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Partial differential equations (PDEs) underlie our understanding andprediction of natural phenomena across numerous fields, including physics,engineering, and finance. However, solving parametric PDEs is a complex taskthat necessitates efficient numerical methods. In this paper, we propose anovel approach for solving parametric PDEs using a Finite Element OperatorNetwork (FEONet). Our proposed method leverages the power of deep learning inconjunction with traditional numerical methods, specifically the finite elementmethod, to solve parametric PDEs in the absence of any paired input-outputtraining data. We performed various experiments on several benchmark problemsand confirmed that our approach has demonstrated excellent performance acrossvarious settings and environments, proving its versatility in terms ofaccuracy, generalization, and computational flexibility. Our FEONet frameworkshows potential for application in various fields where PDEs play a crucialrole in modeling complex domains with diverse boundary conditions and singularbehavior. Furthermore, we provide theoretical convergence analysis to supportour approach, utilizing finite element approximation in numerical analysis.

Finite Element Operator Network for Solving Parametric PDEs