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We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that…

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…

The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. While constraints are popular for modeling and solving, the approaches to learning constraints from data remain…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…

This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…

Many scientific and engineering applications are formulated as inverse problems associated with stochastic models. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…

Nuclear quantum many-body methods rely on integral transform techniques to infer properties of electroweak response functions from ground-state expectation values. Retrieving the energy dependence of these responses is highly non-trivial,…

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

Deep neural networks (DNN) are versatile parametric models utilised successfully in a diverse number of tasks and domains. However, they have limitations---particularly from their lack of robustness and over-sensitivity to out of…

We consider a data-driven newsvendor problem, where one has access to past demand data and the associated feature information. We solve the problem by estimating the target quantile function using a deep neural network (DNN). The remarkable…

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schr\"odinger equation, where the control variable…

There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…

We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…

In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…

In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…