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We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…
Understanding material failure is critical for designing stronger and lighter structures by identifying weaknesses that could be mitigated. Existing full-physics numerical simulation techniques involve trade-offs between speed, accuracy,…
Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in…
We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the…
Morphing materials allow us to create new modalities of interaction and fabrication by leveraging dynamic behaviors of materials. Yet, despite the ongoing rapid growth of computational tools within this realm, current developments are…
In this study, we investigate the problem of tracking objects with unknown shapes using three-dimensional (3D) point cloud data. We propose a Gaussian process-based model to jointly estimate object kinematics, including position,…
Achieving high-precision light manipulation is crucial for delivering information through complex media with high fidelity. However, existing spatial light modulation devices face a fundamental tradeoff between speed and accuracy. Digital…
The quality of plastic parts produced through injection molding depends on many factors. Especially during the filling stage, defects such as weld lines, burrs, or insufficient filling can occur. Numerical methods need to be employed to…
In modern computer vision, the optimal representation of 3D shape continues to be task-dependent. One fundamental operation applied to such representations is differentiable rendering, as it enables inverse graphics approaches in learning…
Rolling bearings are subject to various faults due to its long-time operation under harsh environment, which will lead to unexpected breakdown of machinery system and cause severe accidents. Deep learning methods recently have gained…
We present a new paradigm for creating random features to approximate bi-variate functions (in particular, kernels) defined on general manifolds. This new mechanism of Manifold Random Features (MRFs) leverages discretization of the manifold…
Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a…
Graphical models have found widespread applications in many areas of modern statistics and machine learning. Iterative Proportional Fitting (IPF) and its variants have become the default method for undirected graphical model estimation, and…
In industrial settings, surface defects on steel can significantly compromise its service life and elevate potential safety risks. Traditional defect detection methods predominantly rely on manual inspection, which suffers from low…
The key task of physical simulation is to solve partial differential equations (PDEs) on discretized domains, which is known to be costly. In particular, high-fidelity solutions are much more expensive than low-fidelity ones. To reduce the…
We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…
Articulated objects pose diverse manipulation challenges for robots. Since their internal structures are not directly observable, robots must adaptively explore and refine actions to generate successful manipulation trajectories. While…
The free-form deformation model can represent a wide range of non-rigid deformations by manipulating a control point lattice over the image. However, due to a large number of parameters, it is challenging to fit the free-form deformation…
Traditional sheet metal forming relies on time-consuming and expensive Finite Element Analysis (FEA) for design validation, a process that significantly prolongs design cycles. While surrogate models offer faster iteration, current…
Neural Radiance Fields (NeRFs) have become a rapidly growing research field with the potential to revolutionize typical photogrammetric workflows, such as those used for 3D scene reconstruction. As input, NeRFs require multi-view images…