Related references
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Article
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Summary: This work introduces a novel approach based on physics-informed neural networks (PINNs) for solving stiff ordinary differential equations (ODEs). The proposed method combines PINNs with the theory of functional connections and extreme learning machines, resulting in the so-called extreme theory of functional connections (X-TFC). Unlike regular PINN methodologies, the X-TFC method proves to be efficient and robust in solving challenging stiff ODE systems without the need for artificial techniques to reduce stiffness. The accuracy and performance of X-TFC are demonstrated through comparisons with state-of-the-art methods, and the generalization error of X-TFC frameworks in learning the solutions of ODEs is rigorously analyzed. The flexibility and analytical representation of the solution offered by X-TFC make it a valuable tool for various applications in fields such as chemical dynamics, nuclear dynamics, life sciences, and environmental engineering.
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Summary: This study investigates a physics-informed neural network (PINN) that combines deep learning with physics to solve the nonlinear Schrodinger equation in fiber optics. PINN is systematically investigated and verified for multiple physical effects in optical fibers, and it exhibits better performance than data-driven neural networks while using less data. The results show that PINN is not only an effective partial differential equation solver, but also a prospective technique for scientific computing and automatic modeling in fiber optics.
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Summary: This article discusses the importance and challenges of machine learning techniques in combustion science and engineering. It introduces the sources of data and data-driven techniques, and provides a detailed review of supervised, unsupervised, and semi-supervised machine learning methods. Through case studies and evaluations, the article demonstrates the wide applications of machine learning in combustion. In looking towards the future, it identifies issues such as interpretability, uncertainty quantification, and robustness, and suggests further research opportunities.
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Suyong Kim et al.
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Article
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Weiqi Ji et al.
Summary: The study investigates the performance of physics-informed neural network (PINN) in solving stiff chemical kinetic problems and addresses the challenges faced when using PINN for stiff ODE systems. By employing the quasi-steady-state assumption (QSSA) to reduce stiffness in ODE systems, PINN can be successfully applied to non-/mild-stiff systems after conversion. This suggests that stiffness may be a major reason for the failure of regular PINN in stiff chemical kinetic systems, and the developed stiff-PINN approach utilizing QSSA shows potential for applying PINN to various reaction-diffusion systems with stiff dynamics.
JOURNAL OF PHYSICAL CHEMISTRY A
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Proceedings Paper
Computer Science, Artificial Intelligence
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Summary: This study introduces novel Deep Neural Networks (DNNs) to approximate stiff ODEs and applies them to chemically reacting flows. Experimental results show that considering the physical properties of species is helpful for designing DNNs, and the proposed approach demonstrates good generalization ability.
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