115 research outputs found
Formal Verification of Input-Output Mappings of Tree Ensembles
Recent advances in machine learning and artificial intelligence are now being
considered in safety-critical autonomous systems where software defects may
cause severe harm to humans and the environment. Design organizations in these
domains are currently unable to provide convincing arguments that their systems
are safe to operate when machine learning algorithms are used to implement
their software.
In this paper, we present an efficient method to extract equivalence classes
from decision trees and tree ensembles, and to formally verify that their
input-output mappings comply with requirements. The idea is that, given that
safety requirements can be traced to desirable properties on system
input-output patterns, we can use positive verification outcomes in safety
arguments. This paper presents the implementation of the method in the tool
VoTE (Verifier of Tree Ensembles), and evaluates its scalability on two case
studies presented in current literature.
We demonstrate that our method is practical for tree ensembles trained on
low-dimensional data with up to 25 decision trees and tree depths of up to 20.
Our work also studies the limitations of the method with high-dimensional data
and preliminarily investigates the trade-off between large number of trees and
time taken for verification
Intelligent Data Mining using Kernel Functions and Information Criteria
Radial Basis Function (RBF) Neural Networks and Support Vector Machines (SVM) are two powerful kernel related intelligent data mining techniques. The current major problems with these methods are over-fitting and the existence of too many free parameters. The way to select the parameters can directly affect the generalization performance(test error) of theses models. Current practice in how to choose the model parameters is an art, rather than a science in this research area. Often, some parameters are predetermined, or randomly chosen. Other parameters are selected through repeated experiments that are time consuming, costly, and computationally very intensive. In this dissertation, we provide a two-stage analytical hybrid-training algorithm by building a bridge among regression tree, EM algorithm, and Radial Basis Function Neural Networks together. Information Complexity (ICOMP) criterion of Bozdogan along with other information based criteria are introduced and applied to control the model complexity, and to decide the optimal number of kernel functions. In the first stage of the hybrid, regression tree and EM algorithm are used to determine the kernel function parameters. In the second stage of the hybrid, the weights (coefficients) are calculated and information criteria are scored. Kernel Principal Component Analysis (KPCA) using EM algorithm for feature selection and data preprocessing is also introduced and studied. Adaptive Support Vector Machines (ASVM) and some efficient algorithms are given to deal with massive data
sets in support vector classifications. Versatility and efficiency of the new
proposed approaches are studied on real data sets and via Monte Carlo sim-
ulation experiments
Reliability-based design optimization using kriging surrogates and subset simulation
The aim of the present paper is to develop a strategy for solving
reliability-based design optimization (RBDO) problems that remains applicable
when the performance models are expensive to evaluate. Starting with the
premise that simulation-based approaches are not affordable for such problems,
and that the most-probable-failure-point-based approaches do not permit to
quantify the error on the estimation of the failure probability, an approach
based on both metamodels and advanced simulation techniques is explored. The
kriging metamodeling technique is chosen in order to surrogate the performance
functions because it allows one to genuinely quantify the surrogate error. The
surrogate error onto the limit-state surfaces is propagated to the failure
probabilities estimates in order to provide an empirical error measure. This
error is then sequentially reduced by means of a population-based adaptive
refinement technique until the kriging surrogates are accurate enough for
reliability analysis. This original refinement strategy makes it possible to
add several observations in the design of experiments at the same time.
Reliability and reliability sensitivity analyses are performed by means of the
subset simulation technique for the sake of numerical efficiency. The adaptive
surrogate-based strategy for reliability estimation is finally involved into a
classical gradient-based optimization algorithm in order to solve the RBDO
problem. The kriging surrogates are built in a so-called augmented reliability
space thus making them reusable from one nested RBDO iteration to the other.
The strategy is compared to other approaches available in the literature on
three academic examples in the field of structural mechanics.Comment: 20 pages, 6 figures, 5 tables. Preprint submitted to Springer-Verla
Forward Invariance in Neural Network Controlled Systems
We present a framework based on interval analysis and monotone systems theory
to certify and search for forward invariant sets in nonlinear systems with
neural network controllers. The framework (i) constructs localized first-order
inclusion functions for the closed-loop system using Jacobian bounds and
existing neural network verification tools; (ii) builds a dynamical embedding
system where its evaluation along a single trajectory directly corresponds with
a nested family of hyper-rectangles provably converging to an attractive set of
the original system; (iii) utilizes linear transformations to build families of
nested paralleletopes with the same properties. The framework is automated in
Python using our interval analysis toolbox , in
conjunction with the symbolic arithmetic toolbox , demonstrated
on an -dimensional leader-follower system
Fast modeling of turbulent transport in fusion plasmas using neural networks
We present an ultrafast neural network (NN) model, QLKNN, which predicts core
tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on
a database of 300 million flux calculations of the quasilinear gyrokinetic
transport model QuaLiKiz. The database covers a wide range of realistic tokamak
core parameters. Physical features such as the existence of a critical gradient
for the onset of turbulent transport were integrated into the neural network
training methodology. We have coupled QLKNN to the tokamak modelling framework
JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled
frameworks are demonstrated and validated through application to three JET
shots covering a representative spread of H-mode operating space, predicting
turbulent transport of energy and particles in the plasma core. JINTRAC-QLKNN
and RAPTOR-QLKNN are able to accurately reproduce JINTRAC-QuaLiKiz T i,e and n
e profiles, but 3 to 5 orders of magnitude faster. Simulations which take hours
are reduced down to only a few tens of seconds. The discrepancy in the final
source-driven predicted profiles between QLKNN and QuaLiKiz is on the order
1%-15%. Also the dynamic behaviour was well captured by QLKNN, with differences
of only 4%-10% compared to JINTRAC-QuaLiKiz observed at mid-radius, for a study
of density buildup following the L-H transition. Deployment of neural network
surrogate models in multi-physics integrated tokamak modelling is a promising
route towards enabling accurate and fast tokamak scenario optimization,
Uncertainty Quantification, and control applications.Comment: 18 pages, 11 figures, Physics of Plasmas, ICDDPS 2019 conference
pape
Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels
Optimal design under uncertainty has gained much attention in the past ten
years due to the ever increasing need for manufacturers to build robust systems
at the lowest cost. Reliability-based design optimization (RBDO) allows the
analyst to minimize some cost function while ensuring some minimal performances
cast as admissible failure probabilities for a set of performance functions. In
order to address real-world engineering problems in which the performance is
assessed through computational models (e.g., finite element models in
structural mechanics) metamodeling techniques have been developed in the past
decade. This paper introduces adaptive Kriging surrogate models to solve the
RBDO problem. The latter is cast in an augmented space that "sums up" the range
of the design space and the aleatory uncertainty in the design parameters and
the environmental conditions. The surrogate model is used (i) for evaluating
robust estimates of the failure probabilities (and for enhancing the
computational experimental design by adaptive sampling) in order to achieve the
requested accuracy and (ii) for applying a gradient-based optimization
algorithm to get optimal values of the design parameters. The approach is
applied to the optimal design of ring-stiffened cylindrical shells used in
submarine engineering under uncertain geometric imperfections. For this
application the performance of the structure is related to buckling which is
addressed here by means of a finite element solution based on the asymptotic
numerical method
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