4,717 research outputs found
Invariant Generation for Multi-Path Loops with Polynomial Assignments
Program analysis requires the generation of program properties expressing
conditions to hold at intermediate program locations. When it comes to programs
with loops, these properties are typically expressed as loop invariants. In
this paper we study a class of multi-path program loops with numeric variables,
in particular nested loops with conditionals, where assignments to program
variables are polynomial expressions over program variables. We call this class
of loops extended P-solvable and introduce an algorithm for generating all
polynomial invariants of such loops. By an iterative procedure employing
Gr\"obner basis computation, our approach computes the polynomial ideal of the
polynomial invariants of each program path and combines these ideals
sequentially until a fixed point is reached. This fixed point represents the
polynomial ideal of all polynomial invariants of the given extended P-solvable
loop. We prove termination of our method and show that the maximal number of
iterations for reaching the fixed point depends linearly on the number of
program variables and the number of inner loops. In particular, for a loop with
m program variables and r conditional branches we prove an upper bound of m*r
iterations. We implemented our approach in the Aligator software package.
Furthermore, we evaluated it on 18 programs with polynomial arithmetic and
compared it to existing methods in invariant generation. The results show the
efficiency of our approach
RANS Turbulence Model Development using CFD-Driven Machine Learning
This paper presents a novel CFD-driven machine learning framework to develop
Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an
extension of the gene expression programming method (Weatheritt and Sandberg,
2016), but crucially the fitness of candidate models is now evaluated by
running RANS calculations in an integrated way, rather than using an algebraic
function. Unlike other data-driven methods that fit the Reynolds stresses of
trained models to high-fidelity data, the cost function for the CFD-driven
training can be defined based on any flow feature from the CFD results. This
extends the applicability of the method especially when the training data is
limited. Furthermore, the resulting model, which is the one providing the most
accurate CFD results at the end of the training, inherently shows good
performance in RANS calculations. To demonstrate the potential of this new
method, the CFD-driven machine learning approach is applied to model
development for wake mixing in turbomachines. A new model is trained based on a
high-pressure turbine case and then tested for three additional cases, all
representative of modern turbine nozzles. Despite the geometric configurations
and operating conditions being different among the cases, the predicted wake
mixing profiles are significantly improved in all of these a posteriori tests.
Moreover, the model equation is explicitly given and available for analysis,
thus it could be deduced that the enhanced wake prediction is predominantly due
to the extra diffusion introduced by the CFD-driven model.Comment: Accepted by Journal of Computational Physic
Topologically Driven Swelling of a Polymer Loop
Numerical studies of the average size of trivially knotted polymer loops with
no excluded volume are undertaken. Topology is identified by Alexander and
Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration
radius, and probability density distributions as functions of gyration radius
are generated for loops of up to N=3000 segments. Gyration radii of trivially
knotted loops are found to follow a power law similar to that of self avoiding
walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200
Collaborative Verification-Driven Engineering of Hybrid Systems
Hybrid systems with both discrete and continuous dynamics are an important
model for real-world cyber-physical systems. The key challenge is to ensure
their correct functioning w.r.t. safety requirements. Promising techniques to
ensure safety seem to be model-driven engineering to develop hybrid systems in
a well-defined and traceable manner, and formal verification to prove their
correctness. Their combination forms the vision of verification-driven
engineering. Often, hybrid systems are rather complex in that they require
expertise from many domains (e.g., robotics, control systems, computer science,
software engineering, and mechanical engineering). Moreover, despite the
remarkable progress in automating formal verification of hybrid systems, the
construction of proofs of complex systems often requires nontrivial human
guidance, since hybrid systems verification tools solve undecidable problems.
It is, thus, not uncommon for development and verification teams to consist of
many players with diverse expertise. This paper introduces a
verification-driven engineering toolset that extends our previous work on
hybrid and arithmetic verification with tools for (i) graphical (UML) and
textual modeling of hybrid systems, (ii) exchanging and comparing models and
proofs, and (iii) managing verification tasks. This toolset makes it easier to
tackle large-scale verification tasks
Braids of entangled particle trajectories
In many applications, the two-dimensional trajectories of fluid particles are
available, but little is known about the underlying flow. Oceanic floats are a
clear example. To extract quantitative information from such data, one can
measure single-particle dispersion coefficients, but this only uses one
trajectory at a time, so much of the information on relative motion is lost. In
some circumstances the trajectories happen to remain close long enough to
measure finite-time Lyapunov exponents, but this is rare. We propose to use
tools from braid theory and the topology of surface mappings to approximate the
topological entropy of the underlying flow. The procedure uses all the
trajectory data and is inherently global. The topological entropy is a measure
of the entanglement of the trajectories, and converges to zero if they are not
entangled in a complex manner (for instance, if the trajectories are all in a
large vortex). We illustrate the techniques on some simple dynamical systems
and on float data from the Labrador sea.Comment: 24 pages, 21 figures. PDFLaTeX with RevTeX4 macros. Matlab code
included with source. Fixed an inconsistent convention problem. Final versio
- …