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Since the first optimality proofs for adaptive mesh refinement algorithms in the early 2000s, the theory of optimal mesh refinement for PDEs was inherently limited to stationary problems. The reason for this is that time-dependent problems…
Predicting a potential collision with leading vehicles is an essential functionality of any autonomous/assisted driving system. One bottleneck of existing vision-based solutions is that their updating rate is limited to the frame rate of…
Our current understanding of interstellar carbon fractionation hinges on the interpretation of astrochemical kinetic models. Yet, the various reactions included carry large uncertainties in their (estimated) rate coefficients, notably those…
We consider numerical approximations for a phase field dendritic crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen-Cahn type equation and the heat equation together. We propose two efficient,…
Quantum evolution is crucial for the understanding of complex quantum systems. However, current implementations of time evolution on quantum photonic platforms are limited by both low photon generation efficiency and high propagation loss,…
A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…
The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…
We consider checkpointing strategies that minimize the number of recomputations needed when performing discrete adjoint computations using multistage time-stepping schemes, which requires computing several substeps within one complete time…
We address the problem of enumerating all temporal k-cores given a query time range and a temporal graph, which suffers from poor efficiency and scalability in the state-of-the-art solution. Motivated by an existing concept called core…
The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
The energy cost of computation has emerged as a central challenge at the intersection of physics and computer science. Recent advances in statistical physics -- particularly in stochastic thermodynamics -- enable precise characterizations…
It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced disispative evolution, inspired by existing models of…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to…
Iterative algorithms are widely used in digital signal processing applications. With the case study of radio astronomy calibration processing, this work contributes towards revealing and exploiting the intrinsic error resilience of…
A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several…
Power grid expansion planning requires making large investment decisions in the present that will impact the future cost and reliability of a system exposed to wide-ranging uncertainties. Extreme temperatures can pose significant challenges…
Energy loss through optically thin radiative cooling plays an important part in the evolution of astrophysical gas dynamics and should therefore be considered a necessary element in any numerical simulation. Although the addition of this…
In this work we adapt a prediction-correction algorithm for continuous time-varying convex optimization problems to solve dynamic programs arising from Model Predictive Control. In particular, the prediction step tracks the evolution of the…