Learning System Parameters from Turing Patterns

Schnörr, David; Schnörr, Christoph

doi:10.48550/arxiv.2108.08542

Cited by 1 publication

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the Gierer-Meinhard and Brusselator models we use the same settings as earlier (see Fig. 6, top), which are also comparable to those in the article [19], while each individual pattern in [18] contains significantly more 'wavelengths' and thus more information per pattern. The patterns in the FitzHugh-Nagumo model are more rich, and we must ensure that the single data pattern contains all typical features.…”

Section: Synthetic Likelihood For Limited Datamentioning

confidence: 99%

“…Recently, neural network approaches [18,19] have been applied to Turing models using stationary pattern data. In [18], convolutional neural networks (CNN) are employed to learn the data-toparameter map for the SIR-type rumour propagation models, using a sufficiently large training set and a suitable neural network architecture.…”

Section: Introductionmentioning

confidence: 99%

“…The latter, however, may depend both on the specific model and on its implementation. In [19], a range of machine learning approaches were compared on example of the Gierer-Meinhardt model. The identification process was significantly improved by introducing an invariant pattern representation based on resistance distance histograms, which made it possible to effectively represent the spatial structure of patterns and to compute distances between pattern data.…”

Section: Introductionmentioning

confidence: 99%

“…The identification process was significantly improved by introducing an invariant pattern representation based on resistance distance histograms, which made it possible to effectively represent the spatial structure of patterns and to compute distances between pattern data. Once trained with a sufficiently large data set, methods of [18,19] allowed identifying model parameters accurately, using a single pattern. However, [18] uses pattern data accounting for a large set of 'period cells' containing about 10-15 'wavelengths'.…”

Section: Introductionmentioning

confidence: 99%

“…In the current work, applicability of the CIL approach is significantly expanded. Addressing the criticism raised in [18,19], we test the method using diverse pattern formation models. First, we consider cases with very limited data sets, resembling practical applications.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Bayesian Approach to Modelling Biological Pattern Formation with Limited Data

Kazarnikov¹,

Scheichl²,

Haario³

et al. 2022

Preprint

View full text Add to dashboard Cite

Pattern formation plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has been through reactiondiffusion mechanisms. Alternative models have been proposed, that link dynamics of diffusing molecular signals with tissue mechanics. Model validation is complicated as in many experimental situations only the limiting, stationary regime of the pattern formation process is observable, without any knowledge of the transient behaviour or the initial state. To overcome this problem, the initial state of the model can be randomised. But then fixed values of the model parameters correspond to a family of patterns rather than a fixed stationary solution, and standard estimation approaches, such the least squares, are not suitable. Instead, statistical characteristics of the patterns should be compared, which is difficult given the typically limited amount of available data in practical applications. To deal with this problem, we extend the recently developed statistical approach (the Correlation Integral Likelihood method) for parameter identification by pattern data. We introduce modifications that allow increasing the accuracy of the identification process without resizing the data set. The proposed approach is tested using different classes of pattern formation models and severely limited data sets. For all considered equations, parallel, GPU-based implementations of the numerical solvers with efficient time stepping schemes are provided.

show abstract

Section: Synthetic Likelihood For Limited Datamentioning

confidence: 99%