相关论文: Geometric analysis of nonlinear differential-algeb…

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…

Accurate initial conditions have the task of precisely capturing and fixing the free integration constants of the flow considered. This is trivial for regular ordinary differential equations, but a complex problem for differential-algebraic…

We study the Optimal Control Problem (OCP) for regular linear differential-algebraic systems (DAEs). To this end, we introduce the input index, which allows, on the one hand, to characterize the space of consistent initial values in terms…

This paper develops a fast numerical dual control for exploration and exploitation (DCEE) method to address auto-optimization problems in unknown environments. In auto-optimization problems, the optimal operating condition is unknown a…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

We study the modeling and simulation of gas pipeline networks, with a focus on fast numerical methods for the simulation of transient dynamics. The obtained mathematical model of the underlying network is represented by a nonlinear…

In this paper we construct an infinite horizon minimax state observer for a linear stationary differential-algebraic equation (DAE) with uncertain but bounded input and noisy output. We do not assume regularity or existence of a (unique)…

In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system…

Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are…

The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…

Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…

Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schr\"odinger equations. To relate N^2…

The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying…

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…

In radio frequency applications, electric circuits generate signals, which are amplitude modulated and/or frequency modulated. A mathematical modelling yields typically systems of differential algebraic equations (DAEs). A multivariate…

In in this paper we show how using D.A. it is found a simple change of variables (c.v.) that brings us to obtain differential equations simpler than the original one. In a pedagogical way (at least we try to do that) and in order to make…

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…

Denoising autoencoders (DAEs) have proven useful for unsupervised representation learning, but a thorough theoretical understanding is still lacking of how the input noise influences learning. Here we develop theory for how noise influences…

By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The…