10,456 research outputs found
UNCERTAINTY AND IRREVERSIBILITY IN GROUNDWATER RESOURCE MANAGEMENT
Optimal exploitation of renewable groundwater resources when extraction affects the probability of occurrence of an irreversible event is studied. The term irreversible signifies that the event occurrence renders the resource obsolete. It is found that uncertainty concerning the event occurrence has a profound effect. Under certainty - when the stock level below which the event occurs is known in advance - the optimal state process converges to a unique equilibrium state. Under uncertainty, when the event occurrence level is unknown, we identify equilibrium intervals and show that optimal processes initiated elsewhere converge to a boundary of one of these intervals. Inside an equilibrium interval, the expected loss due to the event occurrence is so high that it does not pay to extract in excess of recharge, even though under certainty doing so would be beneficial. These properties are illuminated by means of an example for which analytic solutions are derived.Resource /Energy Economics and Policy,
A Map of Update Constraints in Inductive Inference
We investigate how different learning restrictions reduce learning power and
how the different restrictions relate to one another. We give a complete map
for nine different restrictions both for the cases of complete information
learning and set-driven learning. This completes the picture for these
well-studied \emph{delayable} learning restrictions. A further insight is
gained by different characterizations of \emph{conservative} learning in terms
of variants of \emph{cautious} learning.
Our analyses greatly benefit from general theorems we give, for example
showing that learners with exclusively delayable restrictions can always be
assumed total.Comment: fixed a mistake in Theorem 21, result is the sam
Approximating Likelihood Ratios with Calibrated Discriminative Classifiers
In many fields of science, generalized likelihood ratio tests are established
tools for statistical inference. At the same time, it has become increasingly
common that a simulator (or generative model) is used to describe complex
processes that tie parameters of an underlying theory and measurement
apparatus to high-dimensional observations .
However, simulator often do not provide a way to evaluate the likelihood
function for a given observation , which motivates a new class of
likelihood-free inference algorithms. In this paper, we show that likelihood
ratios are invariant under a specific class of dimensionality reduction maps
. As a direct consequence, we show that
discriminative classifiers can be used to approximate the generalized
likelihood ratio statistic when only a generative model for the data is
available. This leads to a new machine learning-based approach to
likelihood-free inference that is complementary to Approximate Bayesian
Computation, and which does not require a prior on the model parameters.
Experimental results on artificial problems with known exact likelihoods
illustrate the potential of the proposed method.Comment: 35 pages, 5 figure
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
On-the-fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling
A multi-fidelity surrogate model for highly nonlinear multiscale problems is
proposed. It is based on the introduction of two different surrogate models and
an adaptive on-the-fly switching. The two concurrent surrogates are built
incrementally starting from a moderate set of evaluations of the full order
model. Therefore, a reduced order model (ROM) is generated. Using a hybrid
ROM-preconditioned FE solver, additional effective stress-strain data is
simulated while the number of samples is kept to a moderate level by using a
dedicated and physics-guided sampling technique. Machine learning (ML) is
subsequently used to build the second surrogate by means of artificial neural
networks (ANN). Different ANN architectures are explored and the features used
as inputs of the ANN are fine tuned in order to improve the overall quality of
the ML model. Additional ANN surrogates for the stress errors are generated.
Therefore, conservative design guidelines for error surrogates are presented by
adapting the loss functions of the ANN training in pure regression or pure
classification settings. The error surrogates can be used as quality indicators
in order to adaptively select the appropriate -- i.e. efficient yet accurate --
surrogate. Two strategies for the on-the-fly switching are investigated and a
practicable and robust algorithm is proposed that eliminates relevant technical
difficulties attributed to model switching. The provided algorithms and ANN
design guidelines can easily be adopted for different problem settings and,
thereby, they enable generalization of the used machine learning techniques for
a wide range of applications. The resulting hybrid surrogate is employed in
challenging multilevel FE simulations for a three-phase composite with
pseudo-plastic micro-constituents. Numerical examples highlight the performance
of the proposed approach
On the Complexity of Case-Based Planning
We analyze the computational complexity of problems related to case-based
planning: planning when a plan for a similar instance is known, and planning
from a library of plans. We prove that planning from a single case has the same
complexity than generative planning (i.e., planning "from scratch"); using an
extended definition of cases, complexity is reduced if the domain stored in the
case is similar to the one to search plans for. Planning from a library of
cases is shown to have the same complexity. In both cases, the complexity of
planning remains, in the worst case, PSPACE-complete
- …