EERTIS Profile Tiberiu Popoviciu Institute of Numerical Analysis

Research Services:

Mathematical Modeling and Numerical Simulation: Collaborations on developing and implementing mathematical models to analyze and simulate complex systems. Expertise in fluid dynamics, mathematical biology, environmental modeling.

Numerical Analysis and Scientific Computing: Collaborations focused on the rigorous design, analysis, and implementation of numerical methods to solve challenging scientific problems. Our expertise encompasses the formulation and discretization of partial differential equations, the development of robust and efficient iterative solvers for linear and nonlinear systems.

High-Performance Computing: Joint efforts to design and implement cutting-edge numerical algorithms tailored for parallel and high-performance computing architectures.

Time Series Analysis: Collaborations on trend estimation from various time series, evaluation of their multiscale structure by estimating trends at different time scales, analysis of the residuals, estimation of the volatility of financial time series, superstatistics, optimization methods. We can process time series from astrophysics, finance, biophysics and other domains. We also can evaluate the accuracy of different methods of trend estimation by testing them on generated realistic signals containing nonmonotonic trends with a diversity of shapes comparable with that of the real time series.

Machine Learning and Artificial intelligence: Collaborations on foundational research in artificial intelligence, including the development of new machine learning models, optimization algorithms for training, and theoretical analysis of their properties. Design and applications of neural networks for tackling forward and inverse problems where traditional numerical methods have difficulties and are computationally expensive.

Technology Services:

Stochastic Modeling and Predictive Analytics: Solutions for forecasting and risk assessment by applying rigorous stochastic modeling techniques. Development and calibration of univariate and multivariate time-series models to capture temporal dependencies, seasonality, and volatility. Advanced regression methods and probabilistic forecasting to quantify uncertainty and construct prediction intervals, enabling robust, data-driven decision-making under uncertainty.

Mathematical Optimization and Operations Research: Solving complex decision-making problems by formulating and solving mathematical optimization models. Our expertise covers continuous and discrete optimization, including linear programming, mixed-integer programming, and both convex and non-convex nonlinear programming. Designing and implementing exact algorithms, heuristics, and metaheuristics to find provably optimal or near-optimal solutions for challenges in logistics, scheduling, resource allocation, and industrial process control, subject to a given set of operational constraints.

Data Analysis and Statistical Inference: Extracting insights from complex, high-dimensional datasets using advanced statistical methods for exploratory data analysis, including dimensionality reduction techniques to identify latent structures and key variables. Utilizing robust statistical inference, hypothesis testing, and a variety of clustering algorithms to segment data and uncover significant patterns, providing a rigorous quantitative basis for strategic intelligence.

Signal and Image Processing: Expertise in the analysis and manipulation of temporal and spatial data. Employing time-frequency analysis techniques, including the Fourier and Wavelet transforms, to decompose signals, detect transient phenomena, and extract discriminative features. These methods can be applied to problems in sensor data analysis, quality control, medical imaging, and communications.

Machine Learning and Artificial Intelligence: Designing bespoke machine learning models to solve prediction, classification, and automation challenges. Our services leverage a broad spectrum of algorithms, including supervised learning, unsupervised learning, and deep learning. Developing custom neural network architectures to build high-performance systems for tasks ranging from predictive maintenance and computer vision to natural language processing.