Parameter Inference with Bifurcation Diagrams
- URL: http://arxiv.org/abs/2106.04243v1
- Date: Tue, 8 Jun 2021 10:39:19 GMT
- Title: Parameter Inference with Bifurcation Diagrams
- Authors: Gregory Szep, Neil Dalchau and Attila Csikasz-Nagy
- Abstract summary: We propose a gradient-based approach for inferring the parameters of differential equations that produce a user-specified bifurcation diagram.
The cost function contains a supervised error term that is minimal when the model bifurcations match the specified targets and an unsupervised bifurcation measure.
We demonstrate parameter inference with minimal models which explore the space of saddle-node and pitchfork diagrams and the genetic toggle switch from synthetic biology.
- Score: 1.0312968200748118
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Estimation of parameters in differential equation models can be achieved by
applying learning algorithms to quantitative time-series data. However,
sometimes it is only possible to measure qualitative changes of a system in
response to a controlled condition. In dynamical systems theory, such change
points are known as \textit{bifurcations} and lie on a function of the
controlled condition called the \textit{bifurcation diagram}. In this work, we
propose a gradient-based semi-supervised approach for inferring the parameters
of differential equations that produce a user-specified bifurcation diagram.
The cost function contains a supervised error term that is minimal when the
model bifurcations match the specified targets and an unsupervised bifurcation
measure which has gradients that push optimisers towards bifurcating parameter
regimes. The gradients can be computed without the need to differentiate
through the operations of the solver that was used to compute the diagram. We
demonstrate parameter inference with minimal models which explore the space of
saddle-node and pitchfork diagrams and the genetic toggle switch from synthetic
biology. Furthermore, the cost landscape allows us to organise models in terms
of topological and geometric equivalence.
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