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Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…
A key strategy for balancing performance and cost in modern machine learning systems is to dynamically route queries to either a low-cost model or a more expensive oracle (such as a large pretrained model or human expert), an approach known…
To find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, such that a consistent system is asymptotically…
Energy systems modellers often resort to simplified system representations and deterministic model formulations (i.e., not considering uncertainty) to preserve computational tractability. However, reduced levels of detail and neglected…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The conformal mapping $w=\sqrt{z}$ in the complex plane is used…
Dynamic neural networks are a recent technique that promises a remedy for the increasing size of modern deep learning models by dynamically adapting their computational cost to the difficulty of the inputs. In this way, the model can adjust…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
In safety-critical applications like medical diagnosis, certainty associated with a model's prediction is just as important as its accuracy. Consequently, uncertainty estimation and reduction play a crucial role. Uncertainty in predictions…
This review article focuses on regularised estimation procedures applicable to geostatistical and spatial econometric models. These methods are particularly relevant in the case of big geospatial data for dimensionality reduction or model…
In the past few years, following the differentiable programming paradigm, there has been a growing interest in computing the gradient information of physical processes (e.g., physical simulation, image rendering). However, such processes…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as…
Reinforcement Learning has applications in field of mechatronics, robotics, and other resource-constrained control system. Problem of resource allocation is primarily solved using traditional predefined techniques and modern deep learning…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
Crowd counting from unconstrained scene images is a crucial task in many real-world applications like urban surveillance and management, but it is greatly challenged by the camera's perspective that causes huge appearance variations in…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…