Related papers: Bring the Heat: Rapid Trajectory Optimization with…

In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as…

We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms…

This paper presents a numerical solver for computing continuous trajectories in non-convex environments. Our approach relies on a customized implementation of the Alternating Direction Method of Multipliers (ADMM) built upon two key…

In this study, a smoothed particle hydrodynamics (SPH) model that applies a segment-based boundary treatment is used to simulate natural convection. In a natural convection simulated using an SPH model, the wall boundary treatment is a…

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately,…

Autonomous space systems operating in extreme thermal environments require accurate and efficient thermal modeling to support both pre-mission system design and onboard autonomy. For lunar rovers, large temperature gradients, radiative heat…

Enforcing safety while preventing overly conservative behaviors is essential for autonomous vehicles to achieve high task performance. In this paper, we propose a barrier-enhanced parallel homotopic trajectory optimization (BPHTO) approach…

We consider the steady heat transfer between a collection of impermeable obstacles immersed in an incompressible 2D potential flow, when each obstacle has a prescribed boundary temperature distribution. Inside the fluid, the temperature…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

Thermal Energy Storage (TES) using Phase Change Materials (PCMs) represents a critical technology for sustainable energy management and grid stability. This study presents a novel Physics-Driven Deep Learning (PDDL) framework for modeling…

Path planning is critical for autonomous driving, generating smooth, collision-free, feasible paths based on perception and localization inputs. However, its computationally intensive nature poses significant challenges for…

Current approaches to scheduling workloads on heterogeneous systems with specialized accelerators often rely on manual partitioning, offloading tasks with specific compute patterns to accelerators. This method requires extensive…

ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate…

One of the fundamental tasks of autonomous driving is safe trajectory planning, the task of deciding where the vehicle needs to drive, while avoiding obstacles, obeying safety rules, and respecting the fundamental limits of road. Real-world…

We propose in this paper a motion planning method for legged robot locomotion based on Geometric Heat Flow framework. The motion planning task is challenging due to the hybrid nature of dynamics and contact constraints. We encode the hybrid…

We generalize ideas in the recent literature and develop new ones in order to propose a general class of contour integral methods for linear convection-diffusion PDEs and in particular for those arising in finance. These methods aim to…

We study a scenario where an aircraft has multiple heterogeneous sensors collecting measurements to track a target vehicle of unknown location. The measurements are sampled along the flight path and our goals to optimize sensor placement to…

We present a method to approximate pairwise distance on a graph, having an amortized sub-linear complexity in its size. The proposed method follows the so called heat method due to Crane et al. The only additional input are the values of…