Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems

TL;DR

This paper introduces a differentiable chemistry solver integrated into physics-informed neural networks to effectively solve stiff, parameterized reaction systems, expanding the applicability of PINNs in chemical kinetics.

Contribution

The authors develop a novel framework combining a differentiable chemistry solver with PINNs, enabling the solution of stiff, parameterized chemical reaction systems.

Findings

Successfully applied to hydrogen combustion equations.

Extended PINNs to handle stiff chemical systems.

Demonstrated effectiveness in inverse parameter identification.

Abstract

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.