159 research outputs found
Approximate reduction of heterogenous nonlinear models with differential hulls
We present a model reduction technique for a class of nonlinear ordinary differential equation (ODE) models of heterogeneous systems, where heterogeneity is expressed in terms of classes of state variables having the same dynamics structurally, but which are characterized by distinct parameters. To this end, we first build a system of differential inequalities that provides lower and upper bounds for each original state variable, but such that it is homogeneous in its parameters. Then, we use two methods for exact aggregation of ODEs to exploit this homogeneity, yielding a smaller model of size independent of the number of heterogeneous classes. We apply this technique to two case studies: a multiclass queuing network and a model of epidemics spread
Language-based Abstractions for Dynamical Systems
Ordinary differential equations (ODEs) are the primary means to modelling
dynamical systems in many natural and engineering sciences. The number of
equations required to describe a system with high heterogeneity limits our
capability of effectively performing analyses. This has motivated a large body
of research, across many disciplines, into abstraction techniques that provide
smaller ODE systems while preserving the original dynamics in some appropriate
sense. In this paper we give an overview of a recently proposed
computer-science perspective to this problem, where ODE reduction is recast to
finding an appropriate equivalence relation over ODE variables, akin to
classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366
Lagrangian Reachtubes: The Next Generation
We introduce LRT-NG, a set of techniques and an associated toolset that
computes a reachtube (an over-approximation of the set of reachable states over
a given time horizon) of a nonlinear dynamical system. LRT-NG significantly
advances the state-of-the-art Langrangian Reachability and its associated tool
LRT. From a theoretical perspective, LRT-NG is superior to LRT in three ways.
First, it uses for the first time an analytically computed metric for the
propagated ball which is proven to minimize the ball's volume. We emphasize
that the metric computation is the centerpiece of all bloating-based
techniques. Secondly, it computes the next reachset as the intersection of two
balls: one based on the Cartesian metric and the other on the new metric. While
the two metrics were previously considered opposing approaches, their joint use
considerably tightens the reachtubes. Thirdly, it avoids the "wrapping effect"
associated with the validated integration of the center of the reachset, by
optimally absorbing the interval approximation in the radius of the next ball.
From a tool-development perspective, LRT-NG is superior to LRT in two ways.
First, it is a standalone tool that no longer relies on CAPD. This required the
implementation of the Lohner method and a Runge-Kutta time-propagation method.
Secondly, it has an improved interface, allowing the input model and initial
conditions to be provided as external input files. Our experiments on a
comprehensive set of benchmarks, including two Neural ODEs, demonstrates
LRT-NG's superior performance compared to LRT, CAPD, and Flow*.Comment: 12 pages, 14 figure
Syntactic Markovian Bisimulation for Chemical Reaction Networks
In chemical reaction networks (CRNs) with stochastic semantics based on
continuous-time Markov chains (CTMCs), the typically large populations of
species cause combinatorially large state spaces. This makes the analysis very
difficult in practice and represents the major bottleneck for the applicability
of minimization techniques based, for instance, on lumpability. In this paper
we present syntactic Markovian bisimulation (SMB), a notion of bisimulation
developed in the Larsen-Skou style of probabilistic bisimulation, defined over
the structure of a CRN rather than over its underlying CTMC. SMB identifies a
lumpable partition of the CTMC state space a priori, in the sense that it is an
equivalence relation over species implying that two CTMC states are lumpable
when they are invariant with respect to the total population of species within
the same equivalence class. We develop an efficient partition-refinement
algorithm which computes the largest SMB of a CRN in polynomial time in the
number of species and reactions. We also provide an algorithm for obtaining a
quotient network from an SMB that induces the lumped CTMC directly, thus
avoiding the generation of the state space of the original CRN altogether. In
practice, we show that SMB allows significant reductions in a number of models
from the literature. Finally, we study SMB with respect to the deterministic
semantics of CRNs based on ordinary differential equations (ODEs), where each
equation gives the time-course evolution of the concentration of a species. SMB
implies forward CRN bisimulation, a recently developed behavioral notion of
equivalence for the ODE semantics, in an analogous sense: it yields a smaller
ODE system that keeps track of the sums of the solutions for equivalent
species.Comment: Extended version (with proofs), of the corresponding paper published
at KimFest 2017 (http://kimfest.cs.aau.dk/
PDE and Materials
This meeting brought together a carefully selected group of mathematicians, physicists, material scientists and engineers to discuss and review the impact of modern mathematical methods on the understanding of material behaviour and the design of new materials. A key issue is that the material behaviour is determined by physical processes at many different spatial and temporal scales which cannot be simulataneously resolved by brute force computation. Central themes of the meeting were (spatial) microstructures, the relation between atomistic and continuum models, the treatment of multiple temporal scales, and the influence of randomness and the use of methods from statistical mechanics
Underwater Vehicles
For the latest twenty to thirty years, a significant number of AUVs has been created for the solving of wide spectrum of scientific and applied tasks of ocean development and research. For the short time period the AUVs have shown the efficiency at performance of complex search and inspection works and opened a number of new important applications. Initially the information about AUVs had mainly review-advertising character but now more attention is paid to practical achievements, problems and systems technologies. AUVs are losing their prototype status and have become a fully operational, reliable and effective tool and modern multi-purpose AUVs represent the new class of underwater robotic objects with inherent tasks and practical applications, particular features of technology, systems structure and functional properties
Machine Learning
Machine Learning can be defined in various ways related to a scientific domain concerned with the design and development of theoretical and implementation tools that allow building systems with some Human Like intelligent behavior. Machine learning addresses more specifically the ability to improve automatically through experience
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