RESEARCH GROUP
MOR OF LARGE-SCALE DYNAMICAL SYSTEM
Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical modelling. Many modern mathematical models of real-life processes pose challenges when used in numerical simulations, due to complexity and large size (dimension). Model order reduction aims to lower the computational complexity of such problems, for example, in simulations of large-scale dynamical systems and control systems.
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SPARSE MATRIX SOLVER
In control theory, computational methods refer to the techniques and algorithms used to analyze, design, and implement control systems using computers. These methods involve the application of mathematical models, simulations, and algorithms to study the behavior of dynamic systems and to design controllers that can regulate or manipulate their behavior.
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MATHEMATICAL MODELLING
Mathematical modeling refers to the process of creating a mathematical representation or description of a real-world system or phenomenon. It involves using mathematical structures, equations, algorithms, and rules to understand, predict, or analyze the behavior of complex systems, natural phenomena, or processes. The primary purpose of mathematical modeling is to simplify and capture the essential features of a system or problem, allowing us to study it, make predictions, and test various scenarios without having to directly manipulate the real system. It helps in gaining insights, making informed decisions, and solving problems in various fields such as physics, engineering, biology, economics, ecology, and more.
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MACHINE LEARNING
Machine learning is a field of artificial intelligence centered around enabling computers to learn and make predictions or decisions from data without explicit programming. It involves creating algorithms that improve automatically over time by identifying patterns within datasets. Through supervised learning, where models learn from labeled data, unsupervised learning to uncover hidden structures, or reinforcement learning for decision-making, machine learning algorithms aim to solve complex problems across diverse domains. Leveraging statistical techniques, these algorithms evolve and adapt, utilizing information to make predictions, classify data, or optimize processes. Integral to this process is high-quality data, feature engineering, model selection, and ongoing evaluation, contributing to the continual refinement and application of machine learning in various fields, revolutionizing industries and driving technological advancements.
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ALGORITHM DESIGN
A matrix equation is a mathematical expression involving matrices, which are rectangular arrays of numbers arranged in rows and columns. These equations are written in the form of AX=B, where A represents a given matrix, X is typically an unknown matrix to be determined, and B is another matrix. When solving these equations, the aim is often to find the matrix X that satisfies the equation. Various techniques from linear algebra, such as matrix multiplication, inverse matrices, determinants, and Gaussian elimination, are used to manipulate these equations and solve for the unknown matrix. Matrix equations find wide application in diverse fields like physics, engineering, computer graphics, statistics, and many other areas where complex systems are analyzed and solved using mathematical models represented by matrices.
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