3,609 research outputs found
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
We introduce a derivative-free computational framework for approximating
solutions to nonlinear PDE-constrained inverse problems. The aim is to merge
ideas from iterative regularization with ensemble Kalman methods from Bayesian
inference to develop a derivative-free stable method easy to implement in
applications where the PDE (forward) model is only accessible as a black box.
The method can be derived as an approximation of the regularizing
Levenberg-Marquardt (LM) scheme [14] in which the derivative of the forward
operator and its adjoint are replaced with empirical covariances from an
ensemble of elements from the admissible space of solutions. The resulting
ensemble method consists of an update formula that is applied to each ensemble
member and that has a regularization parameter selected in a similar fashion to
the one in the LM scheme. Moreover, an early termination of the scheme is
proposed according to a discrepancy principle-type of criterion. The proposed
method can be also viewed as a regularizing version of standard Kalman
approaches which are often unstable unless ad-hoc fixes, such as covariance
localization, are implemented. We provide a numerical investigation of the
conditions under which the proposed method inherits the regularizing properties
of the LM scheme of [14]. More concretely, we study the effect of ensemble
size, number of measurements, selection of initial ensemble and tunable
parameters on the performance of the method. The numerical investigation is
carried out with synthetic experiments on two model inverse problems: (i)
identification of conductivity on a Darcy flow model and (ii) electrical
impedance tomography with the complete electrode model. We further demonstrate
the potential application of the method in solving shape identification
problems by means of a level-set approach for the parameterization of unknown
geometries
Transform-based particle filtering for elliptic Bayesian inverse problems
We introduce optimal transport based resampling in adaptive SMC. We consider
elliptic inverse problems of inferring hydraulic conductivity from pressure
measurements. We consider two parametrizations of hydraulic conductivity: by
Gaussian random field, and by a set of scalar (non-)Gaussian distributed
parameters and Gaussian random fields. We show that for scalar parameters
optimal transport based SMC performs comparably to monomial based SMC but for
Gaussian high-dimensional random fields optimal transport based SMC outperforms
monomial based SMC. When comparing to ensemble Kalman inversion with mutation
(EKI), we observe that for Gaussian random fields, optimal transport based SMC
gives comparable or worse performance than EKI depending on the complexity of
the parametrization. For non-Gaussian distributed parameters optimal transport
based SMC outperforms EKI
Stochastic Model Predictive Control for Autonomous Mobility on Demand
This paper presents a stochastic, model predictive control (MPC) algorithm
that leverages short-term probabilistic forecasts for dispatching and
rebalancing Autonomous Mobility-on-Demand systems (AMoD, i.e. fleets of
self-driving vehicles). We first present the core stochastic optimization
problem in terms of a time-expanded network flow model. Then, to ameliorate its
tractability, we present two key relaxations. First, we replace the original
stochastic problem with a Sample Average Approximation (SAA), and characterize
the performance guarantees. Second, we separate the controller into two
separate parts to address the task of assigning vehicles to the outstanding
customers separate from that of rebalancing. This enables the problem to be
solved as two totally unimodular linear programs, and thus easily scalable to
large problem sizes. Finally, we test the proposed algorithm in two scenarios
based on real data and show that it outperforms prior state-of-the-art
algorithms. In particular, in a simulation using customer data from DiDi
Chuxing, the algorithm presented here exhibits a 62.3 percent reduction in
customer waiting time compared to state of the art non-stochastic algorithms.Comment: Submitting to the IEEE International Conference on Intelligent
Transportation Systems 201
On the interaction between Autonomous Mobility-on-Demand systems and the power network: models and coordination algorithms
We study the interaction between a fleet of electric, self-driving vehicles
servicing on-demand transportation requests (referred to as Autonomous
Mobility-on-Demand, or AMoD, system) and the electric power network. We propose
a model that captures the coupling between the two systems stemming from the
vehicles' charging requirements and captures time-varying customer demand and
power generation costs, road congestion, battery depreciation, and power
transmission and distribution constraints. We then leverage the model to
jointly optimize the operation of both systems. We devise an algorithmic
procedure to losslessly reduce the problem size by bundling customer requests,
allowing it to be efficiently solved by off-the-shelf linear programming
solvers. Next, we show that the socially optimal solution to the joint problem
can be enforced as a general equilibrium, and we provide a dual decomposition
algorithm that allows self-interested agents to compute the market clearing
prices without sharing private information. We assess the performance of the
mode by studying a hypothetical AMoD system in Dallas-Fort Worth and its impact
on the Texas power network. Lack of coordination between the AMoD system and
the power network can cause a 4.4% increase in the price of electricity in
Dallas-Fort Worth; conversely, coordination between the AMoD system and the
power network could reduce electricity expenditure compared to the case where
no cars are present (despite the increased demand for electricity) and yield
savings of up $147M/year. Finally, we provide a receding-horizon implementation
and assess its performance with agent-based simulations. Collectively, the
results of this paper provide a first-of-a-kind characterization of the
interaction between electric-powered AMoD systems and the power network, and
shed additional light on the economic and societal value of AMoD.Comment: Extended version of the paper presented at Robotics: Science and
Systems XIV and accepted by TCNS. In Version 4, the body of the paper is
largely rewritten for clarity and consistency, and new numerical simulations
are presented. All source code is available (MIT) at
https://dx.doi.org/10.5281/zenodo.324165
Interfacce uomo-macchina nella realtà virtuale
Questo capitolo fornisce una descrizione dei principali elementi che influenzano l'interazione uomo-macchina in riferimento alla realtà virtuale, per come si configurano attualmente, e per come si prevede si svilupperanno in un prossimo futuro. Il capitolo è organizzato nel modo seguente: la sezione 1.1 presenta il concetto di realtà virtuale soprattutto in relazione alle possibilità offerte per quanto riguarda l’interazione tra uomo e macchina, ed alle applicazioni di nuova generazione. La sezione successiva descrive i principali requisiti ed i vincoli che un sistema di realtà virtuale deve soddisfare per riuscire a fornire all’utente un’impressione convincente e delle esperienze realmente immersive. La sezione 1.3 si concentra sul feedback sensoriale principale, descrivendo le principali tecnologie di nuova generazione per la realizzazione di dispositivi in grado di fornire delle sensazioni visive e tattili estremamente realistiche. Infine la sezione 1.4 descrive brevemente alcuni esempi di applicazioni di realtà virtuale realizzate dagli autori, nel campo della simulazione chirurgica, dei musei virtuali e dei sistemi di visualizzazione autostereoscopici multiutente, e la sezione 1.5 discute brevemente la situazione attuale ed il potenziale futuro della disciplina.289-33
A Bayesian level set method for geometric inverse problems
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the object of the inference. Whilst the level set methodology has been widely used for the solution of geometric inverse problems, the Bayesian formulation that we develop here contains two significant advances: firstly it leads to a well-posed inverse problem in which the posterior distribution is Lipschitz with respect to the observed data, and may be used to not only estimate interface locations, but quantify uncertainty in them; and secondly it leads to computationally expedient algorithms in which the level set itself is updated implicitly via the MCMC methodology applied to the level set function – no explicit velocity field is required for the level set interface. Applications are numerous and include medical imaging, modelling of subsurface formations and the inverse source problem; our theory is illustrated with computational results involving the last two applications
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