Related papers: Optimal use of time dependent probability density …
We propose a formalism for extracting molecular Hamiltonian structure from inversion of time-dependent fluorescence intensity data. The proposed method requires a minimum of \emph{a priori} knowledge about the system and allows for…
From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be…
Efficient extraction of useful knowledge from these data is still a challenge, mainly when the data is distributed, heterogeneous and of different quality depending on its corresponding local infrastructure. To reduce the overhead cost,…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
Deep Learning (DL), in particular deep neural networks (DNN), by default is purely data-driven and in general does not require physics. This is the strength of DL but also one of its key limitations when applied to science and engineering…
This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain and small or zero outside. It is well known that Tikhonov…
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…
We present an algorithm based on maximum likelihood for the estimation and renormalization (marginalization) of exponential densities. The moment-matching problem resulting from the maximization of the likelihood is solved as an…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…
We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover a function from given observations where the function or the data depend on time.…
In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
Inversion of electromagnetic data finds applications in many areas of geophysics. The inverse problem is commonly solved with either deterministic optimization methods (such as the nonlinear conjugate gradient or Gauss-Newton) which are…
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the…
Intermittent renewable energy resources like wind and solar pose great uncertainty of multiple time scales, from minutes to years, on the design and operation of power systems. Energy system optimization models have been developed to find…
We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and…
With the rising number of machine learning competitions, the world has witnessed an exciting race for the best algorithms. However, the involved data selection process may fundamentally suffer from evidence ambiguity and concept drift…
The inverse problem of Kohn-Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the…
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…