融合多精度历史依赖数据，精准预测并量化模型不确定性。
Single- to multi-fidelity history-dependent learning with uncertainty quantification and disentanglement: application to data-driven constitutive modeling
- 构建层次化框架，从单精度到多精度贝叶斯递归网络渐进学习。
- 在含噪与无噪多精度数据上均实现响应准确预测与误差量化。
- 适合需考虑不确定性的工程建模与科学仿真场景。
数据驱动学习被扩展至处理历史依赖的多精度数据，同时量化认知不确定性（epistemic uncertainty）并将其与数据噪声（aleatoric uncertainty）解耦。该方法为分层结构，可适应不同学习场景：从训练最简单的单精度确定性神经网络，到提出的新一代多精度方差估计贝叶斯递归神经网络。通过在多种包含多精度且有/无随机噪声的数据驱动本构建模场景中应用，验证了该方法的通用性与灵活性。该方法不仅能准确预测材料响应并量化模型误差，还能在存在噪声时发现其分布特征。这为未来在复杂科学与工程领域中的实际应用开辟了新路径，尤其适用于涉及设计与分析不确定性的高挑战性问题。
原文摘要 · Abstract (English)
Data-driven learning is generalized to consider history-dependent multi-fidelity data, while quantifying epistemic uncertainty and disentangling it from data noise (aleatoric uncertainty). This generalization is hierarchical and adapts to different learning scenarios: from training the simplest single-fidelity deterministic neural networks up to the proposed multi-fidelity variance estimation Bayesian recurrent neural networks. The versatility and generality of the proposed methodology are demonstrated by applying it to different data-driven constitutive modeling scenarios that include multiple fidelities with and without aleatoric uncertainty (noise). The method accurately predicts the response and quantifies model error while also discovering the noise distribution (when present). This opens opportunities for future real-world applications in diverse scientific and engineering domains; especially, the most challenging cases involving design and analysis under uncertainty.
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