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Preprint
Deep Neural Network in Cusp Catastrophe Model
arXiv
04/05/2020
Abstract
Catastrophe theory was originally proposed to study dynamical systems that exhibit sudden shifts in behavior arising from small changes in input. These
models can generate reasonable explanation behind abrupt jumps in nonlinear dynamic models. Among the different catastrophe models, the Cusp Catastrophe model attracted the most attention due to it's relatively simpler dynamics and rich domain of application. Due to the complex behavior of the response, the parameter space becomes highly non-convex and hence it becomes very hard to optimize to figure out the generating parameters. Instead of solving for these generating parameters, we demonstrated how a Machine learning model can be trained to learn the dynamics of the Cusp catastrophe models, without ever really solving for the generating model parameters. Simulation studies and application on a few famous datasets are used to validate our approach. To our knowledge, this is the first paper of such kind where a neural network based approach has been applied in Cusp Catastrophe model.
Details
- Title
- Deep Neural Network in Cusp Catastrophe Model
- Resource Type
- Preprint
- Publisher
- arXiv
- Format
- link
- Number of pages
- 12
- Identifiers
- 99381300844906600
- Academic Unit
- Hal Marcus College of Science and Engineering ; Mathematics and Statistics
- Language
- English