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The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…
Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…
We present a method of discrete modeling and analysis of multilevel dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. Architectural model of information system supporting simulation…
We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
The evolution of a composite closed system using the integral wave equation with the kernel in the form of path integral is considered. It is supposed that a quantum particle is a subsystem of this system. The evolution of the reduced…
We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…
A multi-physics formulation for Data Driven Prognosis (DDP) is developed. Unlike traditional predictive strategies that require controlled off-line measurements or training for determination of constitutive parameters to derive the…
Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…
The structure of a network has a major effect on dynamical processes on that network. Many studies of the interplay between network structure and dynamics have focused on models of phenomena such as disease spread, opinion formation and…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…
Port-Hamiltonian neural networks (pHNNs) are emerging as a powerful modeling tool that integrates physical laws with deep learning techniques. While most research has focused on modeling the entire dynamics of interconnected systems, the…
Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…