Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs

Wenk, Philippe; Gotovos, Alkis; Bauer, Sebastian; Gorbach, Nico S.; Krause, Andreas; Buhmann, Joachim M.

doi:10.48550/arxiv.1804.04378

Cited by 4 publications

(7 citation statements)

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“…50 equidistant points per sequence were "observed". Following the previous work in ODE inference of parameters and states [13,35], we generated a benchmark trajectory using parameters α 1−4 = [2,1,4,1] (excluded from training). During test phase, we used 50 first points for system identification (domain recognition), and other 150 to evaluate long-term prediction.…”

Section: Experiments -Learning Ode Dynamicsmentioning

confidence: 99%

Disentangled State Space Representations

Miladinović¹,

Gondal²,

Schölkopf³

et al. 2019

Preprint

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Sequential data often originates from diverse domains across which statistical regularities and domain specifics exist. To specifically learn cross-domain sequence representations, we introduce disentangled state space models (DSSM) -a class of SSM in which domain-invariant state dynamics is explicitly disentangled from domain-specific information governing that dynamics. We analyze how such separation can improve knowledge transfer to new domains, and enable robust prediction, sequence manipulation and domain characterization. We furthermore propose an unsupervised VAE-based training procedure to implement DSSM in form of Bayesian filters. In our experiments, we applied VAE-DSSM framework to achieve competitive performance in online ODE system identification and regression across experimental settings, and controlled generation and prediction of bouncing ball video sequences across varying gravitational influences.1 IID -independent and identically distributed.

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Section: Experiments -Learning Ode Dynamicsmentioning

confidence: 99%

Disentangled State Space Representations

Miladinović¹,

Gondal²,

Schölkopf³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Out of the three comparison algorithms we chose, AGM (Dondelinger et al 2013) and FGPGM (Wenk et al 2018) rely on Gaussian processes and MCMC inference, while RKG3 (Niu et al 2016) chooses a frequentist, kernelregression-based approach. For all comparisons, implementations provided by the respective authors are used.…”

Section: State and Parameter Inferencementioning

confidence: 99%

“…Lawrence 2009;Dondelinger et al 2013;Gorbach, Bauer, and Buhmann 2017) or an additional Dirac delta function forcing equality(Wenk et al 2018).The resulting, unified generative model is then used to approximate the posterior of x and θ through Bayesian inference techniques, e.g. MCMC(Calderhead, Girolami, and Lawrence 2009;Dondelinger et al 2013;Wenk et al 2018) or variational mean field(Gorbach, Bauer, and Buhmann …”

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confidence: 99%

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

Wenk¹,

Abbati²,

Osborne³

et al. 2019

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Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian processes and leverage it to build a computationally and data efficient algorithm for state and parameter inference. In an extensive set of experiments, our approach outperforms the current state of the art for parameter inference both in terms of accuracy and computational cost. It also shows promising results for the much more challenging problem of model selection.

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“…The main challenge is then to combine these two distributions, such that more information about y can guide towards better parameter estimates θ. For this purpose, Calderhead et al (2009) propose a product of experts heuristics that was accepted and reused until recently Wenk et al (2018) showed that this heuristic leads to severe theoretical issues. They instead propose an alternative graphical model, forcing equality between the data based and the ODE based model save for a Gaussian distributed slack variable.…”

Section: Deterministic Ode Casementioning

confidence: 99%

“…As shown e.g. in the appendix of Wenk et al (2018), the prior defined in equation ( 11) automatically induces a GP prior on the conditional derivatives of z. Defining…”

Section: Data-based Modelmentioning

confidence: 99%

AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs

Abbati,

Wenk,

Osborne

et al. 2019

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Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.

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Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs

Cited by 4 publications

References 0 publications

Disentangled State Space Representations

Disentangled State Space Representations

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

AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs

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