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A mathematical model for anaerobic digestion in plug-flow reactors is proposed on the basis of mass balance considerations. The model consists of a system of parabolic partial differential equations for the variables representing the…
Trajectory prediction is a fundamental task in Autonomous Vehicles (AVs) and Intelligent Transportation Systems (ITS), supporting efficient motion planning and real-time traffic safety management. Diffusion models have recently demonstrated…
We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have…
Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and…
Adjoint-based design optimizations are usually computationally expensive and those costs scale with resolution. To address this, researchers have proposed machine learning approaches for inverse design that can predict higher-resolution…
Recent advances in motion diffusion models have substantially improved the realism of human motion synthesis. However, existing approaches either rely on full-sequence diffusion models with bidirectional generation, which limits temporal…
By performing molecular dynamics simulations with up to 132 million coarse-grained particles in half-micron sized boxes, we show that hydrodynamics quantitatively explains the finite-size effects on diffusion of lipids, proteins, and carbon…
Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In…
We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used…
In this paper we present a derivation and multiscale analysis of a mathematical model for plant cell wall biomechanics that takes into account both the microscopic structure of a cell wall coming from the cellulose microfibrils and the…
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared…
Continuum mathematical models for collective cell motion normally involve reaction-diffusion equations, such as the Fisher-KPP equation, with a linear diffusion term to describe cell motility and a logistic term to describe cell…
Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…
Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J.…
We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed…
Mathematical models of transport and reactions in biological systems have been traditionally written in terms of partial differential equations (PDEs) that describe the time evolution of population-level variables. In recent years, the use…
Continuous Conditional Generative Modeling (CCGM) estimates high-dimensional data distributions, such as images, conditioned on scalar continuous variables (aka regression labels). While Continuous Conditional Generative Adversarial…
Particle advection is the approach for extraction of integral curves from vector fields. Efficient parallelization of particle advection is a challenging task due to the problem of load imbalance, in which processes are assigned unequal…