Engineering topics

Ghosh, Debojyoti

Publications and source records attributed to Ghosh, Debojyoti.

4 records

DOE OSTI2024

An implicit particle code with exact energy and charge conservation for studies of dense plasmas in axisymmetric geometries

A collisional particle code based on implicit energy- and charge-conserving methods in axisymmetric geometries is presented. A new particle pusher for axisymmetric systems is introduced that is compatible with exact energy and charge conservation and yields improved accuracy compared to other methods. How to appropriately treat all aspects of the algorithm near the r = 0 axis of symmetry is described in detail. Here, the axisymmetric model is verified by simulating the free expansion of a plasma sphere in 2D cylindrical and 1D spherical geometries. The algorithm's ability to study the dynamic compression of a dense plasma is illustrated by simulating the dynamic Z-pinch in 1D cylindrical geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Development of an implicit electromagnetic capability for a hybrid gyrokinetic ion-fluid electron model

Here we report on the development and implementation of a hybrid kinetic ion–fluid electron model for electromagnetic COGENT simulations of edge plasmas. COGENT is a finite-volume gyrokinetic code that employs a locally field-aligned coordinate system combined with a mapped multi-block grid technology to handle strongly anisotropic edge plasma turbulence. The simulation model involves the long-wavelength limit of the ion gyrokinetic equation coupled to the vorticity and Ohm's law equations for the electromagnetic field perturbations. In order to handle the fast Alfvén wave time scales, an implicit-explicit time integration approach with a physics-based preconditioner is used. The model is successfully applied to the simulations of ion-scale resistive-drift ballooning turbulence in a toroidal annulus geometry. Substantial speed-up over a fully explicit time integration approach is observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.

Computational Engineering, Finance, and Science (c↗

DOE OSTI2023

$\text{GPLaSDI}$: Gaussian Process-based interpretable Latent Space Dynamics Identification through deep autoencoder

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating and solving the ODE system in the reduced latent space, fast and accurate ROM predictions can be made by feeding the predicted latent space dynamics into the decoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the ROM predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. Here we demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

97 MATHEMATICS AND COMPUTING↗