Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learning
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908640488718336 |
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| author | Taghikhani, Kianoosh Yamazaki, Yusuke Varghese, Jerry Paul Apel, Markus Asl, Reza Najian Rezaei, Shahed |
| author_facet | Taghikhani, Kianoosh Yamazaki, Yusuke Varghese, Jerry Paul Apel, Markus Asl, Reza Najian Rezaei, Shahed |
| contents | We propose a Newton-based scheme, initialized by neural operator predictions, to accelerate the parametric solution of nonlinear problems in computational solid mechanics. First, a physics informed conditional neural field is trained to approximate the nonlinear parametric solutionof the governing equations. This establishes a continuous mapping between the parameter and solution spaces, which can then be evaluated for a given parameter at any spatial resolution. Second, since the neural approximation may not be exact, it is subsequently refined using a Newton-based correction initialized by the neural output. To evaluate the effectiveness of this hybrid approach, we compare three solution strategies: (i) the standard Newton-Raphson solver used in NFEM, which is robust and accurate but computationally demanding; (ii) physics-informed neural operators, which provide rapid inference but may lose accuracy outside the training distribution and resolution; and (iii) the neural-initialized Newton (NiN) strategy, which combines the efficiency of neural operators with the robustness of NFEM. The results demonstrate that the proposed hybrid approach reduces computational cost while preserving accuracy, highlighting its potential to accelerate large-scale nonlinear simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learning Taghikhani, Kianoosh Yamazaki, Yusuke Varghese, Jerry Paul Apel, Markus Asl, Reza Najian Rezaei, Shahed Machine Learning We propose a Newton-based scheme, initialized by neural operator predictions, to accelerate the parametric solution of nonlinear problems in computational solid mechanics. First, a physics informed conditional neural field is trained to approximate the nonlinear parametric solutionof the governing equations. This establishes a continuous mapping between the parameter and solution spaces, which can then be evaluated for a given parameter at any spatial resolution. Second, since the neural approximation may not be exact, it is subsequently refined using a Newton-based correction initialized by the neural output. To evaluate the effectiveness of this hybrid approach, we compare three solution strategies: (i) the standard Newton-Raphson solver used in NFEM, which is robust and accurate but computationally demanding; (ii) physics-informed neural operators, which provide rapid inference but may lose accuracy outside the training distribution and resolution; and (iii) the neural-initialized Newton (NiN) strategy, which combines the efficiency of neural operators with the robustness of NFEM. The results demonstrate that the proposed hybrid approach reduces computational cost while preserving accuracy, highlighting its potential to accelerate large-scale nonlinear simulations. |
| title | Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.06802 |