We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in numerical simulation control. The structure is ideal for automated network-based since it invariant under power-conserving interconnection, congruence transformations Galerkin projection. Moreover, stability passivity properties are easily shown. Condensed forms orthogonal present easy analysis tools existence, uniqueness, regularity methods to check these properties. After recalling concepts general...

We discuss nonlinear model predictive control (MPC) for multi-body dynamics via physics-informed machine learning methods. In more detail, we use a neural networks (PINNs)-based MPC to solve tracking problem complex mechanical system, multi-link manipulator. PINNs are promising tool approximate (partial) differential equations but not suited tasks in their original form since they designed handle variable actions or initial values. thus follow the strategy of Antonelo et al....

.We present a novel physics-informed system identification method to construct passive linear time-invariant system. In more detail, for given quadratic energy functional, measurements of the input, state, and output in time domain, we find realization that approximates data well while guaranteeing functional satisfies dissipation inequality. To this end, use framework port-Hamiltonian (pH) systems modify dynamic mode decomposition, respectively, operator inference, be feasible...

In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome barrier within MOR, nonlinear projections are used, which often realized numerically using autoencoders. These autoencoders generally consist of a encoder and decoder involve costly training the hyperparameters to obtain good approximation quality reduced system. facilitate process, show that extending...

We present a novel passivity enforcement (passivation) method, called KLAP, for linear time-invariant systems based on the Kalman-Yakubovich-Popov (KYP) lemma and closely related Lur'e equations. The passivation problem in our framework corresponds to finding perturbation given non-passive system that renders passive while minimizing $\mathcal{H}_2$ or frequency-weighted distance between original resulting system. show this can be formulated as an unconstrained optimization whose objective...

In sequential multiscale molecular dynamics simulations, which advantageously combine the increased sampling and at coarse-grained resolution with higher accuracy of atomistic is altered over time. While coarse-graining straightforward once mapping between defined, reintroducing details still a non-trivial process called backmapping. Here, we present ART-SM, fragment-based backmapping framework that learns from simulation data to seamlessly switch resolution. ART-SM requires minimal user...

In sequential multiscale molecular dynamics simulations, which advantageously combine the increased sampling and at coarse-grained resolution with higher accuracy of atomistic is altered over time. While coarse-graining straightforward once mapping between defined, reintroducing details still a nontrivial process called backmapping. Here, we present ART-SM, fragment-based backmapping framework that learns from simulation data to seamlessly switch resolution. ART-SM requires minimal user...

Abstract We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying weak coupling condition. Here, means that the system, which needs to be solved in each step, decouples and hence improves computational efficiency. The construction convergence proof are based on connection differential equation with two time delays, namely one times step size. Numerical experiments confirm theoretical results indicate applicability higher-order schemes.

We investigate an energy-based formulation of the two-field poroelasticity model and related multiple-network as they appear in geosciences or medical applications. propose a port-Hamiltonian system equations, which is beneficial for preserving important properties after discretization model-order reduction. For this, we include commonly omitted second-order term consider corresponding first-order formulation. The quasi-static case then obtained by (formally) setting zero. Further, interpret...

We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our employs time-dependent transformation operators and, especially, generalizes MFEM to arbitrary basis functions. The is suitable obtain low-dimensional approximation with small errors even situations where classical order techniques require much higher dimensions similar quality. Analogously framework, reduced designed minimize residual, which also an...

Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs known be robust for smaller training sets, derive better generalization problems, and faster train. In this paper, we show that using in comparison with purely data-driven is not only favorable performance but allows us extract significant information on quality of approximated solution. Assuming underlying differential equation PINN an...

We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as well multiple-network models used medical applications. The approach decouples system such that each time step requires solution two small and well-structured linear systems rather than one large system. decoupling improves computational efficiency without...

The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form regular matrix pencil, a complete characterization different types given and algebraic criteria terms matrices are developed. analysis, which based method steps, takes into account all possible inhomogeneities history functions thus serves as worst-case scenario. Moreover, it reveals hidden delays DDAE. new...

We propose a new hyper-reduction method for recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited transport-dominated systems. Furthermore, we discuss applying this to wildland fire whose dynamics feature traveling combustion waves local ignition is thus challenging classical schemes linear subspaces. The allows us construct parameter-dependent reduced-order models (ROMs) with efficient offline/online...

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for on smooth manifolds, which emphasizes the nature of objects involved. The crucial ingredient is construction an embedding low-dimensional submanifold compatible map, discuss several options. Our general allows capturing generalizing existing MOR techniques, such as preservation Lagrangian- or...

We study linear time-invariant delay differential-algebraic equations (DDAEs). Such can arise if a feedback controller is applied to descriptor system and the requires some time measure state compute resulting in time-delay. present an existence uniqueness result for DDAEs within space of piecewise-smooth distributions algorithm determine whether DDAE delay-regular.

We introduce a novel model order reduction method for large-scale linear switched systems (LSS) where the coefficient matrices are affected by low-rank switching. The key idea is to replace LSS non-switched system with extended input and output vectors - called envelope which able reproduce dynamical behavior of original applying certain feedback law. can be reduced using standard schemes then transformed back an LSS. Furthermore, we present upper bound error reduced-order show how preserve...

Abstract We present a graph-theoretical approach that can detect which equations of delay differential-algebraic equation (DDAE) need to be differentiated or shifted construct solution the DDAE. Our exploits observation differentiation and shifting are very similar from structural point view, allows us generalize Pantelides algorithm for DDAE setting. The primary tool extension is introduction equivalence classes in graph DDAE, also derive necessary sufficient criterion termination new algorithm.

Abstract Within the time integration of linear elliptic‐parabolic problems such as poroelasticity, large systems have to be solved in every step. With a semi‐explicit approach, these decouple, leading remarkable speed‐up. This paper indicates that this idea can also applied nonlinear poroelasticity with permeability. To see this, we consider related toy problem.