Learning (from) the errors of a systems biology model

Engelhardt, Benjamin; Fröhlich, Holger; Kschischo, Maik

doi:10.1038/srep20772

Cited by 26 publications

(43 citation statements)

References 31 publications

(55 reference statements)

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“…Reconstructing unknown inputs from outputs of open systems is useful in many settings. For modellers, the inputs provide important information about model errors and cues for model improvement or extension [12,13,34]. In biomedical systems, the unknown inputs can represent unmodelled environmental or physiological inputs, which might be interesting for the design of devices or measurement strategies.…”

Section: A Summary and Significance Of The Resultsmentioning

confidence: 99%

“…In electrical or secure networks, the unknown inputs could be attack signals, which need to be reconstructed and then mitigated. Unknown inputs can also be useful for improved state estimation [12][13][14] and data assimilation [53,77]. Thus, from the viewpoint of modellers and engineers, invertibility is a desirable prop- Table I with three different node selection schemes as a function of the number of inputs.…”

Section: A Summary and Significance Of The Resultsmentioning

confidence: 99%

“…There are several algorithms for estimating the unknown input w from measurement data, ranging from feedback controllers via modifications of the nonlinear Kalman filter to moving horizon estimation [9][10][11][12][13][14][15]. We can not discuss all these approaches here, but it is instructive to briefly discuss a simple version of the optimisation based approach, where an error functional J[w] is minimised with respect to w(t).…”

Section: Regularisation Of Unknown Inputsmentioning

confidence: 99%

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Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems

et al. 2019

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Despite recent progress in our understanding of complex dynamic networks, it remains challenging to devise sufficiently accurate models to observe, control or predict the state of real systems in biology, economics or other fields. A largely overlooked fact is that these systems are typically open and receive unknown inputs from their environment. A further fundamental obstacle are structural model errors caused by insufficient or inaccurate knowledge about the quantitative interactions in the real system.Here, we show that unknown inputs to open systems and model errors can be treated under the common framework of invertibility, which is a requirement for reconstructing these disturbances from output measurements. By exploiting the fact that invertibility can be decided from the influence graph of the system, we analyse the relationship between structural network properties and invertibility under different realistic scenarios. We show that sparsely connected scale free networks are the most difficult to invert. We introduce a new sensor node placement algorithm to select a minimum set of measurement positions in the network required for invertibility. This algorithm facilitates optimal experimental design for the reconstruction of inputs or model errors from output measurements. Our results have both fundamental and practical implications for nonlinear systems analysis, modelling and design.

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Section: A Summary and Significance Of The Resultsmentioning

confidence: 99%

Section: A Summary and Significance Of The Resultsmentioning

confidence: 99%

Section: Regularisation Of Unknown Inputsmentioning

confidence: 99%

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Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems

et al. 2019

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“…In this context, extended Kalman filtering [10], unscented Kalman filtering [11], and ensemble Kalman methods [12] have been applied as well. In addition, different methods have also been developed to address the issue of hidden variables and dynamics [13,14].…”

Section: Introductionmentioning

confidence: 99%

Systems biology informed deep learning for inferring parameters and hidden dynamics

Yazdani

Raissi

et al. 2019

Preprint

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Mathematical models of biological reactions at the system-level lead to a large set of ordinary differential equations with many unknown parameters that need to be inferred using relatively few experimental measurements. Having a reliable and robust algorithm for parameter inference and prediction of the hidden dynamics has been one of the core subjects in systems biology, and is the focus of this study. We have developed a novel systems-biology-informed deep learning algorithm that incorporates the system of ordinary differential equations into the neural networks. Enforcing these equations effectively adds constraints to the optimization procedure that manifests itself as an imposed structure on the observational data. Using few scattered and noisy measurements, we are able to infer the dynamics of unobserved species, systematic forcing and the unknown model parameters. We have successfully tested the algorithm for three different benchmark problems. Author summaryThe dynamics of systems biological processes are usually modeled using ordinary differential equations (ODEs), which introduce various unknown parameters that need to be estimated efficiently from noisy measurements of concentration for a few species only. In this work, we present a novel "systems-informed neural network" to infer the dynamics of experimentally unobserved species as well as the unknown parameters in the system of equations. By incorporating the system of ODEs into the neural networks we effectively add constraints to the optimization algorithm, which makes the method robust to measurement noise and few scattered observations. 2 holistic approach to deciphering the complexity of biological systems. To understand 3 the biological systems, we must understand the structures of the systems (both their 4 components and structural relationships), and their dynamics [1]. The dynamics of 5 systems biological processes are usually modeled using ordinary differential equations 6 (ODEs) that describe the time evolution of chemical and molecular species 7 concentrations. Once the pathway structure of chemical reactions is known, the 8 corresponding equations can be derived using widely accepted kinetic laws, such as the 9 law of mass action or the Michaelis-Menten kinetics [2]. 10 November 28, 2019 1/15Most system-level biological models introduce various unknown parameters, which 11 need to be estimated efficiently. Thus, the central challenge in computational modeling 12 of these systems could be the prediction of model parameters such as rate constants or 13 initial concentrations, and model trajectories such as time evolution of experimentally 14 unobserved concentrations. Due to the importance of parameter estimation, a lot of 15 attention has been given to this problem in the systems biology community. A lot of 16 research has been conducted on the applications of several optimization techniques, such 17 as linear and nonlinear least-squares fitting [3], genetic algorithms [4], and evolutionary 18 computation [5]. Considerable interest has a...

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“…This is in contrast to traditional modelling approaches, where alternative hypotheses and assessments of uncertainty are managed only in an ad hoc process taking place implicitly in the brains of the modellers and their collaborating expert biologists. Furthermore, acknowledging uncertainty and integrating it during the model building phase allows making predictions that are associated with specified confidence intervals, which can guide further experimentation[48,49].…”

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confidence: 99%

Respectful Modeling: Addressing Uncertainty in Dynamic System Models for Molecular Biology

Tsigkinopoulou

Baker

Breitling

2017

Trends in Biotechnology

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Although there is still some skepticism in the biological community regarding the value and significance of quantitative computational modeling, important steps are continually being taken to enhance its accessibility and predictive power. We view these developments as essential components of an emerging 'respectful modeling' framework which has two key aims: (i) respecting the models themselves and facilitating the reproduction and update of modeling results by other scientists, and (ii) respecting the predictions of the models and rigorously quantifying the confidence associated with the modeling results. This respectful attitude will guide the design of higher-quality models and facilitate the use of models in modern applications such as engineering and manipulating microbial metabolism by synthetic biology.

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Learning (from) the errors of a systems biology model

Cited by 26 publications

References 31 publications

Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems

Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems

Systems biology informed deep learning for inferring parameters and hidden dynamics

Respectful Modeling: Addressing Uncertainty in Dynamic System Models for Molecular Biology

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