用物理知识改进神经网络，让催化剂反应模拟更稳定可靠。
Physics-informed neural networks need a physicist to be accurate: the case of mass and heat transport in Fischer-Tropsch catalyst particles
- 结合物理规律改造神经网络结构，确保其在极端条件下的行为正确。
- 新方法使有限差分求解器整体稳定，同时保持神经网络带来的加速优势。
- 适合需要高精度模拟的化工反应器研究者，尤其关注复杂传质传热问题。
物理信息神经网络（PINNs）将机器学习的高效性与物理模拟的可靠性相结合，常用于替代多阶段计算流程中的部分或全部步骤，实现显著提速。然而，其广泛应用仍受可靠性限制，尤其在输入参数极端范围时表现不佳。本研究以费托合成中的耦合非线性反应-扩散与传热方程为例，采用有限差分法求解，其中源项由PINN预测。结果表明，传统评估神经网络函数逼近能力的方法可能忽略导致有限差分求解器不稳定的特殊性质。为此，我们提出基于领域知识的PINN架构改进策略，确保其渐近行为正确；结合改进的数值方案作为初始猜测生成器，所提方法有效恢复了模拟的整体稳定性，同时保留了PINN带来的加速效果。讨论了该混合传输方程求解器在化学反应器模拟中的潜在应用。
原文摘要 · Abstract (English)
Physics-Informed Neural Networks (PINNs) have emerged as an influential technology, merging the swift and automated capabilities of machine learning with the precision and dependability of simulations grounded in theoretical physics. PINNs are often employed to solve algebraic or differential equations to replace some or even all steps of multi-stage computational workflows, leading to their significant speed-up. However, wide adoption of PINNs is still hindered by reliability issues, particularly at extreme ends of the input parameter ranges. In this study, we demonstrate this in the context of a system of coupled non-linear differential reaction-diffusion and heat transfer equations related to Fischer-Tropsch synthesis, which are solved by a finite-difference method with a PINN used in evaluating their source terms. It is shown that the testing strategies traditionally used to assess the accuracy of neural networks as function approximators can overlook the peculiarities which ultimately cause instabilities of the finite-difference solver. We propose a domain knowledge-based modifications to the PINN architecture ensuring its correct asymptotic behavior. When combined with an improved numerical scheme employed as an initial guess generator, the proposed modifications are shown to recover the overall stability of the simulations, while preserving the speed-up brought by PINN as the workflow component. We discuss the possible applications of the proposed hybrid transport equation solver in context of chemical reactors simulations.
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