40,550 research outputs found
Neural Simulation of Water Systems for Efficient State Estimation
This paper presents a neural network based technique for the
solution of a water system state estimation problem.The technique
combines a neural linear equations solver with a Newton-Raphson
iterations to obtain a solution to an overdetermined set of
nonlinear equations.
The algorithm has been applied to a realistic 34-node water
network. By changing the values of neural network parameters
both the least squares (LS) and least absolute values (LAV)
estimates have been obtained and assessed with respect to their
sensitivity to measurement errors
Fast Neural Network Predictions from Constrained Aerodynamics Datasets
Incorporating computational fluid dynamics in the design process of jets,
spacecraft, or gas turbine engines is often challenged by the required
computational resources and simulation time, which depend on the chosen
physics-based computational models and grid resolutions. An ongoing problem in
the field is how to simulate these systems faster but with sufficient accuracy.
While many approaches involve simplified models of the underlying physics,
others are model-free and make predictions based only on existing simulation
data. We present a novel model-free approach in which we reformulate the
simulation problem to effectively increase the size of constrained pre-computed
datasets and introduce a novel neural network architecture (called a cluster
network) with an inductive bias well-suited to highly nonlinear computational
fluid dynamics solutions. Compared to the state-of-the-art in model-based
approximations, we show that our approach is nearly as accurate, an order of
magnitude faster, and easier to apply. Furthermore, we show that our method
outperforms other model-free approaches
Integrated Neural Based System for State Estimation and Confidence Limit Analysis in Water Networks
In this paper a simple recurrent neural network (NN) is used as
a basis for constructing an integrated system capable of finding
the state estimates with corresponding confidence limits for water
distribution systems. In the first phase of calculations a neural
linear equations solver is combined with a Newton-Raphson
iterations to find a solution to an overdetermined set of nonlinear
equations describing water networks.
The mathematical model of the water system is derived using
measurements and pseudomeasurements consisting certain
amount of uncertainty. This uncertainty has an impact on the
accuracy to which the state estimates can be calculated. The
second phase of calculations, using the same NN, is carried out in
order to quantify the effect of measurement uncertainty on
accuracy of the derived state estimates. Rather than a single
deterministic state estimate, the set of all feasible states
corresponding to a given level of measurement uncertainty is
calculated. The set is presented in the form of upper and lower
bounds for the individual variables, and hence provides limits on
the potential error of each variable.
The simulations have been carried out and results are presented
for a realistic 34-node water distribution network
Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations
Although double-precision floating-point arithmetic currently dominates
high-performance computing, there is increasing interest in smaller and simpler
arithmetic types. The main reasons are potential improvements in energy
efficiency and memory footprint and bandwidth. However, simply switching to
lower-precision types typically results in increased numerical errors. We
investigate approaches to improving the accuracy of reduced-precision
fixed-point arithmetic types, using examples in an important domain for
numerical computation in neuroscience: the solution of Ordinary Differential
Equations (ODEs). The Izhikevich neuron model is used to demonstrate that
rounding has an important role in producing accurate spike timings from
explicit ODE solution algorithms. In particular, fixed-point arithmetic with
stochastic rounding consistently results in smaller errors compared to single
precision floating-point and fixed-point arithmetic with round-to-nearest
across a range of neuron behaviours and ODE solvers. A computationally much
cheaper alternative is also investigated, inspired by the concept of dither
that is a widely understood mechanism for providing resolution below the least
significant bit (LSB) in digital signal processing. These results will have
implications for the solution of ODEs in other subject areas, and should also
be directly relevant to the huge range of practical problems that are
represented by Partial Differential Equations (PDEs).Comment: Submitted to Philosophical Transactions of the Royal Society
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