ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systems

Wenk, Philippe; Abbati, Gabriele; Osborne, Michael A.; Schölkopf, Bernhard; Krause, Andreas; Bauer, Stefan

doi:10.1609/aaai.v34i04.6106

Cited by 16 publications

(26 citation statements)

References 11 publications

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“…It captures enzyme binding and unbinding with substrate and subsequent irreversible formation of the product [29]. The third system used in the study is the Lotka-Volterra system originally proposed in [33] and used as benchmark to study algorithms of parameter estimations such as in [34,35]. The problem describes the dynamics of two states (reported in SI), that was used to simulate data.…”

Section: Enzyme Kineticsmentioning

confidence: 99%

See 1 more Smart Citation

Functional-Hybrid modeling through automated adaptive symbolic regression for interpretable mathematical expressions

Narayanan

Bournazou²,

Gosálbez

et al. 2022

Chemical Engineering Journal

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Mathematical models used for the representation of (bio)-chemical processes can be grouped into two broad paradigms: white-box or mechanistic models, completely based on knowledge or black-box data-driven models based on patterns observed in data. However, in the past twodecade, hybrid modeling that explores the synergy between the two paradigms has emerged as a pragmatic compromise. The data-driven part of these have been largely based on conventional machine learning algorithm (e.g., artificial neural network, support vector regression), which prevents interpretability of the finally learnt model by the domain-experts.In this work we present a novel hybrid modeling framework, the Functional-Hybrid model, that uses the ranked domain-specific functional beliefs together with symbolic regression to develop dynamic models. We demonstrate the successful implementation of these hybrid models for four benchmark systems and a microbial fermentation reactor, all of which are systems of (bio)chemical relevance. We also demonstrate that compared to a similar implementation with the conventional ANN, the performance of Functional-Hybrid model is at least two times better in interpolation and extrapolation. Additionally, the proposed framework can learn the dynamics in 50% lower number of experiments. This improved performance can be attributed to the structure imposed by the functional transformations introduced in the Functional-Hybrid model.

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Section: Enzyme Kineticsmentioning

confidence: 99%

“…The FHN models, is a system proposed by FitzHugh [37] and Nagumo [38] for modeling giant squid neurons and often used to test parameter estimation robustness for spiky dynamics [34,35]. The dynamics is represented by a system of two ordinary differential equation (ODE), reported in SI.…”

Section: Fitzhugh-nagumo (Fhn) Modelmentioning

confidence: 99%

Functional-Hybrid modeling through automated adaptive symbolic regression for interpretable mathematical expressions

Narayanan

Bournazou²,

Gosálbez

et al. 2022

Chemical Engineering Journal

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“…An open question is to which extend analytical structured models can be combined with numerical integration schemes such that training of such a combined model is done solely on trajectory data. Recent works discuss how to approximate ODEs using GPs [41,104,108] and NNs [17,63] as well as solve initial‐value problems using GPs [82,83].…”

Section: Conclusion and Future Outlookmentioning

confidence: 99%

Structured learning of rigid‐body dynamics: A survey and unified view from a robotics perspective

Geist

Trimpe

2021

GAMM-Mitteilungen

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Accurate models of mechanical system dynamics are often critical for model‐based control and reinforcement learning. Fully data‐driven dynamics models promise to ease the process of modeling and analysis, but require considerable amounts of data for training and often do not generalize well to unseen parts of the state space. Combining data‐driven modeling with prior analytical knowledge is an attractive alternative as the inclusion of structural knowledge into a regression model improves the model's data efficiency and physical integrity. In this article, we survey supervised regression models that combine rigid‐body mechanics with data‐driven modeling techniques. We analyze the different latent functions (such as kinetic energy or dissipative forces) and operators (such as differential operators and projection matrices) underlying common descriptions of rigid‐body mechanics. Based on this analysis, we provide a unified view on the combination of data‐driven regression models, such as neural networks and Gaussian processes, with analytical model priors. Furthermore, we review and discuss key techniques for designing structured models such as automatic differentiation.

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“…The third system used in the study is the Lotka-Volterra system originally proposed in [33] and used as benchmark to study algorithms of parameter estimations such as in [34,35]. The problem describes the dynamics of two states (reported in SI), that was used to simulate data.…”

Section: Lotka-volterramentioning

confidence: 99%

“…20 experiments are planned using a Latin hypercube sampling method [36] for the initial The FHN models, is a system proposed by FitzHugh [37] and Nagumo [38] for modeling giant squid neurons and often used to test parameter estimation robustness for spiky dynamics [34,35]. Time profiles are simulated in the time interval of [0, 10] units and measurements perturbed with 10% gaussian noise at 11 equally space time points are used for modeling.…”

Section: Lotka-volterramentioning

confidence: 99%

Functional-Hybrid Modeling through automated adaptive symbolic regression for interpretable mathematical expressions

Narayanan¹,

Bournazou²,

Guillén‐Gosálbez³

et al. 2021

Preprint

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Mathematical models used for the representation of (bio)-chemical processes can be grouped into two broad paradigms: white-box or mechanistic models, completely based on knowledge or black-box data-driven models based on patterns observed in data. However, in the past two-decade, hybrid modeling that explores the synergy between the two paradigms has emerged as a pragmatic compromise. The data-driven part of these have been largely based on conventional machine learning algorithm (e.g., artificial neural network, support vector regression), which prevents interpretability of the finally learnt model by the domain-experts. In this work we present a novel hybrid modeling framework, the Functional-Hybrid model, that uses the ranked domain-specific functional beliefs together with symbolic regression to develop dynamic models. We demonstrate the successful implementation of these hybrid models for four benchmark systems and a microbial fermentation reactor, all of which are systems of (bio)chemical relevance. We also demonstrate that compared to a similar implementation with the conventional ANN, the performance of Functional-Hybrid model is at least two times better in interpolation and extrapolation. Additionally, the proposed framework can learn the dynamics in 50% lower number of experiments. This improved performance can be attributed to the structure imposed by the functional transformations introduced in the Functional-Hybrid model.

show abstract

ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systems

Cited by 16 publications

References 11 publications

Functional-Hybrid modeling through automated adaptive symbolic regression for interpretable mathematical expressions

Functional-Hybrid modeling through automated adaptive symbolic regression for interpretable mathematical expressions

Structured learning of rigid‐body dynamics: A survey and unified view from a robotics perspective

Functional-Hybrid Modeling through automated adaptive symbolic regression for interpretable mathematical expressions

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