Physics-informed neural networks reproduce Saint-Venant torsion solutions for 2D cross-sections and 1D sharp-transition problems, with reported relative errors as low as 0.1% for simple shapes.
The Deep Ritz Method for Parametric $p$-Dirichlet Problems
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abstract
We establish error estimates for the approximation of parametric $p$-Dirichlet problems deploying the Deep Ritz Method. Parametric dependencies include, e.g., varying geometries and exponents $p\in (1,\infty)$. Combining the derived error estimates with quantitative approximation theorems yields error decay rates and establishes that the Deep Ritz Method retains the favorable approximation capabilities of neural networks in the approximation of high dimensional functions which makes the method attractive for parametric problems. Finally, we present numerical examples to illustrate potential applications.
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cs.LG 1years
2025 1verdicts
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Engineering application of physics-informed neural networks for Saint-Venant torsion
Physics-informed neural networks reproduce Saint-Venant torsion solutions for 2D cross-sections and 1D sharp-transition problems, with reported relative errors as low as 0.1% for simple shapes.