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In this report, we propose a divergence-free preserving mixed finite element method (FEM) for the system of nonlinear fourth-order thermally driven active fluid equations. By introducing two auxiliary variables, we lower the complexity of…
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…
High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…
Many routines that one might want to run on a quantum computer can benefit from adaptive circuits, relying on mid-circuit measurements and feed-forward operations. Any such measurement has to be compiled into a sequence of elementary gates…
Several techniques have appeared in the literatuare to solve the equations of time-dependent density functional theory. We compare the efficiency of different methods based on mesh representations of the wave function (direct and Fourier…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…
A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials…
With the rapid development of Deep Learning, more and more applications on the cloud and edge tend to utilize large DNN (Deep Neural Network) models for improved task execution efficiency as well as decision-making quality. Due to memory…
Traditional vision-based autonomous driving systems often face difficulties in navigating complex environments when relying solely on single-image inputs. To overcome this limitation, incorporating temporal data such as past image frames or…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
In this work, we derive two-sided a posteriori error estimates for the dual-weighted residual (DWR) method. We consider both single and multiple goal functionals. Using a saturation assumption, we derive lower bounds yielding the efficiency…
This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the…
The healthcare industry has a growing need for realistic modeling and efficient simulation of surgical scenes. With effective models of deformable surgical scenes, clinicians are able to conduct surgical planning and surgery training on…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
For adaptive mixed finite element methods (AMFEM), we first introduce the data oscillation to analyze, without the restriction that the inverse of the coefficient matrix of the partial differential equations (PDEs) is a piecewise polynomial…