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

2025-03-18

AI Summary

To address the bottlenecks of slow computation, high memory consumption, and massive storage requirements in ultra-large-scale engineering simulations, this paper proposes TAPS—a training-data-free prior surrogate model. Methodologically, TAPS integrates AI-enhanced finite-element interpolation (C-HiDeNN) with tensor decomposition to formulate a generalized spatio-temporal-parametric Galerkin weak form, enabling direct reduced-order solution of high-dimensional parametrized governing equations with controllable, hyperparameter-tuned convergence rates. Applied to an additive manufacturing simulation with 3.46 billion degrees of freedom, TAPS achieves 1,370× speedup, 14.8× memory reduction, and 955× storage compression, with theoretical scalability to zetta-scale (10²¹) problems. Key contributions include: (i) the first data-free prior modeling paradigm; (ii) a tightly coupled framework unifying C-HiDeNN and tensor decomposition; and (iii) a provably convergent, generalized multi-dimensional Galerkin reduced-order modeling framework.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Matrix & Tensor Methods
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Develops TAPS for ultra large-scale simulations
• Achieves speedup, memory savings, and storage gain
• Applies to high-dimensional parametric problems

Innovation

• Tensor-decomposition-based A Priori Surrogate (TAPS) modeling
• AI-enhanced finite element-type interpolation function
• Generalized space-parameter-time Galerkin weak form