Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems

Miloš Babić; Franz M. Rohrhofer; Stefan Posch

cs.LGMay 6, 2026

Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems

Authors: Miloš Babić, Franz M. Rohrhofer, Stefan Posch

Organizations: CD Laboratory for Physics-driven Machine Learning in Industrial Applications, Graz, Austria · The Institute of Thermodynamics and Sustainable Propulsion Systems, Graz University of Technology, Graz, Austria · Know Center Research GmbH, Graz, Austria

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.

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Aug 5, 2026 · cs.LGJ/K move · Enter open · S save

Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations

Xujia Chen, Xinyue Hu, Letian Chen, Yi Liu+1

Department of Automation, Tsinghua University, Beijing, 100084, China

Physics-informed neural networks (PINNs) incorporate governing equations into neural-network training and can approximate PDE solutions without requiring large observational datasets. Parameterized PINNs (ParamPINNs) further take physical parameters as inputs, allowing a single model to represent a family of PDE solutions over a parameter domain. Existing ParamPINNs, however, still face inefficient training, uneven accuracy across parameters, and overfitting to a limited set of sampled parameter tasks, which can impair generalization to unsampled parameters. To address these issues, we propose a continual-learning physics-informed neural network (CL-PINN), which treats PDE instances at different parameter values as related tasks and learns them sequentially. CL-PINN combines Bayesian-optimization-based active parameter selection, task-wise dynamic loss weighting, sparse physics-constrained replay, and an optional parameter subnetwork to improve task allocation and knowledge retention under bounded active-task capacity. It requires no observational data and is designed to solve parameterized PDEs over relatively broad parameter domains under limited computational resources. Multi-seed evaluations on five benchmarks, including one continuous function and four parameterized PDEs, show that Bayesian selection substantially reduces objective-loss queries relative to grid-greedy search, while sparse replay mitigates forgetting of earlier tasks. Under the prescribed within-case resource protocols, CL-PINN generally provides higher and more balanced solution accuracy than fixed-sampling and grid-greedy baselines. CL-PINN offers a practical route toward learning PDE solutions that generalize across physical parameters and has the potential to support reusable physics-informed surrogates for large-scale engineering parameter studies.

Conventional Physics-Informed Neural Networks Partial Differential Equations Efficient Continual Learning Neural Network Continual Learning Methods

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Abstract

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