Related papers: Bring the Heat: Rapid Trajectory Optimization with…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
Predicting effective thermal conductivity by solving a Partial Differential Equation (PDE) defined on a high-resolution Representative Volume Element (RVE) is a computationally intensive task. In this paper, we tackle the task by proposing…
This paper introduces a novel numerical approach to achieving smooth lane-change trajectories in autonomous driving scenarios. Our trajectory generation approach leverages particle swarm optimization (PSO) techniques, incorporating Neural…
We propose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and…
Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in…
It is well known that closed-form analytical solutions for AC power flow equations do not exist in general. This paper proposes a multi-dimensional holomorphic embedding method (MDHEM) to obtain an explicit approximate analytical AC…
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…
This study compares different methods to predict the simultaneous effects of conductive and radiative heat transfer in a Polymethylmethacrylate (PMMA) sample. PMMA is a kind of polymer utilized in various sensors and actuator devices.…
Three kinds of Fragile Points Methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up of the previous study on the original FPM based…
As a core part of autonomous driving systems, motion planning has received extensive attention from academia and industry. However, real-time trajectory planning capable of spatial-temporal joint optimization is challenged by nonholonomic…
To make relevant predictions about observable emission, hydrodynamical simulation codes must employ schemes that account for radiative losses, but the large dimensionality of accurate radiative transfer schemes is often prohibitive.…
In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on the state and/or control variables. We develop an…
We consider two steady-state heat conduction systems called, $S$ and $S_\alpha$, in a multidimensional bounded domain $D$ for the Poisson equation with source energy $g$. In one system, we impose mixed boundary conditions (temperature $b$…
This paper presents a novel physics-infused reduced-order modeling (PIROM) methodology for efficient and accurate modeling of non-linear dynamical systems. The PIROM consists of a physics-based analytical component that represents the known…
Astrophysical plasmas in relativistic spacetimes, such as black hole accretion flows, are often weakly collisional and require kinetic modeling to capture non-local transport and particle acceleration. However, the extreme scale separation…
Closed-loop shallow geothermal systems are one of the key technologies for decarbonizing the residential heating and cooling sector. The primary type of these systems involves vertical borehole heat exchangers (BHEs). During the planning…
We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of…
Computational Fluid Dynamics (CFD) simulations are essential for analyzing and optimizing fluid flows in a wide range of real-world applications. These simulations involve approximating the solutions of the Navier-Stokes differential…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
Context. The magnetic field in the solar atmosphere continually reconnects and accelerates charged particles to high energies. Simulations of the atmosphere in three dimensions that include the effects of accelerated particles can aid our…