Related papers: A hybrid combinatorial-continuous strategy for sol…
Particulate matter (PM) is a class of malicious environmental pollutants known to be detrimental to human health. Regulatory efforts aimed at curbing PM levels in different countries often require high resolution space-time maps that can…
In this article, we present a three-dimensional anisotropic $hp$-mesh refinement strategy for ultraweak discontinuous Petrov--Galerkin (DPG) formulations with optimal test functions. The refinement strategy utilizes the built-in…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
In this article, a new unified duality theory is developed for Petrov-Galerkin finite element methods. This novel theory is then used to motivate goal-oriented adaptive mesh refinement strategies for use with discontinuous Petrov-Galerkin…
The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…
Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian…
In this paper we present a new multiscale discontinuous Petrov--Galerkin method (MsDPGM) for multiscale elliptic problems. This method utilizes the classical oversampling multiscale basis in the framework of Petrov--Galerkin version of…
This paper presents a hybrid trajectory optimization method designed to generate collision-free, smooth trajectories for autonomous mobile robots. By combining sampling-based Model Predictive Path Integral (MPPI) control with gradient-based…
We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
Motivation: Structure-based drug design (SBDD) has advanced with deep generative models, but bridging the gap between continuous atomic coordinates and discrete atom types remains a challenge. Current approaches, such as diffusion and flow…
Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…
This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional…
We consider evidence integration from potentially dependent observation processes under varying spatio-temporal sampling resolutions and noise levels. We develop a multi-resolution multi-task (MRGP) framework while allowing for both…
Protein flexibility is crucial for understanding protein structures, functions, and dynamics, and it can be measured through experimental methods such as X-ray crystallography. Theoretical approaches have also been developed to predict…
Sequential assembly with geometric primitives has drawn attention in robotics and 3D vision since it yields a practical blueprint to construct a target shape. However, due to its combinatorial property, a greedy method falls short of…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…
The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present…
We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a…