Automated adaptive inference of phenomenological dynamical models

Abstract

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.

Sparse model selection via integral terms

“…In [19], the authors propose a method for learning dynamical models from an appropriate selection of trial functions. The trial functions that are used form a complete basis for smooth dynamics.…”

Reverse-engineering biological networks from large data sets

“…In contrast to this pessimistic view, one may argue that every level of description requires its own proper degrees of freedom for efficient representation [80,85,86], and that the distinction between mechanistic and effective networks is not that clear-cut.…”

“…(4) below: since this matrix is not constrained to be symmetric, couplings between two species can differ in the forward and backward directions. For continuous activation variables {x i }, many popular models can be subsumed as special cases of the general form (though see [86,224] for alternative forms):…”

“…To write down such a system, one needs to first have in mind a particular quantitative form for a dynamical law, according to which activations will be presumed to interact. One then fits the model parameters, typically with some optimization or statistical learning technique that takes time series data as input, and reports the learned values as the weights for the corresponding connections, sometimes adding additional, unobserved, hidden variables in the process [86].…”

Numerical parameter space compression and its application to microtubule dynamic instability

“…More recently, the Manifold Boundary Approximation Method has been developed to fit data while minimizing dimensionality [12]; similarly, Fitness Based Asymptotic Parameter Reduction can extract the "core working module" of a model [13]. Other machine learning approaches can develop realistic models with a minimal number of parameters, e.g., using Bayesian Information Criterion [14]. These methods are focused on ODE-based models, so there is an acute need for universal methods that are applicable to stochastic computational models as well.…”