发表机构
RWTH Aachen University; JARA Center for Simulation and Data Science (CSD); Institute of Climate and Energy Systems ICE-1: Energy Systems Engineering, Forschungszentrum Jülich GmbH（亚琛工业大学; JARA 模拟与数据科学中心; 于利希研究中心气候与能源系统研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文系统比较了硬约束与软约束物理信息分子机器学习方法，发现软约束中增广拉格朗日方法提升性能，硬约束方法在热力学一致性上更优。
AI 中文摘要
在分子机器学习（ML）中，将基本热力学关系整合到ML模型中已取得显著进展。此类物理信息方法可分为硬约束（将热力学关系嵌入模型架构）和软约束（将关系纳入训练损失）。虽然这两种方法已应用于各种性质预测任务，但在实验数据上的系统比较仍缺乏。我们在此比较硬约束和软约束方法在一个数值上具有挑战性的案例研究中的表现：预测单组分汽液平衡中作为温度函数的蒸气压、饱和液体和蒸气摩尔体积以及蒸发焓，这些性质由精确的Clapeyron方程关联。此外，分子ML中的软约束方法通常以固定权重因子平衡数据和物理损失，需要仔细调整。为克服此问题，我们研究了在约束优化中成熟的增广拉格朗日方法（ALM）。我们发现，对于软约束方法，使用ALM在约束满足方面将预测性能提高了2倍，并将训练轮数比使用固定惩罚减少了30%。因此，在软约束方法中，始终建议使用ALM。硬约束方法需要额外的架构设计选择，可以达到与软约束方法相当的精度，且具有更高的热力学一致性，对Clapeyron方程的逼近精度提高了12个数量级。总体而言，当热力学一致性至关重要时，硬约束方法最有前景，但需要根据相应的热力学关系定制ML模型架构。
英文摘要
In molecular machine learning (ML), significant progress has been made on integrating fundamental thermodynamic relations into ML models. Such physics-informed approaches can be categorized as hard-constrained, where the thermodynamic relations are embedded in the model architecture, and soft-constrained, where relations are included in the training loss. While both approaches have been applied to various property prediction tasks, a systematic comparison on experimental data is lacking. We herein compare hard- and soft-constrained approaches on a numerically challenging case study: the prediction of vapor pressure, saturated liquid and vapor molar volumes, and enthalpy of vaporization as functions of temperature for single-species vapor-liquid equilibrium, related by the exact Clapeyron equation. Furthermore, soft-constrained approaches in molecular ML typically balance data and physics losses with a fixed weighting factor, requiring careful tuning. To overcome this, we investigate the augmented Lagrangian method (ALM), well established in constrained optimization. We find that for the soft-constrained approach, using the ALM improves prediction performance in terms of constraint satisfaction by factor 2 and reduces training epochs compared to using a fixed penalty by 30%. Hence, in the soft-constrained approach, the use of the ALM is always recommended. The hard-constrained approach, which entails additional architectural design choices, can reach on par accuracy with the soft-constrained approach, at even higher thermodynamic consistency, reaching 12 orders of magnitude closer approximation of the Clapeyron equation. Overall, the hard-constrained approach is most promising when thermodynamic consistency is critical, yet requires tailoring the ML model architecture to the respective thermodynamic relation.
