Related papers: Probabilistic Constrained Optimization on Flow Net…
This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance…
We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
Reliable propagation of information through large networks, e.g., communication networks, social networks or sensor networks is very important in many applications concerning marketing, social networks, and wireless sensor networks.…
Many optimization problems incorporate uncertainty affecting their parameters and thus their objective functions and constraints. As an example, in chance-constrained optimization the constraints need to be satisfied with a certain…
When a fluid flows over a solid surface, it creates a thin boundary layer where the flow velocity is influenced by the surface through viscosity, and can transition from laminar to turbulent at sufficiently high speeds. Understanding and…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…
Predicting future states or actions of a given system remains a fundamental, yet unsolved challenge of intelligence, especially in the scope of complex and non-deterministic scenarios, such as modeling behavior of humans. Existing…
Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far are based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach,…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
Stochastic network design is a general framework for optimizing network connectivity. It has several applications in computational sustainability including spatial conservation planning, pre-disaster network preparation, and river network…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
We study dynamic network flows with uncertain input data under a robust optimization perspective. In the dynamic maximum flow problem, the goal is to maximize the flow reaching the sink within a given time horizon $T$, while flow requires a…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the…
Safety is a critical concern for the success of urban air mobility, especially in dynamic and uncertain environments. This paper proposes a path planning algorithm based on RRT in conjunction with chance constraints in the presence of…
We employ optimal control theory to study the problem of estimating the probability density function from a data set originating from an unknown probability distribution. The original variational problem is reformulated as a multi-stage…