Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1807.09829

A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials

Zeliang Liu·C. T. Wu·M. Koishi
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE) and advanced machine learning techniques. We propose to use a collection of connected mechanistic building blocks with analytical homogenization solutions which avoids the loss of essential physics in generic neural networks, and this concept is demonstrated for 2-dimensional RVE problems and network depth up to 7. Based on linear elastic RVE data from offline direct numerical simulations, the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm, enhanced by model compression methods. Importantly, the trained network is valid for any local material laws without the need for additional calibration or micromechanics assumption. Its extrapolations to unknown material and loading spaces for a wide range of problems are validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finite-strain hyperelasticity under large deformations. By discovering a proper topological representation of RVE with fewer degrees of freedom, this intelligent material model is believed to open new possibilities of high-fidelity efficient concurrent simulations for a large-scale heterogeneous structure. It also provides a mechanistic understanding of structure-property relations across material length scales and enables the development of parameterized microstructural database for material design and manufacturing.

Explore related subjects

cs.CEphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zeliang Liu, C. T. Wu, M. Koishi. 2018-10-24. A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials. https://doi.org/10.1016/j.cma.2018.09.020

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Dimension Bridging for 3D RANS with Neural Network Accelerated Gaussian Functional Regression

In many computational science and engineering problems, repeatedly solving fully resolved physics-based models to design for a quantity of interest (QoI) can quickly become intractable, requiring the use of low-fidelity models to predict the same QoI but introduce errors where some features are neglected or are otherwise inaccurately resolved. We use Gaussian Functional Regression (GFR) to learn a correction to a 2D Reynolds-Averaged Navier-Stokes (RANS) model to predict the aerodynamic coefficients from a 3D RANS model. This model pair has a disparity in the governing physics from the reduced dimensionality, a previously unexplored application for GFR. Empirically, our results show that with a proper choice of low-dimensional (LD) model, the proposed kernel allows for the use of fewer high-dimensional (HD) evaluations to regress a response surface to the same level of accuracy as standard stationary kernels. Moreover, the new kernel provides more informative uncertainty quantification, which we show is advantageous when used to drive an adaptive sampling algorithm. Finally, we propose a novel neural network accelerated kernel, which we show offers predictions in good agreement while speeding up evaluations by millions of times in wall clock measurements, bringing the computational budget within the real-time regime.

cs.CE↗
arXiv2026

SabreAgent: Language Models at Design Time for Lost-Sales Inventory Control

SabreAgent uses a language model at design time to construct two components for lost-sales inventory control: a product-specific seasonal prior and a validation-selected capped base-stock policy family. During operation, statistical forecasting and inventory optimization use these frozen artifacts to determine orders, with zero language-model calls. We evaluate the approach on the $1{,}320$ instances of InventoryBench. Under the benchmark's cost assumptions, the operations-research core draws on a zero-lead-time optimality result and a projected-inventory rule for positive deterministic lead times. The latter computes replenishment shortfalls by propagating inventory using sales along simulated demand paths. The seasonal prior adds forecast variants alongside the original forecaster, and the selected policy family handles stochastic lead times with order destruction. SabreAgent scores $0.6311$, compared with $0.5380$ for the strongest published baseline, and ranks first in all six benchmark cells. Ablations attribute most of the gain to the OR core. In the paired analysis, the seasonal component adds $1.79\%$ across the three real-data cells, and the search component adds $2.3\%$ across the two stochastic-lead-time cells. These results demonstrate how model-generated priors and policy structure can improve an OR controller through design-time use.

cs.CE↗
arXiv2026

Hierarchical Multi-Task Learning with Liquidity-Aware Signals for Stock Forecasting

Stock price forecasting is a long-standing challenge in computational finance, driven by the inherent randomness of markets and complex temporal patterns. While recent deep-learning models have raised forecasting accuracy by jointly modeling inter-stock and temporal price dynamics, they conflate inter-stock relationships with intra-stock temporal dependencies and focus solely on the univariate objective of price movement. To address these limitations, we propose LiMT, a Hierarchical Multi-Task Learning framework that integrates liquidity-aware signals for stock price forecasting. LiMT employs a Market Regime Encoder (MRE) module that first extracts contemporaneous cross-stock dependencies, then models each stock's temporal dynamics, yielding a unified latent state. Building on this latent state, we introduce a Liquidity-Driven Learning (LDL) module, a mixture-of-experts architecture that features cross-task gating mechanisms to jointly predict price movement, volatility, and trading volume. We further design an Adaptive Portfolio Optimization (APO) mechanism that converts multi-task forecasts into executable portfolio weights under transaction-cost and liquidity constraints. Extensive experiments on the CSI300 and CSI500 benchmarks show that LiMT performs best among strong neural and tree-based baselines across the reported metrics. In realistic CSI300 backtests, APO improves annualized return from 3.99% to 10.01% and Sharpe ratio from 1.22 to 1.86 over equal weighting, showing that the multi-task forecasts translate into deployable portfolio gains.

cs.CE↗