A simplicial complex is a collection of simplices “glued” together along common faces.

The dimension of a simplicial complex is the dimension of the largest simplex in the structure, qmax.

ENSO can be modelled as a complex network, where nodes are geographical locations and edges depend on the statistical similarities in climate records.

Before La Nina, the network's vertex tends to cluster.

These have important connotations in predictions of host of dynamical systems - from climate to engineering applications like aeroelastic flutter.

Fluid flow problems involve complex nonlinear interactions, multiple spatio-temporal scales, heterogeneous data.

Experiments, simulations are slow, expensive, so parametric analysis difficult.

Strong parametric dependence and important qualitative changes: need more database for parametric interpolation and extrapolation,

Strong motivation for the development of more effective ML techniques: hybrid techniques to combine ML wth first principles of physics?

Existing data can help a latent space representation to evolve the spatio-temporal dynamics

Accurate and efficient reduction is size by capturing key flow-features/dominant patterns

We aim to develop general, trainable oscillatory neural network models that can be used to simulate dynamic brain responses. The models might involve oscillator models like Kuramoto oscillator, Hopf oscillator, van der Pol oscillator, or other neural oscillator models like FitzHugh Nagumo, Morris- Lecar or Wilson-Cowan oscillators.

The tools required for this analysis draw from multidisciplinary areas neuroscience, dynamical systems, time series analysis, and recently, machine learning techniques and optogenetics. We hope to analyse the elements of bird song as well as the changes which occur in the structure of the birdsong in the development of the bird using tools such as Hurst exponents, simplicial characterisers, multifractals and complexity measures

In the proposed study we will investigate ciliary propulsion across different length scales using a combination of experimental, theoretical and simulation approaches.

The objective of this approach is to develop data-driven causal network or graphical model representations for industrial processes. These models are useful in determining disturbance propagation pathways, performance assessment/monitoring, fault diagnosis and alarm management.