scholarly journals Toward a Kernel-Based Uncertainty Decomposition Framework for Data and Models

2021 ◽  
pp. 1-35
Author(s):  
Rishabh Singh ◽  
Jose C. Principe
Keyword(s):  
Uncertainty Quantification ◽  
Quantum Physics ◽  
Reproducing Kernel ◽  
Epistemic Uncertainty ◽  
Reproducing Kernel Hilbert Space ◽  
Gradient Flow ◽  
Network Models ◽  
Neural Network Models ◽  
Decomposition Problem ◽  
Predictive Uncertainty

This letter introduces a new framework for quantifying predictive uncertainty for both data and models that rely on projecting the data into a gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density function (PDF) in a way that quantifies the flow of its gradient as a topological potential field quantified at all points in the sample space. This enables the decomposition of the PDF gradient flow by formulating it as a moment decomposition problem using operators from quantum physics, specifically Schrödinger's formulation. We experimentally show that the higher-order modes systematically cluster the different tail regions of the PDF, thereby providing unprecedented discriminative resolution of data regions having high epistemic uncertainty. In essence, this approach decomposes local realizations of the data PDF in terms of uncertainty moments. We apply this framework as a surrogate tool for predictive uncertainty quantification of point-prediction neural network models, overcoming various limitations of conventional Bayesian-based uncertainty quantification methods. Experimental comparisons with some established methods illustrate performance advantages that our framework exhibits.

scholarly journals Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience

2018 ◽  
Author(s):  
Simen Tennøe ◽  
Geir Halnes ◽  
Gaute T. Einevoll
Keyword(s):  
Neural Network ◽  
Sensitivity Analysis ◽  
Action Potential ◽  
Uncertainty Quantification ◽  
Open Source ◽  
Computational Neuroscience ◽  
Network Models ◽  
Model Parameters ◽  
Model Output ◽  
Neural Network Models

AbstractComputational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience.Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it easy and quick to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches.Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to- point comparison of the “raw” model output (e.g. membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, mean interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy.The aim of the current paper is to present Uncertainpy for the neuroscience community in a user- oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis on three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.SIGNIFICANCE STATEMENTA major challenge in computational neuroscience is to specify the often large number of parameters that define the neuron and neural network models. Many of these parameters have an inherent variability, and some may even be actively regulated and change with time. It is important to know how the uncertainty in model parameters affects the model predictions. To address this need we here present Uncertainpy, an open-source Python toolbox tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models.

Global Optimization Under Uncertainty and Uncertainty Quantification Applied to Tractor-Trailer Base Flaps

2016 ◽  
Vol 1 (2) ◽  
Author(s):  
Jacob A. Freeman ◽  
Christopher J. Roy
Keyword(s):  
Global Optimization ◽  
Wind Speed ◽  
Uncertainty Quantification ◽  
Numerical Approximation ◽  
Epistemic Uncertainty ◽  
Optimization Under Uncertainty ◽  
Optimized Design ◽  
Predictive Uncertainty ◽  
Model Form ◽  
Design Variables

Using a global optimization evolutionary algorithm (EA), propagating aleatory and epistemic uncertainty within the optimization loop, and using computational fluid dynamics (CFD), this study determines a design for a 3D tractor-trailer base (back-end) drag reduction device that reduces the wind-averaged drag coefficient by 41% at 57 mph (92 km/h). Because it is optimized under uncertainty, this design is relatively insensitive to uncertain wind speed and direction and uncertain deflection angles due to mounting accuracy and static aeroelastic loading. The model includes five design variables with generous constraints, and this study additionally includes the uncertain effects on drag prediction due to truck speed and elevation, steady Reynolds-averaged Navier–Stokes (RANS) approximation, and numerical approximation. This study uses the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA) optimization and uncertainty quantification (UQ) framework to interface the RANS flow solver, grid generator, and optimization algorithm. The computational model is a simplified full-scale tractor-trailer with flow at highway speed. For the optimized design, the estimate of total predictive uncertainty is +15/−42%; 8–10% of this uncertainty comes from model form (computation versus experiment); 3–7% from model input (wind speed and direction, flap angle, and truck speed); and +0.0/−28.5% from numerical approximation (due to the relatively coarse, 6 × 106 cell grid). Relative comparison of designs to the no-flaps baseline should have considerably less uncertainty because numerical error and input variation are nearly eliminated and model form differences are reduced. The total predictive uncertainty is also presented in the form of a probability box, which may be used to decide how to improve the model and reduce uncertainty.

