让神经网络精准满足非线性焓平衡，提升化工建模的物理一致性。
Picard-KKT-hPINN: Enforcing Nonlinear Enthalpy Balances for Physically Consistent Neural Networks
- 基于皮卡德迭代思想，分步冻结变量实现非线性物理约束
- 在甲醇合成反应器上实现焓平衡与原子守恒的机器精度满足
- 数据稀缺时比普通神经网络更准，适合物理规律强的工业建模
神经网络虽广泛用作代理模型，但难以保证物理一致性，限制其在诸多场景的应用。本文提出一种新方法，可强制神经网络满足非线性物理定律，如焓平衡。该方法受皮卡德逐次逼近法启发，通过依次冻结并投影参与变量，实现乘积可分离的约束强制。我们在甲醇合成的催化填充床反应器上验证了 Picard-KKT-hPINN 方法。结果表明，该方法能以机器级精度同时满足非线性焓平衡和线性原子守恒。此外，在数据稀疏条件下，强制守恒律可显著提升模型预测精度，优于标准多层感知机。
原文摘要 · Abstract (English)
Neural networks are widely used as surrogate models but they do not guarantee physically consistent predictions thereby preventing adoption in various applications. We propose a method that can enforce NNs to satisfy physical laws that are nonlinear in nature such as enthalpy balances. Our approach, inspired by Picard successive approximations method, aims to enforce multiplicatively separable constraints by sequentially freezing and projecting a set of the participating variables. We demonstrate our PicardKKThPINN for surrogate modeling of a catalytic packed bed reactor for methanol synthesis. Our results show that the method efficiently enforces nonlinear enthalpy and linear atomic balances at machine-level precision. Additionally, we show that enforcing conservation laws can improve accuracy in data-scarce conditions compared to vanilla multilayer perceptron.
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