Titles and Abstracts

  • Vagelis Harmandaris, University of Crete & Foundation for Research and Technology, Greece & The Cyprus Institute, Cyprus

Title: Hierarchical Coarse-Graining of Macromolecules: Physics-based vs Data-driven Models


  • Antonis Papapantoleon, TU Delft, Netherlands & Foundation for Research and Technology, Greece

Title: Model uncertainty in finance: a journey through probability, statistics and optimization

Abstract:

Academics, practitioners and regulators have understood that the classical paradigm in mathematical finance, where all computations are based on a single "correct" model, is flawed. Model uncertainty and model-free methods, were computations are based on a variety of models, offer an alternative. In this talk, we will discuss model-free methods and bounds, starting from the improved Fréchet-Hoeffding bounds and their applications in option pricing and risk management, and will present how ideas from probability, statistics, optimal transport and optimization can be applied in this field.


  • Yiannis Kamarianakis, Foundation for Research and Technology, Greece

Title: Projection Predictive Variable Selection for ARMA models

Abstract:

The autoregressive moving average (ARMA) model is a valuable tool in describing and forecasting weakly stationary stochastic processes. Classic ARMA model selection relies on choosing AR order $p$ and MA order $q$ to minimize prediction error (PE). Information criteria such as AIC or BIC discourage overfitting to estimate PE. Treating ARMA as a linear regression model, we explore and evaluate regularization techniques that automate selection and estimation of subset ARMA$(p,q)$. Because of temporal dependence, procedures considered are capable of handling the natural multicollinearity in AR and MA predictors. We extend from the adaptive LASSO (ADLASSO) used in \cite{Chen2011} to the adaptive elastic net (ADENET) which combines $\ell_1$ and $\ell_2$ regularization. Beyond AIC and BIC, we illustrate cross-validation techniques to estimate PE and aid in final model selection. Under the Bayesian framework, horseshoe (HS) priors are utilized to estimate a full ARMA$(p,q)$ reference model. Posterior distributions of sub-models are quickly obtainable through projection, and discrepancy is measured by the Kullback-Leibler distance. A forward selection algorithm identifies the best nested sequence of subset ARMA$(p,q)$ models, and the final model is chosen based on estimated PE. For the full library of methods discussed, model selection is evaluated via simulation and forecasting performance via practical application.


  • Georgia Baxevani, University of Crete, Greece

Title: Modeling transient dynamics of coarse-grained molecular systems.

Abstract: In recent years, the development of coarse-grained models for studying large-scale processes that cannot be practically studied with atomically detailed molecular dynamics simulations is an active research field. Defining the new effective coarse-grained system, which reduces the dimensionality, accounts for finding the model best representing the reference system both in structure and dynamic properties. In the present work, we approximate the dynamics of coarse-grained systems at the transient regime. Under the assumption that it is possible to perform molecular dynamics simulations of the atomistic system only in a short time interval corresponding to the transient regime, we propose a Langevin equation model characterized by time-depended pair potential accounting for the combined interaction forces of the system. We present the application of the path-space force matching method to retrieve the coarse space parametrized drift. At a long time limit, the time-dependent pair potential can reproduce the classical force matching potential of the mean force. In contrast, at transient -short time- regimes, we generate time-dependent drift coefficients describing the coarse-grained systems’ dynamics. The model’s effectiveness is examined by comparing its structural and dynamical properties with the corresponding reference system. The methodology is illustrated for the molecular water system.


  • Panagiota Birmpa, University of Massachusetts Amherst, USA


Title: Uncertainty Quantification and Correctability for directed graphical models and applications in materials design.


