More Like this

1. Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling

   https://doi.org/https://doi.org/10.1016/j.jaerosci.2021.105746  

   Suresh, Vikram; Gopalakrishnan, Ranganathan (February 2021, Journal of aerosol science)

   null (Ed.)

   The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Potential applications and caveats to the usage of LD are included as a summary. 

   more » « less
2. On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it

   https://doi.org/10.1093/imaiai/iaae018  

   García_Trillos, Camilo Andrés; García_Trillos, Nicolás (July 2024, Information and Inference: A Journal of the IMA)

   Abstract We propose iterative algorithms to solve adversarial training problems in a variety of supervised learning settings of interest. Our algorithms, which can be interpreted as suitable ascent-descent dynamics in Wasserstein spaces, take the form of a system of interacting particles. These interacting particle dynamics are shown to converge toward appropriate mean-field limit equations in certain large number of particles regimes. In turn, we prove that, under certain regularity assumptions, these mean-field equations converge, in the large time limit, toward approximate Nash equilibria of the original adversarial learning problems. We present results for non-convex non-concave settings, as well as for non-convex concave ones. Numerical experiments illustrate our results. 

   more » « less
3. Learning to Simulate Complex Physics with Graph Networks

   Sanchez-Gonzalez, A.; Godwin, J.; Pfaff, T.; Ying, R.; Leskovec, J.; Battaglia, P. (April 2020, International Conference on Machine Learning (ICML))

   Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework—which we term “Graph Network-based Simulators” (GNS)—represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems. 

   more » « less
4. Numerical methods for nonlinear equations

   https://doi.org/10.1017/S0962492917000113  

   Kelley, C. T. (May 2018, Acta Numerica)

   This article is about numerical methods for the solution of nonlinear equations. We consider both the fixed-point form $$\mathbf{x}=\mathbf{G}(\mathbf{x})$$ and the equations form $$\mathbf{F}(\mathbf{x})=0$$ and explain why both versions are necessary to understand the solvers. We include the classical methods to make the presentation complete and discuss less familiar topics such as Anderson acceleration, semi-smooth Newton’s method, and pseudo-arclength and pseudo-transient continuation methods. 

   more » « less
5. Computational modeling of multiphase viscoelastic and elastoviscoplastic flows

   https://doi.org/10.1002/fld.4678  

   Izbassarov, Daulet; Rosti, Marco E.; Ardekani, M. Niazi; Sarabian, Mohammad; Hormozi, Sarah; Brandt, Luca; Tammisola, Outi (August 2018, International Journal for Numerical Methods in Fluids)

   Summary In this paper, a three‐dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time three‐dimensional simulations of inertial and turbulent EVP fluids with a large number particles and droplets. This is achieved by combining fast and highly scalable methods such as an FFT‐based pressure solver, with the evolution equation for non‐Newtonian (including EVP) stresses. In this flexible computational framework, the fluid can be modeled by either Oldroyd‐B, neo‐Hookean, FENE‐P, or Saramito EVP models, and the additional equations for the non‐Newtonian stresses are fully coupled with the flow. The rigid particles are discretized on a moving Lagrangian grid, whereas the flow equations are solved on a fixed Eulerian grid. The solid particles are represented by an immersed boundary method with a computationally efficient direct forcing method, allowing simulations of a large numbers of particles. The immersed boundary force is computed at the particle surface and then included in the momentum equations as a body force. The droplets and soft particles on the other hand are simulated in a fully Eulerian framework, the former with a level‐set method to capture the moving interface and the latter with an indicator function. The solver is first validated for various benchmark single‐phase and two‐phase EVP flow problems through comparison with data from the literature. Finally, we present new results on the dynamics of a buoyancy‐driven drop in an EVP fluid. 

   more » « less