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, Sebastian

doi:10.48550/arxiv.1902.06278

Cited by 2 publications

(3 citation statements)

References 11 publications

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“…Moreover, they usually perform inference on each sequence separately. Many machine learning methods have been proposed for this task, for example using reproducing kernel Hilbert space methods (González et al, 2014) and Gaussian Processes (Dondelinger et al, 2013;Barber & Wang, 2014;Gorbach et al, 2017), Fast Gaussian Process Based Gradient Matching (FGPGM, Wenk et al (2018)) and recent follow up work (Wenk et al, 2019). In general these methods assume that the given signal is a the latent signal with independent additive noise.…”

Section: Related Workmentioning

confidence: 99%

“…Method ODE function Emission function θ f and Z identification X extrapolation LSTM (Graves, 2013) not required learned Latent-ODE (Chen et al, 2018) not required learned HNN (Greydanus et al, 2019) can be used learned DSSM (Miladinović et al, 2019) not required learned NbedDyn (Ouala et al, 2019) not required partially given ODIN (Wenk et al, 2019) required given UKF (Wan & Van Der Merwe, 2000) required given GOKU-net required learned…”

Section: Generative Modelmentioning

confidence: 99%

See 1 more Smart Citation

Generative ODE modeling with known unknowns

Linial

Ravid

Eytan

et al. 2021

Proceedings of the Conference on Health, Inference, and Learning

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In several crucial applications, domain knowledge is encoded by a system of ordinary differential equations (ODE). A motivating example is intensive care unit patients: The dynamics of some vital physiological variables such as heart rate, blood pressure and arterial compliance can be approximately described by a known system of ODEs. Typically, some of the ODE variables are directly observed while some are unobserved, and in addition many other variables are observed but not modeled by the ODE, for example body temperature. Importantly, the unobserved ODE variables are "known-unknowns": We know they exist and their functional dynamics, but cannot measure them directly, nor do we know the function tying them to all observed measurements. Estimating these known-unknowns is often highly valuable to physicians. Under this scenario we wish to: (i) learn the static parameters of the ODE generating each observed time-series (ii) infer the dynamic sequence of all ODE variables including the known-unknowns, and (iii) extrapolate the future of the ODE variables and the observations of the time-series. We address this task with a variational autoencoder incorporating the known ODE function, called GOKU-net for Generative ODE modeling with Known Unknowns. We test our method on videos of pendulums with unknown length, and a model of the cardiovascular system.

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Section: Related Workmentioning

confidence: 99%

Section: Generative Modelmentioning

confidence: 99%

Generative ODE modeling with known unknowns

Linial

Ravid

Eytan

et al. 2021

Proceedings of the Conference on Health, Inference, and Learning

View full text Add to dashboard Cite

show abstract

“…Using a differentiable kernel k φ we learn D independent GPs with hyperparameters φ l on observations D T l = {(t i , y l (t i )} i=1,...,N , one for each component of our initial trajectory. Following Wenk et al [Wen+19], we obtain the distribution of the time derivatives as…”

Section: Differentiating Gaussian Processesmentioning

confidence: 99%

Learning ODE Models with Qualitative Structure Using Gaussian Processes

Ridderbusch,

Offen,

Ober-Blöbaum

et al. 2020

Preprint

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Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts, explicit data collection is expensive and learning algorithms must be dataefficient to be feasible. This suggests using additional qualitative information about the system, which is often available from prior experiments or domain knowledge. In this paper, we propose an approach to learning the vector field of differential equations using sparse Gaussian Processes that allows us to combine data and additional structural information, like Lie Group symmetries and fixed points, as well as known input transformations. We show that this combination improves extrapolation performance and longterm behaviour significantly, while also reducing the computational cost.

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

Cited by 2 publications

References 11 publications

Generative ODE modeling with known unknowns

Generative ODE modeling with known unknowns

Learning ODE Models with Qualitative Structure Using Gaussian Processes

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