Related papers: Differential-Equation Constrained Optimization Wit…
Taking uncertainty into account is crucial when making strategic decisions. To guard against the risk of adverse scenarios, traditional optimisation techniques incorporate uncertainty on the basis of prior knowledge on its distribution. In…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
Stochastic optimization problems are generally known to be ill-conditioned to the form of the underlying uncertainty. A framework is introduced for optimal control problems with partial differential equations as constraints that is robust…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation…
Distribution shifts have long been regarded as troublesome external forces that a decision-maker should either counteract or conform to. An intriguing feedback phenomenon termed decision dependence arises when the deployed decision affects…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…