GENERATIVE MODELING

Mathematical models capable of generating instances from high-dimensional and complex distributions in a as-mush-as-possbile controllable manner have revolutionized the AI research. Two of the most common and efficient generative approaches are Variational Autoencoders (VAE) and Generative Adversarial Networks (GAN). Focusing on GANs, it is well-documented that their training often fails due to mode collapse, the fact that the optimal solution is a saddle point as well as limited mathematical understanding of the optimization process.

My research aims to devise new generative adversarial netowrks with improved convergence properties using suitable objective functions and function spaces, to develop novel theory to improve stability and better understand the training of GANs and apply adversarial training to generate realistic images, perform voice conversion and enhance speech quality.

PREDICTIVE MODELING

Predictive modelling combines existing and novel Machine Learning methodologies in order to rapidly understand physical mechanisms and concurrently develop new materials, processes and structures. We explore the enabling power of predictive model in laser-based manufacturing trained on experimental and simulated data aiming to automate and forecast the effect of laser processing on material structures. We envision a systematic methodology towards reducing material design, testing and production cost via the replacement of expensive trial-and-error based manufacturing procedure with a precise pre-fabrication predictive tool. Such a systematic approach requires concepts and algorithms from active learning, Bayesian analysis, unceratinty quantification and control theory

INFORMATION-THEORETIC UNCERTAINTY QUANTIFICATION

Stochastic modeling and simulation provide powerful predictive methods for the understanding of fundamental mechanisms in various complex systems. Parametric sensitivity analysis is an essential mathematical and computational tool for understanding the overall behavior of a system. We developed and continue to extent a novel sensitivity analysis methodology for complex stochastic dynamics based on the relative entropy rate of path distributions as well as on the corresponding pathwise Fisher information matrix. The proposed pathwise sensitivity analysis approach is applicable in a wide class of stochastic processes ranging from discrete or continuous time Markov chains, Markov processes, stochastic differential equations, semi-Markov processes, etc.

SPEECH PROCESSING

Sinusoidal modeling has gained a lot of popularity in signal and speech processing since it is able to represent non-stationary time-series very accurately. The estimation of the instantaneous components (i.e. instantaneous amplitude, instantaneous frequency and instantaneous phase) is an active area of research. We have developed and tested models and algorithms for the estimation of the instantaneous components of sinusoidal representation. Our goal is to reduce the estimation error due to the non-stationary character of the analyzed signals by taking advantage of time-domain information.

During the last years, advancements in deep learning led to human-level performance in text-to-speech synthesis as more generally to speech processing and manipulation. We devise, train and validate deep neural networks for speaker-independent speech synthesis, speech enhancement and voice conversion. Both convolutional and recurrent neural nets are utilized which are often trained with adversarial losses. We aim towards light and generalizable neural-based speech processing systems which take advantage of the characteristics of speech and audio sound generation.