15 research outputs found
Kernel Analog Forecasting: Multiscale Test Problems
Data-driven prediction is becoming increasingly widespread as the volume of
data available grows and as algorithmic development matches this growth. The
nature of the predictions made, and the manner in which they should be
interpreted, depends crucially on the extent to which the variables chosen for
prediction are Markovian, or approximately Markovian. Multiscale systems
provide a framework in which this issue can be analyzed. In this work kernel
analog forecasting methods are studied from the perspective of data generated
by multiscale dynamical systems. The problems chosen exhibit a variety of
different Markovian closures, using both averaging and homogenization;
furthermore, settings where scale-separation is not present and the predicted
variables are non-Markovian, are also considered. The studies provide guidance
for the interpretation of data-driven prediction methods when used in practice.Comment: 30 pages, 14 figures; clarified several ambiguous parts, added
references, and a comparison with Lorenz' original method (Sec. 4.5
Kernel Analog Forecasting: Multiscale Test Problems
Data-driven prediction is becoming increasingly widespread as the volume of data available grows and as algorithmic development matches this growth. The nature of the predictions made, and the manner in which they should be interpreted, depends crucially on the extent to which the variables chosen for prediction are Markovian, or approximately Markovian. Multiscale systems provide a framework in which this issue can be analyzed. In this work kernel analog forecasting methods are studied from the perspective of data generated by multiscale dynamical systems. The problems chosen exhibit a variety of different Markovian closures, using both averaging and homogenization; furthermore, settings where scale-separation is not present and the predicted variables are non-Markovian, are also considered. The studies provide guidance for the interpretation of data-driven prediction methods when used in practice
Data-Induced Interactions of Sparse Sensors
Large-dimensional empirical data in science and engineering frequently has
low-rank structure and can be represented as a combination of just a few
eigenmodes. Because of this structure, we can use just a few spatially
localized sensor measurements to reconstruct the full state of a complex
system. The quality of this reconstruction, especially in the presence of
sensor noise, depends significantly on the spatial configuration of the
sensors. Multiple algorithms based on gappy interpolation and QR factorization
have been proposed to optimize sensor placement. Here, instead of an algorithm
that outputs a singular "optimal" sensor configuration, we take a thermodynamic
view to compute the full landscape of sensor interactions induced by the
training data. The landscape takes the form of the Ising model in statistical
physics, and accounts for both the data variance captured at each sensor
location and the crosstalk between sensors. Mapping out these data-induced
sensor interactions allows combining them with external selection criteria and
anticipating sensor replacement impacts.Comment: 17 RevTeX pages, 10 figure
Optimal Sensor Placement with Adaptive Constraints for Nuclear Digital Twins
Given harsh operating conditions and physical constraints in reactors,
nuclear applications cannot afford to equip the physical asset with a large
array of sensors. Therefore, it is crucial to carefully determine the placement
of sensors within the given spatial limitations, enabling the reconstruction of
reactor flow fields and the creation of nuclear digital twins. Various design
considerations are imposed, such as predetermined sensor locations, restricted
areas within the reactor, a fixed number of sensors allocated to a specific
region, or sensors positioned at a designated distance from one another. We
develop a data-driven technique that integrates constraints into an
optimization procedure for sensor placement, aiming to minimize reconstruction
errors. Our approach employs a greedy algorithm that can optimize sensor
locations on a grid, adhering to user-defined constraints. We demonstrate the
near optimality of our algorithm by computing all possible configurations for
selecting a certain number of sensors for a randomly generated state space
system. In this work, the algorithm is demonstrated on the Out-of-Pile Testing
and Instrumentation Transient Water Irradiation System (OPTI-TWIST) prototype
vessel, which is electrically heated to mimic the neutronics effect of the
Transient Reactor Test facility (TREAT) at Idaho National Laboratory (INL). The
resulting sensor-based reconstruction of temperature within the OPTI-TWIST
minimizes error, provides probabilistic bounds for noise-induced uncertainty
and will finally be used for communication between the digital twin and
experimental facility