将可微化学求解器融入PINN,攻克刚性反应系统建模难题。
Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems

- 用可微化学求解器替代传统数值方法,实现物理约束可训练
- 在氢燃烧模型上成功求解刚性微分方程与反演参数问题
- 适合需要高精度模拟复杂化学反应的科研人员使用
从神经微分方程到连续时间机器学习,可微求解器使物理、优化与仿真成为深度学习系统的可训练组件。这为科学计算开启新一代深度学习框架,诸多应用正不断涌现。本文将可微化学求解器集成至改进的物理信息神经网络(PINN),用于求解固有刚性的参数化反应系统。所提框架引入多个关键组件以克服标准PINN的局限:包括可微化学求解器、支持参数化解的网络架构,以及针对刚性反应设计的残差加权机制。我们在氢燃烧相关微分方程上进行评估,涵盖初值/边值问题、反演参数识别及参数化偏微分方程。结果表明,该方法可有效拓展PINN对以往难以处理的刚性化学系统的建模能力。
原文摘要 · Abstract (English)
From neural ODEs to continuous-time machine learning, differentiable solvers allow physics, optimization, and simulation to become trainable components within deep learning systems. This has opened the path to a new generation of deep learning frameworks for scientific computing, with many promising applications still emerging. In this paper, we integrate a differentiable chemistry solver into a modified physics-informed neural network to solve parameterized reaction systems that are inherently stiff. The proposed framework introduces several key components required to overcome limitations of standard physics-informed neural networks. These include a differentiable chemistry solver, a network architecture for parameterized solutions, and residual weighting tailored to stiff reactions. We evaluate the framework on a set of differential equations related to hydrogen combustion, which include initial/boundary value problems, inverse parameter identification, and a parameterized partial differential equation. Our results highlight the ability of the proposed approach to extend physics-informed neural networks to stiff chemical systems that were previously inaccessible.
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。