Tensor-decomposition-based A Priori Surrogate (TAPS) modeling for ultra large-scale simulations

TL;DR

The document introduces the elsarticle.cls LaTeX class designed for Elsevier submission workflows, aiming to minimize package conflicts and align with standard LaTeX practices. It builds on the article class and integrates essential tools such as natbib and hyperref, while providing robust front matter handling and flexible formatting options (preprint, final, one- and two-column formats). The authors detail required and optional packages, author-affiliation handling, and front matter constructs to support the publication process. Installation guidance covers obtaining the .dtx/.ins sources from Elsevier CTAN, generating the class with LaTeX, and updating TeX databases to ensure availability across systems.

Abstract

A data-free, predictive scientific AI model, Tensor-decomposition-based A Priori Surrogate (TAPS), is proposed for tackling ultra large-scale engineering simulations with significant speedup, memory savings, and storage gain. TAPS can effectively obtain surrogate models for high-dimensional parametric problems with equivalent zetta-scale ($10^{21}$) degrees of freedom (DoFs). TAPS achieves this by directly obtaining reduced-order models through solving governing equations with multiple independent variables such as spatial coordinates, parameters, and time. The paper first introduces an AI-enhanced finite element-type interpolation function called convolution hierarchical deep-learning neural network (C-HiDeNN) with tensor decomposition (TD). Subsequently, the generalized space-parameter-time Galerkin weak form and the corresponding matrix form are derived. Through the choice of TAPS hyperparameters, an arbitrary convergence rate can be achieved. To show the capabilities of this framework, TAPS is then used to simulate a large-scale additive manufacturing process as an example and achieves around 1,370x speedup, 14.8x memory savings, and 955x storage gain compared to the finite difference method with $3.46$ billion spatial degrees of freedom (DoFs). As a result, the TAPS framework opens a new avenue for many challenging ultra large-scale engineering problems, such as additive manufacturing and integrated circuit design, among others.