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Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here,…

A central task in many applications is reasoning about processes that change in a continuous time. The mathematical framework of Continuous Time Markov Processes provides the basic foundations for modeling such systems. Recently, Nodelman…

We present a new class of equivariant neural networks, hereby dubbed Lattice-Equivariant Neural Networks (LENNs), designed to satisfy local symmetries of a lattice structure. Our approach develops within a recently introduced framework…

Spiking Neural Networks (SNNs) hold great potential to realize brain-inspired, energy-efficient computational systems. However, current SNNs still fall short in terms of multi-scale temporal processing compared to their biological…

We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles…

Simulation of fluid flow in porous media has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of flow in porous media…

Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional…

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

The transient time correlation function method (TTCF) has emerged as a powerful methodology for accurately probing systems at low shear rates. In the present study, TTCF was used to evaluate the shear rate dependence of the slip length in a…

At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…

Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic…

Combining discrete and continuous data is an important capability for generative models. We present Discrete Flow Models (DFMs), a new flow-based model of discrete data that provides the missing link in enabling flow-based generative models…

We investigate the behavior of the slip length in Newtonian liquids subject to planar shear bounded by substrates with mixed boundary conditions. The upper wall, consisting of a homogenous surface of finite or vanishing slip, moves at a…

Steady-state electrothermal systems involve strongly coupled heat transfer, fluid flow, and electric-potential transport, creating severe numerical challenges for standard physics-informed neural networks (PINNs) due to stark disparities in…

We consider the stochastic dynamics of an array of two closely spaced atomic force microscope cantilevers in a viscous fluid for use as a possible biomolecule sensor. The cantilevers are not driven externally, as is common in applications…

Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for…

A new consistent, spatially adaptive, smoothed particle hydrodynamics (SPH) method for Fluid-Structure Interactions (FSI) is presented. The method combines several attributes that have not been simultaneously satisfied by other SPH methods.…

Stellar streams retain a memory of their gravitational interactions with small-scale perturbations. While perturbative models for streams have been formulated in action-angle coordinates, a direct transformation to these coordinates is only…

We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under non-negativity assumptions of covariance functions and some further minor conditions, we show that the asymptotic behaviour of…

We present TTCF4LAMMPS, a toolkit for performing non-equilibrium molecular dynamics (NEMD) simulations to study fluid behaviour at low shear rates using the LAMMPS software. By combining direct NEMD simulations and the transient-time…