# Dr Naratip Santitissadeekorn

### Biography

### Biography

I received my PhD from Clarkson University, under the supervision of Professor Erik Bollt, in 2008. My dissertation is titled "Transport Analysis and Motion Estimation of Dynamical Systems of Time-Series data". From 2008-2011, I was a postdoctoral research associate at the University of New South Wales, Sydney, Australia, working with Professor Gary Froyland in a development of numerical techniques for finite-time Lagrangian coherent set identification. The techniques were applied to delimiting the polar vortex and Agulhas rings. From 2011-2014, I was a postdoctoral researcher at the University of North Carolina-Chapel Hill, working with Professor Chris Jones on a data assimilation project.

### Research interests

- Inverse Problem and Data Assimilation in Geophysical Fluid Dyanmics
- Applications of Lagrangian Coherent Structures (LCS)
- Computational Ergodic Theory

### Teaching

MAT1031: Seminar (Alegebra), Semester 1, 2014/2015

MAT3003: Bayesian Statistics, Semester 2, 2014/2015

### PhD Scholarship Opportunity

I have a PhD scholarship funded by the Natural Environment Research Council (NERC) available to start in August 2015 at the University of Surrey for the following project.

SC2015-13: Parameter estimation and inverse problem for reactive transport models in bioirrigated sediments

The scholarship will be of 3.5 years duration with stipend and university fees will be paid for a UK student.

The scholarship will be awarded on the basis of interview, CV, research interests, and undergraduate qualifications.

Please contact me directly to discuss further details of the projects and scholarships.

### My publications

### Publications

passive tracers by directly assimilating Lagrangian Coherent Structures. Our approach differs

from the usual Lagrangian Data Assimilation approach, where parameters are estimated based

on tracer trajectories. We employ the Approximate Bayesian Computation (ABC) framework to

avoid computing the likelihood function of the coherent structure, which is usually unavailable.

We solve the ABC by a Sequential Monte Carlo (SMC) method, and use Principal Component

Analysis (PCA) to identify the coherent patterns from tracer trajectory data. Our new method

shows remarkably improved results compared to the bootstrap particle filter when the physical

model exhibits chaotic advection.

fluid flows. An existing velocity field is perturbed in a C

1 neighborhood to maximize the

mixing rate for flows generated by velocity fields in this neighborhood. Our numerical

approach is based on the infinitesimal generator of the flow and is solved by standard

linear programming methods. The perturbed flow may be easily constrained to preserve

the same steady state distribution as the original flow, and various natural geometric

constraints can also be simply applied. The same technique can also be used to optimize

the mixing rate of advection-diffusion flow models by manipulating the drift term in a

small neighborhood.

with application to urban crime data, Computational Statistics and Data Analysis 128 pp. 163-183 Elsevier

? have been used to understand how crime rates evolve in time and/or

space. Within the context of these models and actual crime data, parameters

are often estimated using maximum likelihood estimation (MLE) on batch

data, but this approach has several limitations such as limited tracking in

real-time and uncertainty quantification. For practical purposes, it would be

desirable to move beyond batch data estimation to sequential data assimilation.

A novel and general Bayesian sequential data assimilation algorithm is

developed for joint state-parameter estimation for an inhomogeneous Poisson

process by deriving an approximating Poisson-Gamma ?Kalman? filter

that allows for uncertainty quantification. The ensemble-based implementation

of the filter is developed in a similar approach to the ensemble Kalman

filter, making the filter applicable to large-scale real world applications unlike

nonlinear filters such as the particle filter. The filter has the advantage

that it is independent of the underlying model for the process intensity,

and can therefore be used for many different crime models, as well as other

application domains. The performance of the filter is demonstrated on synthetic

data and real Los Angeles gang crime data and compared against a

very large sample-size particle filter, showing its effectiveness in practice. In addition the forecast skill of the Hawkes model is investigated for a forecast

system using the Receiver Operating Characteristic (ROC) to provide a useful

indicator for when predictive policing software for a crime type is likely

to be useful. The ROC and Brier scores are used to compare and analyse

the forecast skill of sequential data assimilation and MLE. It is found that

sequential data assimilation produces improved probabilistic forecasts over

the MLE.

The multi- resolution Horn- Schunck method is employed here because it can cope with the sometimes fictitious ?large? displacements that fluid deformation seems to produce [2]. But some of the recovered divergences here have unrealistically ?large? magnitudes (relative to those near the injection location) where they ought to be comparatively ?small? [2].

Quantifying error in flow fields is difficult when the true solution is unknown. One can subjectively define uncertainty in their components, and observations, to follow Gaussian distributions which are updated using Kalman filtering [2]. Given a pair of synthetic images, posterior variances seem to get reduced most where angular errors are comparatively ?small? [2]. So posterior variances are used to infer errors when the true solution is unknown here because they are independent of it [2].

Unrealistic ?large? divergence magnitudes (relative to those near injection locations) still appear where they ought to be comparatively ?small? [2]. In line with previous research, one tries modelling flows induced by bioirrigating Arenicola marina as two- dimensional incompressible point sources. Only three parameters, namely the source strength, x- and y- coordinates, need estimating rather than flow components at each grid cell. A Markov chain Monte- Carlo method is employed for this task, instead of the Kalman filter, because the state being estimated is no longer proportional to observations. Although comparatively ?large? divergence magnitudes now only appear near locations of fluid injection, this approach seems computationally expensive on one?s Dell Optiplex 7010 computer.

Outflow appears to be induced at the sediment- water interface by a two- dimensional incompressible point source beneath it. One questions whether there should be a little inflow as well because when an organism burrows forwards, the volume that it previously occupied ought to refill with surrounding fluid. This could be accounted for here by considering an additional two- dimensional incompressible flow at the sediment- water interface, as well as a point source at the injection location. But more parameters would need estimating. In an attempt to reduce computation times, the simulations involving the Markov chain Monte- Carlo method are rerun using two iterative ensemble Kalman filters (respectively).

such as a fluid

flow), this work develops an ensemble data assimilation method to estimate the

transition probability that represents a finite approximation of the Frobenius-Perron operator.

This allows a dynamical systems knowledge to be incorporated into a prior ensemble, which provides

sensible estimates in instances of limited observation. We demonstrate improved estimates over a constrained optimization approach (based on a quadratic programming problem) which does not impose a prior on the solution except for Markov properties. The estimated transition

probability then enables several probabilistic analysis of dynamical systems. We focus only on the identification of coherent patterns from the estimated Markov transition to demonstrate its application as a proof-of-concept. To the best of our knowledge, there have not been many

works on data-driven methods to identify coherent patterns from this type of data. While here the results are presented only in the context of dynamical systems applications, this work we present here has the potential to make a contribution in wider application areas that require the

estimation of transition probabilities from a time-ordered spatio-temporal distribution data.