learn the state and parameters, but their applicability can be limited, or produce uncertainties that are hard to interpret. Inspired by the Integrated Nested Laplace Approximation (INLA) method in spatial statistics, we propose an alternative approach to DA based on iteratively linearising the dynamical model. This produces a Gaussian Markov random field at each iteration, enabling one to use INLA to infer the state and parameters. Our approach can be used for arbitrary nonlinear systems, while retaining interpretability, and is furthermore demonstrated to outperform existing methods on the DA task. By providing a more nuanced approach to handling nonlinear PDE priors, our methodology offers improved accuracy and robustness in predictions, especially where data sparsity is prevalent.
APA
Anderka, R., Deisenroth, M.P. & Takao, S.. (2024). Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:50-76 Available from https://proceedings.mlr.press/v244/anderka24a.html.

Related Material