发表机构
Technische Universität Dresden; Technical University of Munich; ACCESS e.V.（德累斯顿工业大学; 慕尼黑工业大学; ACCESS协会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出无数据弱形式交错神经算子框架，用于有限应变弹性体的磁-机械耦合问题，通过交替训练磁性和机械算子，准确预测耦合响应。
AI 中文摘要
磁活性弹性体作为一类智能材料，在有限应变下表现出强耦合的磁和机械行为。考虑微结构、材料属性和几何形状的变化可能导致计算成本高昂的分析。基于有限算子学习（FOL）框架，本研究开发了一种无数据、物理信息驱动的算子学习框架，用于一族耦合的有限应变磁-机械边值问题。控制静磁和机械方程通过有限元弱形式残差强制执行，使得神经算子无需标记的有限元解数据即可训练。本研究的主要贡献是开发了一种弱形式交错神经算子（WSNO）框架，用于强耦合的磁-机械鞍点问题。磁性和机械神经算子分别通过交错优化策略交替训练，而其物理耦合通过本构关系和残差评估得以保留。所得到的框架学习从参数化的材料和几何描述到相应的耦合磁和机械解场的映射。所提出的框架在多种设置下进行了研究，包括异质随机夹杂微结构、变化的磁相衬度、依赖于面积分数的几何形状、强分布外材料形态以及三维几何参数化问题。此外，学习到的算子与神经初始化的牛顿策略相结合，其中非线性有限元求解器使用神经预测进行初始化。结果表明，所提出的算子学习框架能够在广泛的参数化问题设置中准确捕获耦合的磁-机械响应。
英文摘要
Magneto-active elastomers, as a class of smart materials, exhibit strongly coupled magnetic and mechanical behavior at finite strains. Considering variations in microstructure, material properties, and geometry can lead to computationally expensive analyses. Building on the finite operator learning (FOL) framework, this study develops a data-free, physics-informed operator-learning framework for families of coupled finite-strain magneto-mechanical boundary-value problems. The governing magnetostatic and mechanical equations are enforced through finite-element weak-form residuals, allowing the neural operators to be trained without labeled finite-element solution data. The main contribution of this study is the development of a weak-form staggered neural operator (WSNO) framework for strongly coupled magneto-mechanical saddle-point problems. Separate magnetic and mechanical neural operators are trained alternately using a staggered optimization strategy, while their physical coupling is retained through the constitutive relations and residual evaluations. The resulting framework learns mappings from parameterized material and geometric descriptions to the corresponding coupled magnetic and mechanical solution fields. The proposed framework is investigated across several settings, including heterogeneous random-inclusion microstructures, varying magnetic phase contrast, area-fraction-dependent geometries, strongly out-of-distribution material morphologies, and three-dimensional geometry-parametric problems. In addition, the learned operator is combined with a neural-initialized Newton strategy, in which the nonlinear finite-element solver is initialized using the neural prediction. The results demonstrate that the proposed operator-learning framework can accurately capture coupled magneto-mechanical responses across a broad range of parametric problem settings.
