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

A data-free predictive scientific AI model, termed 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 does not require any training data and can effectively obtain surrogate models for high-dimensional parametric problems with equivalently zetta-scale ($10^{21}$) degrees of freedom (DoFs) using a single GPU. TAPS achieves this by directly obtaining reduced-order models through solving the weak form of the 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, different convergence rates can be achieved. To show the capabilities of this framework, TAPS is then used to simulate a large-scale additive manufacturing process 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 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.