
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method
The majority of the most common physical phenomena can be described usin...
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Approximate Nearest Neighbors in the Space of Persistence Diagrams
Persistence diagrams are important tools in the field of topological dat...
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Multiple shooting with neural differential equations
Neural differential equations have recently emerged as a flexible datad...
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Topological Approximate Bayesian Computation for Parameter Inference of an Angiogenesis Model
Inferring the parameters of models describing biological systems is an i...
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Algebraic 3D Graphic Statics: reciprocal constructions
The recently developed 3D graphic statics (3DGS) lacks a rigorous mathem...
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Towards improving architectural diagram consistency using system descriptors
Communication between practitioners is essential for the system's qualit...
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ResiduumCondition Diagram and Reduction of OverComplete EndmemberSets
Extracting reference spectra, or endmembers (EMs) from a given multi or...
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Parameter Inference with Bifurcation Diagrams
Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative timeseries 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 bifurcations and lie on a function of the controlled condition called the bifurcation diagram. In this work, we propose a gradientbased semisupervised approach for inferring the parameters of differential equations that produce a userspecified 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 saddlenode 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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