[Paper Review] 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 Science0 citations

TL;DR

FilDeep is a neural operator framework designed to learn and predict large elastic-plastic deformations by leveraging multi-fidelity data, enabling accurate and efficient simulations beyond traditional single-fidelity approaches.

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.

Motivation & Objective

• Motivate the challenge of modeling large deformations in elastic-plastic solids where material nonlinearity and history dependence are significant.
• Propose a neural-operator framework (FilDeep) that leverages multi-fidelity data to improve prediction accuracy and generalization.
• Develop and evaluate a Transformer-based architecture (with attention) for learning deformation fields across varying loads and material parameters.
• Benchmark FilDeep against established operator-learning methods (e.g., DeepONet, IDeepONet, FNO) to demonstrate advantages in accuracy and efficiency.

Proposed method

• Adopt neural-operator modeling to map input fields (e.g., loading, material properties) to deformation outputs in elastic-plastic solids.
• Incorporate multi-fidelity data to balance high-fidelity accuracy with low-fidelity coverage for broader generalization.
• Utilize a Transformer-style architecture with attention mechanisms to capture complex dependencies in deformation fields.
• Compare against baseline operator-learning methods such as DeepONet, IDeepONet, and FNO to assess performance gaps.
• Evaluate on benchmarks involving large deformations to demonstrate robustness and computational efficiency.

Experimental results

Research questions

• RQ1 How well can FilDeep predict large elastic-plastic deformations under diverse loading scenarios and material parameters?
• RQ2 What is the impact of multi-fidelity data on accuracy and generalization for deformation prediction?
• RQ3 How does a Transformer-based neural-operator approach compare to existing operators (DeepONet, IDeepONet, FNO) in this context?
• RQ4 Can FilDeep achieve favorable accuracy-efficiency trade-offs for practical engineering-scale problems?

Key findings

• FilDeep demonstrates improved predictive accuracy for large elastic-plastic deformations over baseline operator models.
• Incorporating multi-fidelity data enhances generalization across unseen material parameters and loading conditions.
• The Transformer-based architecture effectively captures complex spatial and loading dependencies in deformation fields.
• Compared to DeepONet, IDeepONet, and FNO, FilDeep offers favorable accuracy and efficiency on chosen benchmarks.
• The approach shows potential for scalable simulation workflows that require multiple fidelity levels.