Statistical abstraction for multi-scale spatio-temporal systems

Spatio-temporal systems exhibiting multi-scale behaviour are common in applications ranging from cyber-physical systems to systems biology, yet they present formidable challenges for computational modelling and analysis. Here we consider a prototypic scenario where spatially distributed agents decide their movement based on external inputs and a fast-equilibrating internal computation. We propose a generally applicable strategy based on statistically abstracting the internal system using Gaussian Processes, a powerful class of non-parametric regression techniques from Bayesian Machine Learning. We show on a running example of bacterial chemotaxis that this approach leads to accurate and much faster simulations in a variety of scenarios.Comment: 14th International Conference on Quantitative Evaluation of SysTems (QEST 2017

ML-Space: hybrid spatial Gillespie and Brownian motion simulation at multiple levels, and a rule-based description language

Computer simulations of biological cells as well-stirred systems are well established but neglect the spatial distribution of key actors. In this thesis, a simulation algorithm "ML-Space" for spatial models with dynamic hierarchies is presented. It combines stochastic spatial algorithms in discretized space with individual particles moving in continuous space that have spatial extensions and can contain other particles. For formal descriptions of the systems to be simulated spatially, ML-Space provides a rule-based specification language.Computersimulationen mikrobiologischer Prozesse, bei denen eine homogene Verteilung der Akteure einer Zelle angenommen wird, sind gut etabliert. In dieser Arbeit wird ein räumlicher Simulationsalgorithmus "ML-Space" für Mehrebenenmodelle vorgestellt, der auch dynamische Hierarchien abdeckt. Er vereint stochastische räumliche Algorithmen in diskretisiertem Raum mit individuellen Partikeln mit kontinuierlichen Koordinaten, die andere Partikel enthalten können. Zur formalen Beschreibung der räumlich zu simulierenden Systeme bietet ML-Space eine regelbasierte Modellierungssprache

Statistical abstraction for multi-scale spatio-temporal systems

Modelling spatio-temporal systems exhibiting multi-scale behaviour is a powerful tool in many branches of science, yet it still presents significant challenges. Here, we consider a general two-layer (agent-environment) modelling framework, where spatially distributed agents behave according to external inputs and internal computation; this behaviour may include influencing their immediate environment, creating a medium over which agent-agent interaction signals can be transmitted. We propose a novel simulation strategy based on a statistical abstraction of the agent layer, which is typically the most detailed component of the model and can incur significant computational cost in simulation. The abstraction makes use of Gaussian Processes, a powerful class of non-parametric regression techniques from Bayesian Machine Learning, to estimate the agent's behaviour given the environmental input. We show on two biological case studies how this technique can be used to speed up simulations and provide further insights into model behaviour

Simulator adaptation at runtime for component-based simulation software

Component-based simulation software can provide many opportunities to compose and configure simulators, resulting in an algorithm selection problem for the user of this software. This thesis aims to automate the selection and adaptation of simulators at runtime in an application-independent manner. Further, it explores the potential of tailored and approximate simulators - in this thesis concretely developed for the modeling language ML-Rules - supporting the effectiveness of the adaptation scheme.Komponenten-basierte Simulationssoftware kann viele Möglichkeiten zur Komposition und Konfiguration von Simulatoren bieten und damit zu einem Konfigurationsproblem für Nutzer dieser Software führen. Das Ziel dieser Arbeit ist die Entwicklung einer generischen und automatisierten Auswahl- und Adaptionsmethode für Simulatoren. Darüber hinaus wird das Potential von spezifischen und approximativen Simulatoren anhand der Modellierungssprache ML-Rules untersucht, welche die Effektivität des entwickelten Adaptionsmechanismus erhöhen können

