[论文解读] FilDeep: Learning Large Deformations of Elastic-Plastic Solids with Multi-Fidelity Data

Jianheng Tang, Shilong Tao+5 more|arXiv (Cornell University)|Jan 15, 2026

Machine Learning in Materials Science被引用 0

一句话总结

FilDeep 是一个神经算子框架，利用多保真数据学习并预测大规模弹塑性变形，从而实现高效且准确的仿真，超越传统单保真方法。

ABSTRACT

The scientific computation of large deformations in elastic-plastic solids is crucial in various manufacturing applications. Traditional numerical methods exhibit several inherent limitations, prompting Deep Learning (DL) as a promising alternative. The effectiveness of current DL techniques typically depends on the availability of high-quantity and high-accuracy datasets, which are yet difficult to obtain in large deformation problems. During the dataset construction process, a dilemma stands between data quantity and data accuracy, leading to suboptimal performance in the DL models. To address this challenge, we focus on a representative application of large deformations, the stretch bending problem, and propose FilDeep, a Fidelity-based Deep Learning framework for large Deformation of elastic-plastic solids. Our FilDeep aims to resolve the quantity-accuracy dilemma by simultaneously training with both low-fidelity and high-fidelity data, where the former provides greater quantity but lower accuracy, while the latter offers higher accuracy but in less quantity. In FilDeep, we provide meticulous designs for the practical large deformation problem. Particularly, we propose attention-enabled cross-fidelity modules to effectively capture long-range physical interactions across MF data. To the best of our knowledge, our FilDeep presents the first DL framework for large deformation problems using MF data. Extensive experiments demonstrate that our FilDeep consistently achieves state-of-the-art performance and can be efficiently deployed in manufacturing.

研究动机与目标

• 推动在材料非线性和历史依赖性显著的弹塑性固体中对大变形建模的挑战性理解。
• 提出一个利用多保真数据来提升预测准确性和泛化能力的神经算子框架（FilDeep）。
• 开发并评估基于 Transformer 的架构（带注意力机制）以学习在不同荷载和材料参数下的变形场。
• 将 FilDeep 与成熟的算子学习方法（如 DeepONet、IDeepONet、FNO）进行基准比较，以展示在准确性和效率方面的优势。

提出的方法

• 采用神经算子建模将输入场（如荷载、材料性质）映射到弹塑性固体中的变形输出。
• 引入多保真数据，以在高保真精度与低保真覆盖之间取得平衡，从而实现更广泛的泛化。
• 利用带注意力机制的 Transformer 风格架构，捕获变形场中的复杂依赖关系。
• 与基线算子学习方法（如 DeepONet、IDeepONet、FNO）进行对比，以评估性能差距。
• 在涉及大变形的基准测试上进行评估，以展示鲁棒性和计算效率。

实验结果

研究问题

• RQ1 FilDeep 在多样荷载情景和材料参数下对大规模弹塑性变形的预测能力有多高？
• RQ2 多保真数据对变形预测的准确性和泛化性有何影响？
• RQ3 在此背景下，基于 Transformer 的神经算子方法与现有算子（DeepONet、IDeepONet、FNO）相比有何差异？
• RQ4 FilDeep 是否能够在实际工程级问题中实现有利的准确性-效率权衡？

主要发现

• FilDeep 在大规模弹塑性变形的预测准确性方面优于基线算子模型。
• 引入多保真数据能提升对未见材料参数与荷载条件的泛化能力。
• 基于 Transformer 的架构能够有效捕捉变形场中的复杂空间和荷载依赖性。
• 与 DeepONet、IDeepONet、FNO 相比，FilDeep 在所选基准上表现出有利的准确性与效率。
• 该方法有望用于需要多保真等级的可扩展仿真工作流。