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Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately…
We develop continuous-stage Runge-Kutta methods based on weighted orthogonal polynomials in this paper. There are two main highlighted merits for developing such methods: Firstly, we do not need to study the tedious solution of…
Reduced Rank Extrapolation (RRE) is a polynomial type method used to accelerate the convergence of sequences of vectors $\{\boldsymbol{x}_m\}$. It is applied successfully in different disciplines of science and engineering in the solution…
In order to solve continuous-time optimal control problems, direct methods transcribe the infinite-dimensional problem to a nonlinear program (NLP) using numerical integration methods. In cases where the integration error can be manipulated…
Regularization plays a crucial role in machine learning models, especially for deep neural networks. The existing regularization techniques mainly rely on the i.i.d. assumption and only consider the knowledge from the current sample,…
Video frame interpolation aims at synthesizing intermediate frames from nearby source frames while maintaining spatial and temporal consistencies. The existing deep-learning-based video frame interpolation methods can be roughly divided…
This paper considers a variational inequality (VI) problem arising from a game among multiple agents, where each agent aims to minimize its own cost function subject to its constrained set represented as the intersection of a (possibly…
We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics. The three main types of problems we…
Capturing the intricate multiscale features of turbulent flows remains a fundamental challenge due to the limited resolution of experimental data and the computational cost of high-fidelity simulations. In many practical scenarios only…
Rapid and accurate urban wind field prediction is essential for modeling particle transport in emergency scenarios. Traditional Computational Fluid Dynamics (CFD) approaches are too slow for real-time applications, necessitating surrogate…
In the last few years, several methods have been developed to deal with jump singularities in parametric or stochastic hyperbolic PDEs. They typically use some alignment of the jump-sets in physical space before performing well established…
Many recent successful (deep) reinforcement learning algorithms make use of regularization, generally based on entropy or Kullback-Leibler divergence. We propose a general theory of regularized Markov Decision Processes that generalizes…
We explore the problem of view synthesis from a narrow baseline pair of images, and focus on generating high-quality view extrapolations with plausible disocclusions. Our method builds upon prior work in predicting a multiplane image (MPI),…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
Finding well-defined clusters in data represents a fundamental challenge for many data-driven applications, and largely depends on good data representation. Drawing on literature regarding representation learning, studies suggest that one…
For singularly perturbed reaction-diffusion problems in 1D and 2D, we study a local discontinuous Galerkin (LDG) method on a Shishkin mesh. In these cases, the standard energy norm is too weak to capture adequately the behavior of the…
Recent advances in Image Restoration (IR) have been largely driven by generative methods such as Diffusion Models and Flow Matching, which excel in synthesizing realistic textures while suffering from slow multi-step inference and…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
For min-max optimization and variational inequalities problems (VIP) encountered in diverse machine learning tasks, Stochastic Extragradient (SEG) and Stochastic Gradient Descent Ascent (SGDA) have emerged as preeminent algorithms. Constant…
Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…