Chair of Computational Science
Clausiusstrasse 33
ETH-Zentrum, CLT E 12
CH-8092 Zürich

#### Contact Information

Email: garampat@ethz.ch

## Georgios Arampatzis

Post-doctoral Fellow

### Research and Interests

• Bayesian Uncertainty Quantification
• Hierarchical Bayesian Statistics
• Optimal Sensor Placement

### Education

• Ph.D. Applied Mathematics, University of Crete, Greece. 2014
• M.S. Applied Mathematics, University of Crete, Greece. 2011

### 2018

• G. Arampatzis, D. Wälchli, P. Angelikopoulos, S. Wu, P. Hadjidoukas, and P. Koumoutsakos, “Langevin diffusion for population based sampling with an application in bayesian inference for pharmacodynamics,” SIAM journal on scientific computing, vol. 40, iss. 3, p. B788–B811, 2018.
[BibTeX] [PDF] [DOI]
@article{arampatzis2018a,
author = {Georgios Arampatzis and Daniel W\"alchli and Panagiotis Angelikopoulos and Stephen Wu and Panagiotis Hadjidoukas and Petros Koumoutsakos},
doi = {10.1137/16m1107401},
journal = {{SIAM} Journal on Scientific Computing},
month = {jan},
number = {3},
pages = {B788--B811},
publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
title = {Langevin Diffusion for Population Based Sampling with an Application in Bayesian Inference for Pharmacodynamics},
url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/arampatzis2018a.pdf},
volume = {40},
year = {2018}
}

• J. Lipková, G. Arampatzis, P. Chatelain, B. Menze, and P. Koumoutsakos, “S-leaping: an adaptive, accelerated stochastic simulation algorithm, bridging τ-leaping and r-leaping,” Bulletin of mathematical biology, 2018.
[BibTeX] [PDF] [DOI]
@article{lipkova2018a,
author = {Jana Lipkov{\'{a}} and Georgios Arampatzis and Philippe Chatelain and Bjoern Menze and Petros Koumoutsakos},
doi = {10.1007/s11538-018-0464-9},
journal = {Bulletin of Mathematical Biology},
month = {jul},
publisher = {Springer Nature},
title = {S-Leaping: An Adaptive, Accelerated Stochastic Simulation Algorithm, Bridging -Leaping and R-Leaping},
url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/lipkova2018a.pdf},
year = {2018}
}

### 2017

• L. Kulakova, G. Arampatzis, P. Angelikopoulos, P. Hadjidoukas, C. Papadimitriou, and P. Koumoutsakos, “Data driven inference for the repulsive exponent of the Lennard-Jones potential in molecular dynamics simulations,” Scientific reports, vol. 7, iss. 1, p. 16576, 2017.
[BibTeX] [Abstract] [PDF] [DOI]

The Lennard-Jones (LJ) potential is a cornerstone of Molecular Dynamics (MD) simulations and among the most widely used computational kernels in science. The LJ potential models atomistic attraction and repulsion with century old prescribed parameters (, respectively), originally related by a factor of two for simplicity of calculations. We propose the inference of the repulsion exponent through Hierarchical Bayesian uncertainty quantification We use experimental data of the radial distribution function and dimer interaction energies from quantum mechanics simulations. We find that the repulsion exponent provides an excellent fit for the experimental data of liquid argon, for a range of thermodynamic conditions, as well as for saturated argon vapour. Calibration using the quantum simulation data did not provide a good fit in these cases. However, values obtained by dimer quantum simulations are preferred for the argon gas while lower values are promoted by experimental data. These results show that the proposed LJ 6-p potential applies to a wider range of thermodynamic conditions, than the classical LJ 6-12 potential. We suggest that calibration of the repulsive exponent in the LJ potential widens the range of applicability and accuracy of MD simulations.

@article{kulakova2017a,
author = {Kulakova, Lina and Arampatzis, Georgios and Angelikopoulos, Panagiotis and Hadjidoukas, Panagiotis and Papadimitriou, Costas and Koumoutsakos, Petros},
doi = {10.1038/s41598-017-16314-4},
issn = {2045-2322},
journal = {Scientific Reports},
number = {1},
pages = {16576},
title = {Data driven inference for the repulsive exponent of the {L}ennard-{J}ones potential in molecular dynamics simulations},
url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/kulakova2017a.pdf},
volume = {7},
year = {2017}
}

• B. Mosimann, G. Arampatzis, S. Amylidi-Mohr, A. Bessire, M. Spinelli, P. Koumoutsakos, D. Surbek, and L. Raio, “Reference ranges for fetal atrioventricular and ventriculoatrial time intervals and their ratios during normal pregnancy,” Fetal diagnosis and therapy, 2017.
[BibTeX] [PDF] [DOI]
@article{mosimann2017a,
author = {Beatrice Mosimann and Georgios Arampatzis and Sofia Amylidi-Mohr and Anice Bessire and Marialuigia Spinelli and Petros Koumoutsakos and Daniel Surbek and Luigi Raio},
doi = {10.1159/000481349},
journal = {Fetal Diagnosis and Therapy},
month = {oct},
publisher = {S. Karger {AG}},
title = {Reference Ranges for Fetal Atrioventricular and Ventriculoatrial Time Intervals and Their Ratios during Normal Pregnancy},
url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/mosimann2017a.pdf},
year = {2017}
}

