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In this work we consider the Allen--Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifurcation parameter. Going beyond the state-of-the-art, we…
The understanding of geographical reality is a process of data representation and pattern discovery. Former studies mainly adopted continuous-field models to represent spatial variables and to investigate the underlying spatial…
Input variables in numerical models are often subject to several levels of uncertainty, usually modeled by probability distributions. In the context of uncertainty quantification applied to these models, studying the robustness of output…
In this paper, we proposed a non-uniform power delivery network (PDN) synthesis methodology. It first constructs initial PDN using uniform approach. Then preliminary power integrity analysis is performed to derive IR-safe candidate window.…
In today's era of smart cyber-physical systems, Deep Neural Networks (DNNs) have become ubiquitous due to their state-of-the-art performance in complex real-world applications. The high computational complexity of these networks, which…
This manuscript deals with the analysis of numerical methods for the full discretization (in time and space) of the linear heat equation with Neumann boundary conditions, and it provides the reader with error estimates that are uniform in…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
In the numerical simulation of ideal MHD, keeping the pressure and density positive is essential for both physical considerations and numerical stability. This is a challenge, due to the underlying relation between such…
In the critical task of making generative models trustworthy and robust, methods for Uncertainty Quantification (UQ) have begun to show encouraging potential. However, many of these methods rely on rigid heuristics that fail to generalize…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
Nielsen's geometric approach to quantum circuit complexity provides a Riemannian framework for quantifying the cost of implementing unitary (closed--system) dynamics. For open dynamics, however, the reduced evolution is described by quantum…
The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently…
An undirected weighted graph (UWG) is frequently adopted to describe the interactions among a solo set of nodes from real applications, such as the user contact frequency from a social network services system. A graph convolutional network…
Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…
This paper presents a highly efficient implicit unified gas-kinetic particle (IUGKP) method for obtaining steady-state solutions of multi-scale phonon transport. The method adapts and reinterprets the integral solution of the BGK equation…
In this work we describe the Correlative Method of Unsymmetrized Self-Consistent Field (CUSF). This method is based on a set of nonlinear integrodifferential equations for the one-particle configurational distribution functions and for the…
Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the…
The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive…
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling by a cost function. Although this problem is inherently…
The present work stemmed from the study of the problem of harmonic analysis on the infinite-dimensional unitary group U(\infty). That problem consisted in the decomposition of a certain 4-parameter family of unitary representations, which…