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Meshfree particle methods, such as Smoothed Particle Hydrodynamics (SPH) and the Moving Particle Semi-Implicit (MPS) method, are widely used to simulate complex free-surface and multiphase flows. A key challenge in these methods is the…
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…
Real-time vision-based system of fault detection (RVBS-FD) for freight trains is an essential part of ensuring railway transportation safety. Most existing vision-based methods still have high computational costs based on convolutional…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
The ever-increasing demand for processing data with larger machine learning models requires more efficient hardware solutions due to limitations such as power dissipation and scalability. Optics is a promising contender for providing lower…
In the paper, we present an integrated data-driven modeling framework based on process modeling, material homogenization, mechanistic machine learning, and concurrent multiscale simulation. We are interested in the injection-molded short…
Peridynamics (PD), as a nonlocal theory, is well-suited for solving problems with discontinuities, such as cracks. However, the nonlocal effect of peridynamics makes it computationally expensive for dynamic fracture problems in large-scale…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
Despite great successes, model predictive control (MPC) relies on an accurate dynamical model and requires high onboard computational power, impeding its wider adoption in engineering systems, especially for nonlinear real-time systems with…
Recent years have seen many successful applications of machine learning (ML) to facilitate fluid dynamic computations. As simulations grow, generating new training datasets for traditional offline learning creates I/O and storage…
The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we…
Fast algorithms for the computation of $N$-body problems can be broadly classified into mesh-based interpolation methods, and hierarchical or multiresolution methods. To this last class belongs the well-known fast multipole method (FMM),…
Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…
Data-driven modal decompositions are useful tools for compressing data or identifying dominant structures. Popular ones like the dynamic mode decomposition (DMD) and the proper orthogonal decomposition (POD) are defined with continuous…
Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given…
Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a…
The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop…
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…