Method of complex copper-zinc ore typification using neural network models

2020 ◽  
Vol 5 ◽  
pp. 140-147 ◽  
Author(s):  
T.N. Aleksandrova ◽  
◽  
E.K. Ushakov ◽  
A.V. Orlova ◽  
◽  
...  
Keyword(s):  
Neural Network ◽  
Network Models ◽  
Neural Network Models ◽  
Copper Zinc ◽  
Complex Copper

Digital twin of equipment as a basis for the consumer in digital production

2020 ◽  
Keyword(s):  
Neural Network ◽  
Tool Wear ◽  
Chip Formation ◽  
Network Models ◽  
Machining Accuracy ◽  
Neural Network Models ◽  
Digital Twin ◽  
The Neural Network ◽  
Digital Production ◽  
Cyberphysical System

The neural network models series used in the development of an aggregated digital twin of equipment as a cyber-physical system are presented. The twins of machining accuracy, chip formation and tool wear are examined in detail. On their basis, systems for stabilization of the chip formation process during cutting and diagnose of the cutting too wear are developed. Keywords cyberphysical system; neural network model of equipment; big data, digital twin of the chip formation; digital twin of the tool wear; digital twin of nanostructured coating choice

Measuring the World

2018 ◽  
Author(s):  
Ann-Sophie Barwich
Keyword(s):  
Sensory Information ◽  
Network Models ◽  
Model System ◽  
Stimulus Input ◽  
Expectancy Effects ◽  
Neural Network Models ◽  
Perceptual Object ◽  
External Objects ◽  
The Common ◽  
The Brain

How much does stimulus input shape perception? The common-sense view is that our perceptions are representations of objects and their features and that the stimulus structures the perceptual object. The problem for this view concerns perceptual biases as responsible for distortions and the subjectivity of perceptual experience. These biases are increasingly studied as constitutive factors of brain processes in recent neuroscience. In neural network models the brain is said to cope with the plethora of sensory information by predicting stimulus regularities on the basis of previous experiences. Drawing on this development, this chapter analyses perceptions as processes. Looking at olfaction as a model system, it argues for the need to abandon a stimulus-centred perspective, where smells are thought of as stable percepts, computationally linked to external objects such as odorous molecules. Perception here is presented as a measure of changing signal ratios in an environment informed by expectancy effects from top-down processes.

scholarly journals Lebesgue Decomposition of Non-Commutative Measures

2020 ◽  
Author(s):  
Michael T Jury ◽  
Robert T W Martin
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Fock Space ◽  
Reproducing Kernel Hilbert Space ◽  
Semigroup Algebra ◽  
Space Theory ◽  
Lebesgue Decomposition ◽  
Sesquilinear Forms ◽  
Positive Linear Functionals ◽  
Algebra Theory

Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.

scholarly journals Prediction of Stress in Power Transformer Winding Conductors Using Artificial Neural Networks: Hyperparameter Analysis

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4242
Author(s):  
Fausto Valencia ◽  
Hugo Arcos ◽  
Franklin Quilumba
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Finite Element ◽  
Power Transformer ◽  
Network Models ◽  
Activation Function ◽  
Neural Network Models ◽  
Transformer Winding ◽  
Artificial Neural ◽  
Femm Software

The purpose of this research is the evaluation of artificial neural network models in the prediction of stresses in a 400 MVA power transformer winding conductor caused by the circulation of fault currents. The models were compared considering the training, validation, and test data errors’ behavior. Different combinations of hyperparameters were analyzed based on the variation of architectures, optimizers, and activation functions. The data for the process was created from finite element simulations performed in the FEMM software. The design of the Artificial Neural Network was performed using the Keras framework. As a result, a model with one hidden layer was the best suited architecture for the problem at hand, with the optimizer Adam and the activation function ReLU. The final Artificial Neural Network model predictions were compared with the Finite Element Method results, showing good agreement but with a much shorter solution time.

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