Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data

Bhouri, Mohamed Aziz; Perdikaris, Paris

doi:10.1098/rsta.2021.0201

Cited by 13 publications

(9 citation statements)

References 34 publications

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“…In Eq. (29b) the same strategy is applied for p l , l ∈ [10, 11, 12], and p m , m ∈ [13, …, 16]. That is: Choosing j = 4, k = 7, l = 11, m = 14, the resulting structurally identifiable model is: where ∗ denotes a reparameterized parameter.…”

Section: Resultsmentioning

confidence: 99%

Distilling identifiable and interpretable dynamic models from biological data

Banga

Massonis

Villaverde

2023

Preprint

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Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam's razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable.

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Section: Resultsmentioning

confidence: 99%

Distilling identifiable and interpretable dynamic models from biological data

Banga

Massonis

Villaverde

2023

Preprint

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“…It is worth mentioning that there are literature [40][41][42] on the more general topic of Bayesian NODE (similar to the MLP case shown above). However, B-CRNN is still valuable since it is dedicated to the modeling of chemical reaction systems with domain-specific physical laws embedded, eventually leading to better interpretability and tighter uncertainty bounds.…”

Section: The Importance Of Embedding Physical Lawsmentioning

confidence: 99%

Bayesian chemical reaction neural network for autonomous kinetic uncertainty quantification

Chen

Koenig

et al. 2023

Phys. Chem. Chem. Phys.

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“…Most existing data-driven systems identification techniques heavily depend on the quality of the available observations and learning dynamics from noisy and irregular observations is still a challenge. Bhouri & Perdikaris [ 191 ] present a machine learning framework (GPNODE) for Bayesian model discovery from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling and Gaussian Process priors over the observed system states.…”

Section: The General Content Of the Issuementioning

confidence: 99%

Data-driven prediction in dynamical systems: recent developments

Ghadami

Epureanu

2022

Phil. Trans. R. Soc. A.

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In recent years, we have witnessed a significant shift toward ever-more complex and ever-larger-scale systems in the majority of the grand societal challenges tackled in applied sciences. The need to comprehend and predict the dynamics of complex systems have spurred developments in large-scale simulations and a multitude of methods across several disciplines. The goals of understanding and prediction in complex dynamical systems, however, have been hindered by high dimensionality, complexity and chaotic behaviours. Recent advances in data-driven techniques and machine-learning approaches have revolutionized how we model and analyse complex systems. The integration of these techniques with dynamical systems theory opens up opportunities to tackle previously unattainable challenges in modelling and prediction of dynamical systems. While data-driven prediction methods have made great strides in recent years, it is still necessary to develop new techniques to improve their applicability to a wider range of complex systems in science and engineering. This focus issue shares recent developments in the field of complex dynamical systems with emphasis on data-driven, data-assisted and artificial intelligence-based discovery of dynamical systems. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

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Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data

Cited by 13 publications

References 34 publications

Distilling identifiable and interpretable dynamic models from biological data

Distilling identifiable and interpretable dynamic models from biological data

Bayesian chemical reaction neural network for autonomous kinetic uncertainty quantification

Data-driven prediction in dynamical systems: recent developments

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