### 2016

• G. Arampatzis, M. A. Katsoulakis, and L. Rey-Bellet, “Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics,” Journal of chemical physics, vol. 144, iss. 10, p. 1–9, 2016.
[BibTeX] [Abstract] [DOI]

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

@article{Arampatzis2016a,
author = {Arampatzis, Georgios and Katsoulakis, Markos A. and Rey-Bellet, Luc},
doi = {10.1063/1.4943388},
isbn = {0021-9606},
issn = {00219606},
journal = {Journal of Chemical Physics},
number = {10},
pages = {1--9},
pmid = {26979681},
title = {{Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics}},
url = {http://dx.doi.org/10.1063/1.4943388},
volume = {144},
year = {2016}
}

### 2015

• G. Arampatzis, M. A. Katsoulakis, and Y. Pantazis, “Accelerated sensitivity analysis in high-dimensional stochastic reaction networks,” Plos one, vol. 10, iss. 7, p. 1–24, 2015.
[BibTeX] [Abstract] [DOI]

Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in “sloppy” systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over the number of the sensitive parameters.

@article{Arampatzis2015,
archivePrefix = {arXiv},
arxivId = {1412.2153},
author = {Arampatzis, Georgios and Katsoulakis, Markos A. and Pantazis, Yannis},
doi = {10.1371/journal.pone.0130825},
eprint = {1412.2153},
issn = {19326203},
journal = {PLoS ONE},
number = {7},
pages = {1--24},
pmid = {26161544},
title = {{Accelerated sensitivity analysis in high-dimensional stochastic reaction networks}},
volume = {10},
year = {2015}
}

• G. Arampatzis, M. A. Katsoulakis, and Y. Pantazis, Pathwise sensitivity analysis in transient regimes, , 2015, vol. 20.
[BibTeX] [Abstract] [DOI]

{\textcopyright} Springer International Publishing Switzerland 2015The instantaneous relative entropy (IRE) and the corresponding instantaneous Fisher information matrix (IFIM) for transient stochastic processes are presented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corresponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-timeMarkov chains, continuous-timeMarkov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example.

@book{Arampatzis2015a,
author = {Arampatzis, G. and Katsoulakis, M.A. and Pantazis, Y.},
booktitle = {Mathematical Engineering},
doi = {10.1007/978-3-319-18206-3_5},
issn = {21924740 21924732},
title = {{Pathwise sensitivity analysis in transient regimes}},
volume = {20},
year = {2015}
}

### 2014

• G. Arampatzis and M. A. Katsoulakis, “Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations,” Journal of chemical physics, vol. 140, iss. 12, 2014.
[BibTeX] [Abstract] [DOI]

In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated- “coupled”- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz algorithm’s philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.

@article{Arampatzis2014a,
author = {Arampatzis, G. and Katsoulakis, M.A.},
doi = {10.1063/1.4868649},
issn = {00219606},
journal = {Journal of Chemical Physics},
number = {12},
title = {{Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations}},
volume = {140},
year = {2014}
}

### 2012

• G. Arampatzis, M. A. Katsoulakis, P. Plecháč, M. Taufer, and L. Xu, “Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms,” Journal of computational physics, vol. 231, iss. 23, 2012.
[BibTeX] [Abstract] [DOI]

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.

@article{Arampatzis2012b,
author = {Arampatzis, G. and Katsoulakis, M.A. and Plech{\'{a}}{\v{c}}, P. and Taufer, M. and Xu, L.},
doi = {10.1016/j.jcp.2012.07.017},
issn = {00219991 10902716},
journal = {Journal of Computational Physics},
keywords = {Kinetic Monte Ca,[Graphical Processing Unit (GPU)},
number = {23},
title = {{Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms}},
volume = {231},
year = {2012}
}

### 2007

• G. Arambatzis, P. Vavilis, I. Toulopoulos, and J. a. Ekaterinaris, “Implicit High-Order Time-Marching Schemes for the Linearized Euler Equations,” Aiaa journal, vol. 45, iss. 8, p. 1819–1826, 2007.
[BibTeX] [Abstract] [DOI]

High-order-accurate implicit time-marching methods are presented for discontinuous Galerkin and spectral volume high-order-accurate spatial discretizations of the linearized Euler equations that govern propagation of aeroacoustic disturbances. It is found that despite the additional computational time that is required for the solution of the large, sparse linear system for the degrees of freedom of high-order spectral volume or discontinuous Galerkin discretizations, implicit methods offer an attractive alternative for practical aeroacoustic computations with these high-order methods. Several explicit and implicit methods for time advancement are tested. The advantages of implicit higher-order-accurate (in time) methods that involve multiple implicit steps are demonstrated. The efficiency and accuracy of time-marching methods is evaluated for test problems with exact solutions. It isshown that complex domain aeroacoustic predictions can be obtained at a reduced computational cost with the use of high- order-accurate implicit methods.

@article{Arambatzis2007,
author = {Arambatzis, George and Vavilis, Panagiotis and Toulopoulos, Ioannis and Ekaterinaris, John a.},
doi = {10.2514/1.25336},
isbn = {1563478102},
issn = {0001-1452},
journal = {AIAA Journal},
number = {8},
pages = {1819--1826},
title = {{Implicit High-Order Time-Marching Schemes for the Linearized Euler Equations}},
url = {http://doi.aiaa.org/10.2514/1.25336},
volume = {45},
year = {2007}
}