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We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value…
Self-stabilization ensures that, after any transient fault, the system recovers in a finite time and eventually exhibits a correct behaviour. Speculation consists in guaranteeing that the system satisfies its requirements for any execution…
The two-step time discretization proposed by Dahlquist, Liniger and Nevanlinna is variable step $G$-stable. (In contrast, for increasing time steps, the BDF2 method loses $A$-stability and suffers non-physical energy growth in the…
We introduce two models of industrial drying - a simplified one-equation model, and a detailed three-equation model. The purpose of the simplified model is rigorous validation of numerical methods for PDE-constrained optimal control. The…
In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities and/or small time steps. We consider different…
The paper proposes an algorithm for a discretization (sampled-time implementation) of a homogeneous control preserving the finite-time and nearly fixed-time stability property of the original (sampling-free) system. The sampling period is…
This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…
This paper discusses discretization methods for implementing nonlinear model predictive controllers using Iterative Linear Quadratic Regulator (ILQR). Finite-difference approximations are mostly used to derive a discrete-time state equation…
In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for…
We consider the dynamics of a parabolic and a hyperbolic equation coupled on a common interface and develop time-stepping schemes that can use different time-step sizes for each of the subproblems. The problem is formulated in a strongly…
We present a new method for developing time step controllers based on a technique from the field of machine learning. This method is applicable to stable time integrators that have an embedded scheme, i.e., that have local error estimation…
We construct a higher-order adaptive method for strong approximations of exit times of It\^o stochastic differential equations (SDE). The method employs a strong It\^o--Taylor scheme for simulating SDE paths, and adaptively decreases the…
Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…
We present a numerical method for convergence acceleration for multifidelity models of parameterized ordinary differential equations. The hierarchy of models is defined as trajectories computed using different timesteps in a time…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…
Modeling time series is a research focus in cryospheric sciences because of the complexity and multiscale nature of events of interest. Highly non-uniform sampling of measurements from different sensors with different levels of accuracy, as…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretisation and a stochastic trigonometric scheme for the temporal…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…