Related papers: Structure-preserving model reduction for dynamical…

We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…

Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference…

Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…

With a specific emphasis on control design objectives, achieving accurate system modeling with limited complexity is crucial in parametric system identification. The recently introduced deep structured state-space models (SSM), which…

This work presents structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs)…

We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system and its parameters, we modularize the design…

For Hamiltonian systems with non-canonical structure matrices, a new family of fourth-order energy-preserving integrators is presented. The integrators take a form of a combination of Runge--Kutta methods and continuous-stage Runge--Kutta…

This paper outlines reduced-order models for grid-forming virtual-oscillator-controlled inverters with nested current- and voltage-control loops, and current-limiting action for over-current protection. While a variety of model-reduction…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial…

We provide an explicit method to construct dynamical systems which admit an a-priori prescribed attracting set. As application, we provide a method to construct perturbations of conservative dynamical systems, which admit an a-priori…

The predominant knowledge-based approach to automated model construction, compositional modelling, employs a set of models of particular functional components. Its inference mechanism takes a scenario describing the constituent interacting…

We introduce a new restarting scheme for a continuous inertial dynamics with Hessian driven-damping, and establish a linear convergence rate for the function values along the restarted trajectories. The proposed routine is implemented…

Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…

Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…

The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…