Related papers: Linear ordinary differential equations constrained…
Optimization of problems with high computational power demands is a challenging task. A probabilistic approach to such optimization called Bayesian optimization lowers performance demands by solving mathematically simpler model of the…
We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…
We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with…
By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…
Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on…
We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly…
To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…
Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural networks parameterize the velocity fields. This paper…
We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
Unpredictable and complex aerodynamic effects pose significant challenges to achieving precise flight control, such as the downwash effect from upper vehicles to lower ones. Conventional methods often struggle to accurately model these…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…
Pharmacokinetic modeling using ordinary differential equations (ODEs) has an important role in dose optimization studies, where dosing must balance sustained therapeutic efficacy with the risk of adverse side effects. Such ODE models…
Algorithmic approach to the problem of linearization by point transformation of ordinary differential equation of arbitrary order is presented. Test-linearization is purely algorithmic.
Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies.…