Keywords: Linear algebra, Probability theory, statistics, Optimization, Numerical analysis, Signal and image processing, Machine Learning, Bayesian inference, regularization methods, data driven methods

Inverse problems refer to a type of mathematical problems where the goal is to determine the cause or source of an observed effect. In other words, given some measurable output or result, the inverse problem seeks to identify the input that produced it.

Inverse problems are often challenging because they are inherently ill-posed, meaning that there are multiple possible solutions that could explain the observed data. This makes it difficult to determine the correct solution or to quantify the uncertainty associated with the estimated solution.

Inverse problems are a multidisciplinary field that requires a range of mathematical expertise to address different aspects of the problem. To solve inverse problems, various mathematical techniques have been developed, including regularization methods, optimization techniques, and Bayesian inference. These methods aim to find a solution that is consistent with the observed data while also minimizing some measure of complexity or uncertainty. In many cases, solving inverse problems requires a combination of numerical algorithms and domain-specific knowledge.

Inverse problems often involve the solution of complex, nonlinear, and high-dimensional problems. Numerical analysis provides the tools and techniques for solving these problems, including finite difference, finite element, and boundary element methods. Inverse problems often involve uncertainty, and probabilistic methods are used to quantify and propagate this uncertainty. Bayesian inference is a popular probabilistic framework for solving inverse problems, which involves combining prior knowledge with observed data to obtain a posterior distribution over the unknown parameters.

Inverse problems have many applications in various fields of science and engineering, such that medical imaging, Geophysics, Material science.

We are considering research in the following topics:

• Multi-physics inverse problems and control,
• Model Reduction and inverse problems,
• Incomplete data / limited computational resources / noisy data,
• Structural identification and identifying control inputs of nonlinear systems,
• Data-driven modeling of dynamical systems and partial differential equations,
• System identification with partial observations,
• Machine Learning of dynamical systems,

Keywords: Linear algebra, Differential equations, Probability theory, statistics, Optimization, Numerical analysis, Machine Learning,

Optimal control and design refer to the process of finding the best control or design strategy for a given system or process, based on a set of criteria or objectives.

In optimal control, the goal is to find the best control inputs to a dynamic system that will achieve a desired outcome, while considering constraints such as physical limitations, cost, and safety considerations. Optimal control problems are often formulated as optimization problems, where the objective is to minimize a cost function that captures the difference between the desired outcome and the actual system behavior, subject to constraints on the control inputs and the system dynamics.

In optimal design, the goal is to find the best design parameters or architecture for a given system or process that will optimize a set of performance criteria, such as efficiency, reliability, or cost. Optimal design problems are often formulated as optimization problems, where the objective is to minimize a cost function that captures the trade-offs between the different performance criteria, subject to constraints on the design parameters.

Optimal control and design are used in a wide range of applications, including robotics, aerospace, energy systems, and biomedical engineering. These techniques can help to optimize the performance of complex systems, reduce costs, and improve safety and reliability. However, finding optimal solutions can be challenging, as the optimization problems involved are often high-dimensional and nonlinear, and may involve trade-offs between conflicting objectives. Various numerical optimization techniques, such as gradient descent, genetic algorithms, and stochastic optimization, are used to solve these problems.

We are considering research in the following topics:

• Machine learning for optimal control and design,
• Optimization under uncertainty,
• Distributed control and optimization,
• Optimal control for energy systems,
• Topology and shape optimization,
• Optimal control of dynamical systems,

Keywords: Probability theory, statistics, Nonlinear dynamics, Graph theory, network science, Game theory, Information theory, Machine learning

Collective behavior refers to the coordinated actions of a large group of individuals that arise from interactions between them, rather than being driven by a central authority. Examples of collective behavior include the flocking of birds, the swarming of insects, and the formation of schools of fish.

One of the key features of collective behavior is the emergence of properties that are not present in the individuals themselves but arise from their interactions. For example, the coordinated movement of a flock of birds can give rise to complex patterns and structures that are not present in any individual bird. These emergent properties can often be observed at different scales, from the behavior of individual agents to the behavior of the group.

Emergent properties can also arise in other complex systems, such as in the behavior of cells in a tissue or in the interactions between neurons in the brain. In these cases, the emergent properties can be related to the function of the system, such as in the formation of patterns of neural activity that underlie perception and cognition.

Understanding the emergence of properties in complex systems is an active area of research in many fields, including physics, biology, and computer science. By studying these systems, researchers hope to gain insights into the fundamental principles that govern complex behavior and to develop new tools and techniques for controlling and manipulating complex systems.

Collective behavior has numerous applications in various fields of science and engineering, such that Animal behavior, Robotics, Social science, Traffic flow, financial markets, Dynamic of Organization.

We are considering research in the following topics:

• Multi-agent reinforcement learning,
• Dynamic network analysis,
• Human-robot interaction,
• Swarm robotics,
• Collective decision-making,
• Link between Agent Systems and Mean Field Games,

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