mlsanityData to 14 Oct 2026

The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

arXiv 1710.00211 ↗First posted 30 Sep 2017cs.LG stat.MLcited by 583

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Abstract (arXiv)

We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally adaptive and has the potential to work in rather high dimensions. The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning. We illustrate the method on several problems including some eigenvalue problems.

Key facts. Cited by 583 papers in the map (data through 14 Oct 2026). First posted on arXiv 30 Sep 2017.

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Citing papers per year: 2021: 69; 2022: 94; 2023: 104; 2024: 121; 2025: 99; 2026: 96.

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