Boosting Bayesian Parameter Inference of Nonlinear Stochastic Differential Equation Models by Hamiltonian Scale Separation

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model, for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact and very efficient approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.Comment: 15 pages, 8 figure

Exploring the limits of the geometric copolymerization model

The geometric copolymerization model is a recently introduced statistical Markov chain model. Here, we investigate its practicality. First, several approaches to identify the optimal model parameters from observed copolymer fingerprints are evaluated using Monte Carlo simulated data. Directly optimizing the parameters is robust against noise but has impractically long running times. A compromise between robustness and running time is found by exploiting the relationship between monomer concentrations calculated by ordinary differential equations and the geometric model. Second, we investigate the applicability of the model to copolymerizations beyond living polymerization and show that the model is useful for copolymerizations involving termination and depropagation reactions

Microstructural Quantification, Property Prediction, and Stochastic Reconstruction of Heterogeneous Materials Using Limited X-Ray Tomography Data

abstract: An accurate knowledge of the complex microstructure of a heterogeneous material is crucial for quantitative structure-property relations establishment and its performance prediction and optimization. X-ray tomography has provided a non-destructive means for microstructure characterization in both 3D and 4D (i.e., structural evolution over time). Traditional reconstruction algorithms like filtered-back-projection (FBP) method or algebraic reconstruction techniques (ART) require huge number of tomographic projections and segmentation process before conducting microstructural quantification. This can be quite time consuming and computationally intensive. In this thesis, a novel procedure is first presented that allows one to directly extract key structural information in forms of spatial correlation functions from limited x-ray tomography data. The key component of the procedure is the computation of a “probability map”, which provides the probability of an arbitrary point in the material system belonging to specific phase. The correlation functions of interest are then readily computed from the probability map. Using effective medium theory, accurate predictions of physical properties (e.g., elastic moduli) can be obtained. Secondly, a stochastic optimization procedure that enables one to accurately reconstruct material microstructure from a small number of x-ray tomographic projections (e.g., 20 - 40) is presented. Moreover, a stochastic procedure for multi-modal data fusion is proposed, where both X-ray projections and correlation functions computed from limited 2D optical images are fused to accurately reconstruct complex heterogeneous materials in 3D. This multi-modal reconstruction algorithm is proved to be able to integrate the complementary data to perform an excellent optimization procedure, which indicates its high efficiency in using limited structural information. Finally, the accuracy of the stochastic reconstruction procedure using limited X-ray projection data is ascertained by analyzing the microstructural degeneracy and the roughness of energy landscape associated with different number of projections. Ground-state degeneracy of a microstructure is found to decrease with increasing number of projections, which indicates a higher probability that the reconstructed configurations match the actual microstructure. The roughness of energy landscape can also provide information about the complexity and convergence behavior of the reconstruction for given microstructures and projection number.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

Modeling of RAFT polymerization processes using an efficient Monte Carlo algorithm in Julia

A kinetic Monte Carlo model of a RAFT process is presented. The algorithm has been developed and implemented in Julia for the three main RAFT theories under current discussion (Slow Fragmentation, Intermediate Radical Termination and Intermediate Radical Termination with Oligomers). Julia is a modern programming language designed to achieve high-performance in numerical and scientific computing. Thanks to a careful optimization of the code, it is possible to simulate a RAFT reaction scheme in short computing times for any of the three theories. The code is benchmarked against other programming languages (MATLAB, Python, FORTRAN and C), showing that Julia presents advantages for this particular system. The model offers an efficient method for predicting average properties and molecular weight distributions of the polymer species, including the bivariate MWD of the intermediate two-arm adduct. The proposed model can also be employed to obtain additional detailed information regarding the polymer microstructure at any reaction time.Fil: Pintos, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Química; ArgentinaFil: Sarmoria, Claudia. Universidad Nacional del Sur. Departamento de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Brandolin, Adriana. Universidad Nacional del Sur. Departamento de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Asteasuain, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Química; Argentin

Influence of wettability on liquid water transport in gas diffusion layer of proton exchange membrane fuel cells (PEMFC)

Water management is a key factor that limits PEFC's performance. We show how insights into this problem can be gained from pore-scale simulations of water invasion in a model fibrous medium. We explore the influence of contact angle on the water invasion pattern and water saturation at breakthrough and show that a dramatic change in the invasion pattern, from fractal to compact, occurs as the system changes from hydrophobic to hydrophilic. Then, we explore the case of a system of mixed wettability, i.e. containing both hydrophilic and hydrophobic pores. The saturation at breakthrough is studied as a function of the fraction of hydrophilic pores. The results are discussed in relation with the water management problem, the optimal design of a GDL and the fuel cell performance degradation mechanisms. We outline how the study could be extended to 3D systems, notably from binarised images of GDLs obtained by X ray microtomography

Inverse design of anisotropic spinodoid materials with prescribed diffusivity

The three-dimensional microstructure of functional materials determines its effective properties, like the mass transport properties of a porous material. Hence, it is desirable to be able to tune the properties by tuning the microstructure accordingly. In this work, we study a class of spinodoid i.e. spinodal decomposition-like structures with tunable anisotropy, based on Gaussian random fields. These are realistic yet computationally efficient models for bicontinuous porous materials. We use a convolutional neural network for predicting effective diffusivity in all three directions. We demonstrate that by incorporating the predictions of the neural network in an approximate Bayesian computation framework for inverse problems, we can in a computationally efficient manner design microstructures with prescribed diffusivity in all three directions