Automated adaptive inference of phenomenological dynamical models

By Bryan C. Daniels, Ilya Nemenman. 2015

208 citations recorded by the source corpus.

Dynamics of complex systems is often driven by large and intricate networks of microscopic interactions, whose sheer size obfuscates understanding. With limited experimental data, many parameters of such dynamics are unknown, and thus detailed, mechanistic models risk overfitting and making faulty predictions. At the other extreme, simple ad hoc models often miss defining features of the underlying systems. Here we develop an approach that instead constructs phenomenological, coarse-grained models of network dynamics that automatically adapt their complexity to the available data. Such adaptive models produce accurate predictions even when microscopic details are unknown. The approach is computationally tractable, even for a relatively large number of dynamical variables. Using simulated data, it correctly infers the phase space structure for planetary motion, avoids overfitting in a biological signalling system and produces accurate predictions for yeast glycolysis with tens of data points and over half of the interacting species unobserved. Mechanistic modelling of dynamical phenomena with many degrees of freedom runs the risk of overfitting and making faulty predictions, whereas ad hocmodels may miss defining features. Here the authors develop an approach to construct dynamical models that adapt their complexity to the amount of available data.

Subfields: Molecular Biology

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Citations in the corpus

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, methodology): “…behavior [11], automated inference of dynamics [12, 13, 14], normal form identiﬁcation in climate [15], nonlinear Laplacian spectral analysis [16], modeling emergent behavior [11], Koopman analysis [17, 18, 19, 20], automated inference of dynamics [12, 13, 14], and symbolic regression [21, 22].”
Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, background): “IEEE Trans Inf Theory 53(12):4655–4666.”
Learning Powerful Policies by Using Consistent Dynamics Model (2019, background): “On the other hand, there’s enough evidence that humans learn the environment dynamics not just by observing the environment but also by interacting with the environment (Cook et al., 2011; Daniels & Nemenman, 2015).”
Data-driven discovery of coordinates and governing equations (2019, background): “Numerous recent approaches leverage machine learning to identify dynamical systems models from data [19–26], with many using neural networks to model time-series data [18, 27–38].”
Deep learning of physical laws from scarce data (2020, background): “s 6:8133. 5. Brunton SL, Proctor JL, Kutz JN (2016) Discovering governing equations from data by sparse identication of nonlinear dynamical systems. Proceedings of the National Academy of Sciences 113(15):39323937. 6.Rudy SH, Brunton SL, Proctor JL, Kutz JN (2017) Data-driven discovery of partial di”
Learning Symbolic Physics with Graph Networks (2019, background): “Some other interesting approaches for learning low-dimensional general dynamical models include Packard et al. [1980], Daniels and Nemenman [2015], and Jaques et al. [2019].”
Explainable Machine Learning for Scientific Insights and Discoveries (2019, methodology): “[2019] use their ML algorithm ‘Sir Isaac’ [Daniels and Nemenman, 2015] to infer a dynamical model of biological time series data to understand and predict dynamics of worm behavior.”
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020, background): “…Koopman theory [6–9], nonlinear autoregressive models [10, 11], neural networks [12–20], Gaussian process regression [21, 22], nonlinear Laplacian spectral analysis [23], diffusion maps [24], genetic programming [25–27], and sparse regression [28, 29], to highlight some of the recent developments.”