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High-performance scientific applications require more and more compute power. The concurrent use of multiple distributed compute resources is vital for making scientific progress. The resulting distributed system, a so-called Jungle…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or to by far too small time scales. To overcome this problem multiscale techniques are being…
Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems,…
Many physical problems involve spatial and temporal inhomogeneities that require a very fine discretization in order to be accurately simulated. Using an adaptive mesh, a high level of resolution is used in the appropriate areas while…
Multi-view learning primarily aims to fuse multiple features to describe data comprehensively. Most prior studies implicitly assume that different views share similar dimensions. In practice, however, severe dimensional disparities often…
This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
In this work, we provide a detailed theoretical analysis, supported by numerical tests, of the reliability of the adaptive resolution simulation (AdResS) technique in sampling the Grand Canonical ensemble. We demonstrate that the correct…
Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent…
We present an open-source, performant, pure-python molecular dynamics (MD) suite for non-ideal plasmas. The code, Sarkas, aims to accelerate the research process by providing an MD code but also pre- and post-processing tools. Sarkas offers…
Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret…
A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local…
Molecular dynamics (MD) simulations provide atomistic insights into the structure, dynamics, and function of biomolecules by generating time-resolved, high-dimensional trajectories. Analyzing such data benefits from estimating the minimal…
Super-resolution tasks oriented to images captured in ultra-dark environments is a practical yet challenging problem that has received little attention. Due to uneven illumination and low signal-to-noise ratio in dark environments, a…
With the rapid development of data-driven techniques, data has played an essential role in various computer vision tasks. Many realistic and synthetic datasets have been proposed to address different problems. However, there are lots of…
Solving optimization problems in which functions are blackboxes and variables involve different types poses significant theoretical and algorithmic challenges. Nevertheless, such settings frequently occur in simulation-based engineering…
Machine learning has emerged as a transformative tool for solving differential equations (DEs), yet prevailing methodologies remain constrained by dual limitations: data-driven methods demand costly labeled datasets while model-driven…
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…