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Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and…
Accurate parameter dependent electro-chemical numerical models for lithium-ion batteries are essential in industrial application. The exact parameters of each battery cell are unknown and a process of estimation is necessary to infer them.…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
In this paper we present new algorithms and analysis for the linear inverse sensor placement and scheduling problems over multiple time instances with power and communications constraints. The proposed algorithms, which deal directly with…
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…
The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic…
This paper presents a novel partitioning method designed to minimize control performance degradation resulting from partitioning a system for distributed control while maintaining the computational benefits of these methods. A…
We study the problem of multi-compression and reconstructing a stochastic signal observed by several independent sensors (or compressors) that transmit compressed information to a fusion center. { The key aspect of this problem is to find…
In the classical source coding problem, the compressed source is reconstructed at the decoder with respect to some distortion metric. Motivated by settings in which we are interested in more than simply reconstructing the compressed source,…
The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task has to be accomplished by modelling the relevant processes in the complex system made up of different…
Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of…
With the popularity of electric vehicles, the demand for lithium-ion batteries is increasing. Temperature significantly influences the performance and safety of batteries. Battery thermal management systems can effectively control the…