1,556 research outputs found
Hybrid Process Models in Electrochemical Syntheses under Deep Uncertainty
Chemical process engineering and machine learning are merging rapidly, and hybrid process models have shown promising results in process analysis and process design. However, uncertainties in first-principles process models have an adverse effect on extrapolations and inferences based on hybrid process models. Parameter sensitivities are an essential tool to understand better the underlying uncertainty propagation and hybrid system identification challenges. Still, standard parameter sensitivity concepts may fail to address comprehensive parameter uncertainty problems, i.e., deep uncertainty with aleatoric and epistemic contributions. This work shows a highly effective and reproducible sampling strategy to calculate simulation uncertainties and global parameter sensitivities for hybrid process models under deep uncertainty. We demonstrate the workflow with two electrochemical synthesis simulation studies, including the synthesis of furfuryl alcohol and 4-aminophenol. Compared with Monte Carlo reference simulations, the CPU-time was significantly reduced. The general findings of the hybrid model sensitivity studies under deep uncertainty are twofold. First, epistemic uncertainty has a significant effect on uncertainty analysis. Second, the predicted parameter sensitivities of the hybrid process models add value to the interpretation and analysis of the hybrid models themselves but are not suitable for predicting the real process/full first-principles process model’s sensitivities
GINNs:Graph-Informed Neural Networks for Multiscale Physics
We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid
approach combining deep learning with probabilistic graphical models (PGMs)
that acts as a surrogate for physics-based representations of multiscale and
multiphysics systems. GINNs address the twin challenges of removing intrinsic
computational bottlenecks in physics-based models and generating large data
sets for estimating probability distributions of quantities of interest (QoIs)
with a high degree of confidence. Both the selection of the complex physics
learned by the NN and its supervised learning/prediction are informed by the
PGM, which includes the formulation of structured priors for tunable control
variables (CVs) to account for their mutual correlations and ensure physically
sound CV and QoI distributions. GINNs accelerate the prediction of QoIs
essential for simulation-based decision-making where generating sufficient
sample data using physics-based models alone is often prohibitively expensive.
Using a real-world application grounded in supercapacitor-based energy storage,
we describe the construction of GINNs from a Bayesian network-embedded
homogenized model for supercapacitor dynamics, and demonstrate their ability to
produce kernel density estimates of relevant non-Gaussian, skewed QoIs with
tight confidence intervals.Comment: 20 pages, 8 figure
Describing condensed matter from atomically resolved imaging data: from structure to generative and causal models
The development of high-resolution imaging methods such as electron and
scanning probe microscopy and atomic probe tomography have provided a wealth of
information on structure and functionalities of solids. The availability of
this data in turn necessitates development of approaches to derive quantitative
physical information, much like the development of scattering methods in the
early XX century which have given one of the most powerful tools in condensed
matter physics arsenal. Here, we argue that this transition requires adapting
classical macroscopic definitions, that can in turn enable fundamentally new
opportunities in understanding physics and chemistry. For example, many
macroscopic definitions such as symmetry can be introduced locally only in a
Bayesian sense, balancing the prior knowledge of materials' physics and
experimental data to yield posterior probability distributions. At the same
time, a wealth of local data allows fundamentally new approaches for the
description of solids based on construction of statistical and physical
generative models, akin to Ginzburg-Landau thermodynamic models. Finally, we
note that availability of observational data opens pathways towards exploring
causal mechanisms underpinning solid structure and functionality
A Partially Reflecting Random Walk on Spheres Algorithm for Electrical Impedance Tomography
In this work, we develop a probabilistic estimator for the voltage-to-current
map arising in electrical impedance tomography. This novel so-called partially
reflecting random walk on spheres estimator enables Monte Carlo methods to
compute the voltage-to-current map in an embarrassingly parallel manner, which
is an important issue with regard to the corresponding inverse problem. Our
method uses the well-known random walk on spheres algorithm inside subdomains
where the diffusion coefficient is constant and employs replacement techniques
motivated by finite difference discretization to deal with both mixed boundary
conditions and interface transmission conditions. We analyze the global bias
and the variance of the new estimator both theoretically and experimentally. In
a second step, the variance is considerably reduced via a novel control variate
conditional sampling technique
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