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Understanding interphase mass transfer is essential for a variety of applications in porous media, ranging from groundwater remediation to geologic energy storage. While X-ray micro-Computed Tomography (microCT) provides critical in situ…
Random walks (or Markov chains) are models extensively used in theoretical computer science. Several tools, including analysis of quantities such as hitting and mixing times, are helpful for devising randomized algorithms. A notable example…
The ability to quantify the directional flow of information is vital to understanding natural systems and designing engineered information-processing systems. A widely used measure to quantify this information flow is the transfer entropy.…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for…
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…
For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front,…
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
We present a novel, realtime algorithm to compute the trajectory of each pedestrian in moderately dense crowd scenes. Our formulation is based on an adaptive particle filtering scheme that uses a multi-agent motion model based on…
Given a demonstration of a complex manipulation task, such as pouring liquid from one container to another, we seek to generate a motion plan for a new task instance involving objects with different geometries. This is nontrivial since we…
Outer sphere electron transfer rates can be calculated from simulation data by sampling the equilibrium statistics of the canonical reaction coordinate -- the vertical energy gap. For these calculations, electron transfer is typically…
Classical paradigms for distributed learning, such as federated or decentralized gradient descent, employ consensus mechanisms to enforce homogeneity among agents. While these strategies have proven effective in i.i.d. scenarios, they can…
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard…
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
Distributed-memory matrix multiplication (MM) is a key element of algorithms in many domains (machine learning, quantum physics). Conventional algorithms for dense MM rely on regular/uniform data decomposition to ensure load balance. These…
The correspondence between the telegraph random process and transport within a binary stochastic Markovian mixture is established. This equivalence is used to derive the distribution function for the transit length, defined as the distance…
Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the…