Related papers: The Research and Optimization of Parallel Finite E…
Important computational physics problems are often large-scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly address these problems. However, it is no trivial task to…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called…
Kernel machines often yield superior predictive performance on various tasks; however, they suffer from severe computational challenges. In this paper, we show how to overcome the important challenge of speeding up kernel machines. In…
We present the first rigorous convergence analysis of the smoothed adaptive finite element method (S-AFEM) proposed in [Mulita, Giani, Heltai: SIAM J. Sci. Comput. 43, 2021]. S-AFEM modifies the classical adaptive finite element method…
We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the…
Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…
In our recently proposed Integrated Finite Element Neural Network (I-FENN) framework (Pantidis and Mobasher, 2023) we showcased how PINNs can be deployed on a finite element-level basis to swiftly approximate a state variable of interest,…
Fully Homomorphic Encryption (FHE) imposes substantial memory bandwidth demands, presenting significant challenges for efficient hardware acceleration. Near-memory Processing (NMP) has emerged as a promising architectural solution to…
The mixture-of-experts (MoE) architecture scales model size with sublinear computational increase but suffers from memory-intensive inference due to KV caches and sparse expert activation. Recent disaggregated expert parallelism (DEP)…
A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward…
We compare the Finite Element Method (FEM) simulation of a standard Partial Differential Equation thermal problem of a plate with a hole with a Neural Network (NN) simulation. The largest deviation from the true solution obtained from FEM…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
Improvements in computer systems have historically relied on two well-known observations: Moore's law and Dennard's scaling. Today, both these observations are ending, forcing computer users, researchers, and practitioners to abandon the…
Numerical modeling of slope failures seeks to predict two key phenomena: the initiation of failure and the post-failure runout. Currently, most modeling methods for slope failure analysis excel at one of these two but are deficient in the…
The exponential growth of Internet of Things (IoT) applications has intensified the demand for efficient, high-throughput, and energy-efficient data processing at the edge. Conventional CPU-centric encryption methods suffer from performance…
In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across…
Several manufacturers have already started to commercialize near-bank Processing-In-Memory (PIM) architectures. Near-bank PIM architectures place simple cores close to DRAM banks and can yield significant performance and energy improvements…
Estimating parameters of Partial Differential Equations (PDEs) is of interest in a number of applications such as geophysical and medical imaging. Parameter estimation is commonly phrased as a PDE-constrained optimization problem that can…