34,734 research outputs found
A General Spatio-Temporal Clustering-Based Non-local Formulation for Multiscale Modeling of Compartmentalized Reservoirs
Representing the reservoir as a network of discrete compartments with
neighbor and non-neighbor connections is a fast, yet accurate method for
analyzing oil and gas reservoirs. Automatic and rapid detection of coarse-scale
compartments with distinct static and dynamic properties is an integral part of
such high-level reservoir analysis. In this work, we present a hybrid framework
specific to reservoir analysis for an automatic detection of clusters in space
using spatial and temporal field data, coupled with a physics-based multiscale
modeling approach. In this work a novel hybrid approach is presented in which
we couple a physics-based non-local modeling framework with data-driven
clustering techniques to provide a fast and accurate multiscale modeling of
compartmentalized reservoirs. This research also adds to the literature by
presenting a comprehensive work on spatio-temporal clustering for reservoir
studies applications that well considers the clustering complexities, the
intrinsic sparse and noisy nature of the data, and the interpretability of the
outcome.
Keywords: Artificial Intelligence; Machine Learning; Spatio-Temporal
Clustering; Physics-Based Data-Driven Formulation; Multiscale Modelin
Maximum Likelihood Estimation for Single Particle, Passive Microrheology Data with Drift
Volume limitations and low yield thresholds of biological fluids have led to
widespread use of passive microparticle rheology. The mean-squared-displacement
(MSD) statistics of bead position time series (bead paths) are either applied
directly to determine the creep compliance [Xu et al (1998)] or transformed to
determine dynamic storage and loss moduli [Mason & Weitz (1995)]. A prevalent
hurdle arises when there is a non-diffusive experimental drift in the data.
Commensurate with the magnitude of drift relative to diffusive mobility,
quantified by a P\'eclet number, the MSD statistics are distorted, and thus the
path data must be "corrected" for drift. The standard approach is to estimate
and subtract the drift from particle paths, and then calculate MSD statistics.
We present an alternative, parametric approach using maximum likelihood
estimation that simultaneously fits drift and diffusive model parameters from
the path data; the MSD statistics (and consequently the compliance and dynamic
moduli) then follow directly from the best-fit model. We illustrate and compare
both methods on simulated path data over a range of P\'eclet numbers, where
exact answers are known. We choose fractional Brownian motion as the numerical
model because it affords tunable, sub-diffusive MSD statistics consistent with
typical 30 second long, experimental observations of microbeads in several
biological fluids. Finally, we apply and compare both methods on data from
human bronchial epithelial cell culture mucus.Comment: 29 pages, 12 figure
Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
This work derives a residual-based a posteriori error estimator for reduced
models learned with non-intrusive model reduction from data of high-dimensional
systems governed by linear parabolic partial differential equations with
control inputs. It is shown that quantities that are necessary for the error
estimator can be either obtained exactly as the solutions of least-squares
problems in a non-intrusive way from data such as initial conditions, control
inputs, and high-dimensional solution trajectories or bounded in a
probabilistic sense. The computational procedure follows an offline/online
decomposition. In the offline (training) phase, the high-dimensional system is
judiciously solved in a black-box fashion to generate data and to set up the
error estimator. In the online phase, the estimator is used to bound the error
of the reduced-model predictions for new initial conditions and new control
inputs without recourse to the high-dimensional system. Numerical results
demonstrate the workflow of the proposed approach from data to reduced models
to certified predictions
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