THINNs用热力学原理改进神经网络对非平衡系统的建模。
THINNs: Thermodynamically Informed Neural Networks
- 基于大偏差原理设计惩罚项，使误差惩罚更符合物理规律
- 相比传统方法，能更准确捕捉非平衡系统中的罕见波动行为
- 适合研究复杂物理系统中稀有事件的建模与分析
物理信息神经网络（PINNs）是一类旨在通过训练神经网络最小化方程残差来逼近偏微分方程解的深度学习模型。针对非平衡涨落系统，本文提出一种基于物理规律的惩罚选择，该选择与底层涨落结构一致，由大偏差原理刻画。此方法构建了一种新型PINN形式，其中惩罚项用于惩罚不可能发生的偏离，而非凭经验设定。由此得到的热力学一致性扩展模型称为THINNs，其通过建立解析后验估计，并与现有惩罚策略进行实证比较，验证了其有效性。
原文摘要 · Abstract (English)
Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that is consistent with the underlying fluctuation structure, as characterized by a large deviations principle. This approach yields a novel formulation of PINNs in which the penalty term is chosen to penalize improbable deviations, rather than being selected heuristically. The resulting thermodynamically consistent extension of PINNs, termed THINNs, is subsequently analyzed by establishing analytical a posteriori estimates, and providing empirical comparisons to established penalization strategies.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。