相关论文: HAZniCS -- Software Components for Multiphysics Pr…
MiMiC is a framework for performing multiscale simulations in which loosely coupled external programs describe individual subsystems at different resolutions and levels of theory. To make it highly efficient and flexible, we adopt an…
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…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In…
We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…
In the present work, advanced spatial and temporal discretization techniques are tailored to hyperelastic physics-augmented neural networks, i.e., neural network based constitutive models which fulfill all relevant mechanical conditions of…
Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with multiple solutions is a challenging task. To address this, we…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomena. A significant portion of researcher time is typically dedicated to the development of…
The convergence of cross-modal adversarial learning and physics-driven methods represents a cutting-edge direction for tackling challenges in complex multi-modal tasks and scientific computing. This review focuses on systematically…
Recently, computational modeling has shifted towards the use of deep learning, and other data-driven modeling frameworks. Although this shift in modeling holds promise in many applications like design optimization and real-time control by…
Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be…
This study established a quantum-classical hybrid framework that integrates quantum computing paradigm with meshfree finite particle method. By harnessing quantum superposition and entanglement, it hybridized the critical computational…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…
In this study, we introduce general frame of MAny Connected Intelligent Particles Systems (MACIPS). Connections and interconnections between particles get a complex behavior of such merely simple system (system in system).Contribution of…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering…
MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods…
Simflowny is an open platform which automatically generates efficient parallel code of scientific dynamical models for different simulation frameworks. Here we present major upgrades on this software to support simultaneously a quite…