08:30
An Embedded Deep Learning Model Discrepancy for Uncertainty Quantification on Combustion Computational Simulation
Rodolfo de Freitas | Federal University of Rio de Janeiro | Brazil
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Rodolfo de Freitas | Federal University of Rio de Janeiro | Brazil
Fernando Rochinha | Federal University of Rio de Janeiro | Brazil
Lower fidelity computational models make feasible the simulation of complex systems that requires a high number of computer runs of the corresponding forward solver, like in optimization, design, or uncertainty quantification. However, it typically introduces flaws in the predictions due to the limitations of such lower-fidelity models to completely capture the underlying physics. Model discrepancy terms can characterize such type of weakness. In combustion simulations, such discrepancies result from employing simplified physics or chemistry closure models for achieving a balance between easiness of computation and accuracy. Here, the focus is devoted to errors introduced by modeling the reactive process chemistry by reduced kinetics. Key questions involving modeling the discrepancy rely on where to introduce it within the model and on assuming its functional form. A deep neural network is embedded as an additive function to model the temporal evolution of chemical species concentrations that serves as a source to the heat equation. Embedding the model discrepancy naturally allows the consistency with the underlying model physics. The deep neural network is supposed to capture an appropriate functional form for the model correction. The neural network is trained with data produced by numerical simulation of detailed mechanisms, in a model-to-model Bayesian calibration. The proposed method is evaluated in a zero-dimensional reactor.
08:50
Time-Accurate Calibration of a Thermoacoustic Model on Experimental Images of a Forced Premixed Flame
Hans Yu | University of Cambridge | United Kingdom
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Hans Yu | University of Cambridge | United Kingdom
Ushnish Sengupta | University of Cambridge | United Kingdom
Matthew Juniper | University of Cambridge | United Kingdom
Luca Magri | University of Cambridge | United Kingdom
Thermoacoustic instabilities are a persistent challenge in the design of jet and rocket engines.
The time-accurate calculation of thermoacoustic instabilities is challenging due to the presence of both aleatoric and epistemic uncertainties, as well as the extreme sensitivity to small changes in certain parameters. We extend our previous work (Yu et al., CTR summer program 2018; Yu et al., J. Eng. Gas Turbines Power 2019) by applying our recently published level-set data assimilation framework (Yu et al., J. Comput. Phys. 2019) to experimental images of a forced premixed flame.
We force a Bunsen flame with a loudspeaker and record videos at different frequencies and amplitudes. Data assimilation provides an optimal estimate of the true state of a system, and improves the predicted shape and location of the flame. Parameter estimation uses the data to find a maximum-likelihood set of parameters for the model while simultaneously quantifying their uncertainty and identifying deficiencies in the model. We demonstrate our level-set data assimilation framework using both the ensemble Kalman filter and smoother. More generally, we take a physics-informed, reduced-order model and use statistical learning techniques to make it quantitatively accurate.
09:10
- CANCELED - Quantifying Uncertainty In Multi-Scale Catalysis Models
Himaghna Bhattacharjee | University of Delaware | United States
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Himaghna Bhattacharjee | University of Delaware | United States
Dionisios Vlachos | University of Delaware | United States
Catalysis is an inherently multiscale phenomenon. Quantum chemical calculations are used to parametrize multiscale models of catalysis from first principles. These calculations are a recognized source of uncertainty in catalysis models. Specifically, Density Functional Theory methods using approximate “exchange correlation” (xc) functionals are widely used in computational quantum chemistry. While making the calculations tractable, these approximate functionals introduce errors. These errors then propagate in a multiscale model. The exact magnitude and behavior of such errors is not known. There is also no systematic way to propagate the resultant uncertainty to the macroscale. Thus, the macroscopic predictions of these multi-scale models are often point estimates with no in-built diagnostic check to suggest pathological errors coming from the quantum scale.
In this work, we investigate the error behavior of xc functionals. We show that these errors are non-normally distributed, systematic and often highly correlated among various chemical species, invalidating common error estimates. We introduce a probabilistic formulation for the resultant uncertainty over the space of geometric and electronic descriptors. These distributions can then be propagated. To our knowledge, this is the first statistical study of the error behavior of quantum chemical calculations in hierarchical models of catalysis.