Abstract:

In this talk, we focus on probabilistic graphical models and especially directed graphical models as they allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest (QoI). For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. We present information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through the graph of multi-sourced model uncertainties to QoIs. We use these methods to rank the different sources of uncertainty and provide a mathematically rigorous approach to correctability that guarantees a systematic selection for improvement of the most under-performing components of a graphical model while controlling potential new errors created in the process in other parts of the model. We demonstrate these methods in Bayesian networks built for trustworthy prediction of materials screening to increase the efficiency of chemical reactions in catalysis. We focus on Oxygen Reduction Reaction, a known performance bottleneck in fuel cells. Based on the Sabatier's principle, the optimal oxygen binding energy has to be our QoI while a Bayesian network is built from expert knowledge (volcano curves), as well as various available experimental and computational data and their correlations or conditional independence. We quantify the model uncertainties entering the construction of the Bayesian network, we rank their impact from least to most influential, and we correct the most under-performing ones. This is a joint work Jinchao Feng (John Hopkins University), Markos A. Katsoulakis (University of Massachusetts Amherst) and Luc Rey-Bellet (University of Massachusetts Amherst).



  • Ramakrishna Tipireddy, Pacific Northwest National Laboratory, USA

Title: Stochastic basis adaptation and domain decomposition methods for high dimensional SPDEs

Abstract:

We present a stochastic dimension reduction method based on the basis adaptation in combination with the spatial domain decomposition method for partial differential equations (PDEs) with random coefficients. We use polynomial chaos-based uncertainty quantification (UQ) methods to solve stochastic PDEs and model random coefficient using Hermite polynomials in Gaussian random variables. We decompose the spatial domain into a set of non-overlapping subdomains and find in each subdomain a low-dimensional stochastic basis to represent the local solution in that subdomain accurately. The local basis in each subdomain is obtained by an appropriate linear transformation of the original set of Gaussian random variables spanning the Gaussian Hilbert space. The local solution in each subdomain is solved independently of each other while the continuity conditions for the solution and flux across the interface of the subdomains is maintained. We employ Neumann-Neumann algorithm to systematically compute the solution in the interior and at the interface of the subdomains. To impose continuity, we project local solution in each subdomain onto a common basis. The numerical experiments show that the proposed approach significantly reduces the computational cost of the stochastic solution

  • Yiannis Pantazis, Foundation for Research and Technology, Greece


Title: Adversarial Training of Generative Networks via Divergence Minimization


Abstract:

The generation of synthetic data that follow the distribution of real data has become a pervasive tool in several industrial and engineering fields. Generic applications of generative models include among others data balancing, data augmentation and domain adaptation. One of the most successful families of generative models is the so called Generative Adversarial Networks (GANs). In this talk, I will present the main ingredients of GANs and how they are formulated as a divergence minimization problem. Using variational representations (a.k.a. duality formulas) of divergences, I will demonstrate how the intractable divergence minimization problem becomes a tractable two-player zero-sum game.

It is however well-documented that GANs are notoriously difficult to train and several issues concerning their stability and convergence still exist. In order to improve the convergence behaviour of GAN training algorithms, we have developed a rigorous and general framework for constructing tailored divergences which interpolate between f-divergences and integral probability metrics. I will show that the proposed divergences inherit important stability properties from both families of divergences. I will present several numerical convergence results for heavy-tailed distributions as well as performance improvements over the standard GAN models in image processing applications.

  • Ivi Tsantili, Foundation for Research and Technology, Greece

Title: Statistical inference of Markovian and non-Markovian Stochastic Differential Equations


Abstract:

Methods for statistical inference of stochastic differential equations have become especially important lately that the enhanced availability of data and computational power allows for rich datasets from different scales and mechanisms of system interactions. Many methods have been developed for the statistical inference of diffusion processes that follow the Markovian property. However, in many systems encountered in engineering, finance, and biology this property is not a plausible simplification. This is the case for example for complex molecular systems described by generalized Langevin equations. We consider a stochastic differential equation under a general colored noise excitation, without a priori assuming that this can be equivalently written as an augmented diffusion process. Given a discrete sample associated with the response of the stochastic equation we infer the model parameters by maximizing an approximate likelihood function written in terms of the solution of the moment system. We use the two-time, response-excitation moment equations which include equations for the two-time response-excitation cross-correlations. We present results of the proposed methodology for some benchmark examples. We also discuss a recent approach where we model the short-time non-Markovian dynamics of complex molecular systems by Markovian dynamics with a time-dependent force field.



  • Evangelia Kalligiannaki, Foundation for Research and Technology, Greece

Title: Statistical inference for Stochastic Differential Equations and applications.