1,503 research outputs found
Fast Dynamic System Identification with Karhunen-Lo\`eve Decomposed Gaussian Processes
A promising approach for scalable Gausian processes (GPs) is the
Karhunen-Lo\`eve (KL) decomposition, in which the GP kernel is represented by a
set of basis functions which are the eigenfunctions of the kernel operator.
Such decomposed kernels have the potential to be very fast, and do not depend
on the selection of a reduced set of inducing points. However KL decompositions
lead to high dimensionality, and variable selection becomes paramount. This
paper reports a new method of forward variable selection, enabled by the
ordered nature of the basis functions in the KL expansion of the Bayesian
Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in
a fully Bayesian approach. It quickly and effectively limits the number of
terms, yielding a method with competitive accuracies, training and inference
times for tabular datasets of low feature set dimensionality. The inference
speed and accuracy makes the method especially useful for dynamic systems
identification, by modeling the dynamics in the tangent space as a static
problem, then integrating the learned dynamics using a high-order scheme. The
methods are demonstrated on two dynamic datasets: a `Susceptible, Infected,
Recovered' (SIR) toy problem, with the transmissibility used as forcing
function, along with the experimental `Cascaded Tanks' benchmark dataset.
Comparisons on the static prediction of time derivatives are made with a random
forest (RF), a residual neural network (ResNet), and the Orthogonal Additive
Kernel (OAK) inducing points scalable GP, while for the timeseries prediction
comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along
with a number of basis set / optimizer combinations within the SINDy package
Statistical extraction of process zones and representative subspaces in fracture of random composite
We propose to identify process zones in heterogeneous materials by tailored
statistical tools. The process zone is redefined as the part of the structure
where the random process cannot be correctly approximated in a low-dimensional
deterministic space. Such a low-dimensional space is obtained by a spectral
analysis performed on pre-computed solution samples. A greedy algorithm is
proposed to identify both process zone and low-dimensional representative
subspace for the solution in the complementary region. In addition to the
novelty of the tools proposed in this paper for the analysis of localised
phenomena, we show that the reduced space generated by the method is a valid
basis for the construction of a reduced order model.Comment: Submitted for publication in International Journal for Multiscale
Computational Engineerin
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