09:30
Stochastic Systems in Biochemical Systems
Erika Hausenblas | Montanuniversität Leoben | Austria
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Erika Hausenblas | Montanuniversität Leoben | Austria
Chemical and biochemical kinetics has been a rich source to produce a variety of spatial-temporal patterns since the discovery of the oscillating wave in the Belousov-Zhabotinsky reaction in 1950s. These phenomena and observations have been transferred to challenging mathematical problems throughvarious mathematical models, especially reaction-diffusion equations.
In the talk, we will present some models from biochemistry with an underlying stochastic perturbation. In particular, we will consider the Gray Scott system and the stochastic Gierer Meinhardt system with a stochastic force and highlight the impact of the random perturbation. We will present under which condition a solution to these systems exists, and give the idea of the proof. Finally, we will present some numerical modelling of these systems.
09:50
Origin identification and uncertainty quantification for epidemic spread on networks
Karen Larson | Brown University | United States
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Karen Larson | Brown University | United States
Anastasios Matzavinos | Brown University | United States
Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model parameters for a disease spreading on a network of communities from limited, noisy observations; the state-of-the-art computational framework compensates for the model complexity by exploiting massively parallel computing architectures. Using noisy, synthetic data, we show the potential of the approach to perform robust model fitting and additionally demonstrate that we can effectively identify the disease origin via Bayesian model selection. As disease-related data are increasingly available, the proposed framework has broad practical relevance for the prediction and management of epidemics.
10:10
Bayesian Learning Machines for Glioblastoma Multiforme Brain Tumor Evolution
Ali Daher | Massachusetts Institute of Technology | United States
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Ali Daher | Massachusetts Institute of Technology | United States
Abhinav Gupta | Massachusetts Institute of Technology | United States
Wael Hajj Ali | Massachusetts Institute of Technology | United States
Pierre F.J Lermusiaux | Massachusetts Institute of Technology | United States
With less than 5% of patients surviving 5 years following diagnosis, Glioblastoma multiforme (GBM) is the most common and aggressive form of primary brain tumor. We attempt to model the evolution of GBM tumor, however, significant amount of uncertainty exists in the functional form of model equations and parameterizations. This is due to the complexity and lack of understanding of the processes involved, along with patient-specific differences in brain cell density and geometry. These challenges motivate the objective of the present work, in which we implement the mathematical model for GBM in a rigorous PDE-based machine-learning framework, which combines our Gaussian Mixture Model (GMM) - dynamically orthogonal (DO) filter for nonlinear reduced-dimension Bayesian inference with the ability to simultaneously learn the state variables, parameters, parameterizations and constitutive relations. We use sparse (in time) and noisy data extracted from magnetic resonance (MR) images of the patient to learn the model. Such data-driven predictive models of the tumor growth could be very useful in a clinical setting, in coming up with a patient-specific treatment plan such as a chemotherapy schedule, or for scheduling surgeries.
10:30
Adjoint-based parameter estimator for highly unsteady blood flow in the brain vasculature
Robert Epp | Institute of Fluid Dynamics, ETH Zurich | Switzerland
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Authors:
Robert Epp | Institute of Fluid Dynamics, ETH Zurich | Switzerland
Franca Schmid | Institute of Pharmacology and Toxicology, University of Zurich | Switzerland
Bruno Weber | Institute of Pharmacology and Toxicology, University of Zurich | Switzerland
Patrick Jenny | Institute of Fluid Dynamics, ETH Zurich | Switzerland
The brain is capable of regulating cerebral blood flow based on local changes in neural activity. However, the precise mechanisms of the underlying vasodynamics are still poorly understood. The goal of our work is to predict how individual blood vessels need to dilate or constrict in order to locally adjust the blood flow in the brain vasculature.
In our numerical model, we solve an inverse problem to estimate the most likely diameter changes that are required to achieve desired flow distributions. This is done by minimizing a cost function J, where the sensitivity of J with regard to the diameters is calculated with the adjoint method. The vasculature is represented by a flow network and the impact of red blood cells (RBCs) on flow resistance is taken into account, i.e., by tracking individual RBCs as they move through the network. Due to the stochastic behaviour of RBCs at divergent bifurcations, the instantaneous flow characteristics are highly unsteady. Therefore, our inverse problem is solved iteratively and the adjoint equation is solved based on time averaged flow rates and pressures.
Our study with realistic networks revealed that diameter changes of individual capillaries are necessary to achieve a very localized flow increase in one specific brain region. Furthermore, we used our method in data assimilation applications to infer simulation parameters such as boundary conditions and to reduce general modelling uncertainties based on sparse experimental measurements.