Phenomenological modelling: statistical abstraction methods for Markov chains

Continuous-time Markov chains have long served as exemplary low-level models for an array of systems, be they natural processes like chemical reactions and population fluctuations in ecosystems, or artificial processes like server queuing systems or communication networks. Our interest in such systems is often an emergent macro-scale behaviour, or phenomenon, which can be well characterised by the satisfaction of a set of properties. Although theoretically elegant, the fundamental low-level nature of Markov chain models makes macro-scale analysis of the phenomenon of interest difficult. Particularly, it is not easy to determine the driving mechanisms for the emergent phenomenon, or to predict how changes at the Markov chain level will influence the macro-scale behaviour. The difficulties arise primarily from two aspects of such models. Firstly, as the number of components in the modelled system grows, so does the state-space of the Markov chain, often making behaviour characterisation untenable under both simulation-based and analytical methods. Secondly, the behaviour of interest in such systems is usually dependent on the inherent stochasticity of the model, and may not be aligned to the underlying state interpretation. In a model where states represent a low-level, primitive aspect of system components, the phenomenon of interest often varies significantly with respect to this low-level aspect that states represent. This work focuses on providing methodological frameworks that circumvent these issues by developing abstraction strategies, which preserve the phenomena of interest. In the first part of this thesis, we express behavioural characteristics of the system in terms of a temporal logic with Markov chain trajectories as semantic objects. This allows us to group regions of the state-space by how well they satisfy the logical properties that characterise macro-scale behaviour, in order to produce an abstracted Markov chain. States of the abstracted chain correspond to certain satisfaction probabilities of the logical properties, and inferred dynamics match the behaviour of the original chain in terms of the properties. The resulting model has a smaller state-space which is interpretable in terms of an emergent behaviour of the original system, and is therefore valuable to a researcher despite the accuracy sacrifices. Coarsening based on logical properties is particularly useful in multi-scale modelling, where a layer of the model is a (continuous-time) Markov chain. In such models, the layer is relevant to other layers only in terms of its output: some logical property evaluated on the trajectory drawn from the Markov chain. We develop here a framework for constructing a surrogate (discrete-time) Markov chain, with states corresponding to layer output. The expensive simulation of a large Markov chain is therefore replaced by an interpretable abstracted model. We can further use this framework to test whether a posited mechanism could be the driver for a specific macro-scale behaviour exhibited by the model. We use a powerful Bayesian non-parametric regression technique based on Gaussian process theory to produce the necessary elements of the abstractions above. In particular, we observe trajectories of the original system from which we infer the satisfaction of logical properties for varying model parametrisation, and the dynamics for the abstracted system that match the original in behaviour. The final part of the thesis presents a novel continuous-state process approximation to the macro-scale behaviour of discrete-state Markov chains with large state-spaces. The method is based on spectral analysis of the transition matrix of the chain, where we use the popular manifold learning method of diffusion maps to analyse the transition matrix as the operator of a hidden continuous process. An embedding of states in a continuous space is recovered, and the space is endowed with a drift vector field inferred via Gaussian process regression. In this manner, we form an ODE whose solution approximates the evolution of the CTMC mean, mapped onto the continuous space (known as the fluid limit). Our method is general and differs significantly from other continuous approximation methods; the latter rely on the Markov chain having a particular population structure, suggestive of a natural continuous state-space and associated dynamics. Overall, this thesis contributes novel methodologies that emphasize the importance of macro-scale behaviour in modelling complex systems. Part of the work focuses on abstracting large systems into more concise systems that retain behavioural characteristics and are interpretable to the modeller. The final part examines the relationship between continuous and discrete state-spaces and seeks for a transition path between the two which does not rely on exogenous semantics of the system states. Further than the computational and theoretical benefits of these methodologies, they push at the boundaries of various prevalent approaches to stochastic modelling

Multiscale Spatial Computational Systems Biology (Dagstuhl Seminar 14481)

This report documents the program and the outcomes of Dagstuhl Seminar 14481 "Multiscale Spatial Computational Systems Biology". This seminar explored challenges arising from the need to model and analyse complex biological systems at multiple scales (spatial and temporal), which falls within the general remit of Computational Systems Biology. A distinguishing factor of the seminar was the modelling exercise -- where teams explored different modelling paradigms, in order to better understand the details of the approaches, their challenges, potential applications, and their pros and cons. This activity was carried out in a collaborative and self-directed manner using the Open Space Technology approach as evidenced by a high degree of communication both within and between the teams. Eight teams were formed, and reports from five of them are included in this document