Physics-informed fine-tuning of foundation models for partial differential equations
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908889670221824 |
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| author | Medvedev, Vlad Armbruster, Leon Straub, Christopher Kruse, Georg Rosskopf, Andreas |
| author_facet | Medvedev, Vlad Armbruster, Leon Straub, Christopher Kruse, Georg Rosskopf, Andreas |
| contents | Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and distribution shifts. While fine-tuning has proven transformative in natural language processing, best practices for adapting PDE foundation models remain underexplored. Although physics-informed training has successfully trained accurate solvers across a wide range of PDE problems, its potential for fine-tuning data-based foundation models has not been systematically studied. In this work, we introduce a physics-informed fine-tuning framework that adapts pre-trained PDE foundation models by incorporating physical constraints (PDE residuals and boundary conditions) directly into the fine-tuning objective. This enables effective adaptation in data-scarce regimes while promoting physical consistency. We evaluate our method on a downstream task composed of an unseen PDE class and compare it with data-driven finetuning counterparts. Our results demonstrate that physics-informed fine-tuning achieves competitive accuracy without requiring PDE solutions for training. Furthermore, a hybrid fine-tuning strategy yields superior generalization to out-of-distribution scenarios when only minimal training data is available. These findings establish physics-informed fine-tuning as a scalable and data-efficient paradigm, providing a physically interpretable pathway for adapting foundation models in scientific machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Physics-informed fine-tuning of foundation models for partial differential equations Medvedev, Vlad Armbruster, Leon Straub, Christopher Kruse, Georg Rosskopf, Andreas Machine Learning Artificial Intelligence Numerical Analysis Analysis of PDEs Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and distribution shifts. While fine-tuning has proven transformative in natural language processing, best practices for adapting PDE foundation models remain underexplored. Although physics-informed training has successfully trained accurate solvers across a wide range of PDE problems, its potential for fine-tuning data-based foundation models has not been systematically studied. In this work, we introduce a physics-informed fine-tuning framework that adapts pre-trained PDE foundation models by incorporating physical constraints (PDE residuals and boundary conditions) directly into the fine-tuning objective. This enables effective adaptation in data-scarce regimes while promoting physical consistency. We evaluate our method on a downstream task composed of an unseen PDE class and compare it with data-driven finetuning counterparts. Our results demonstrate that physics-informed fine-tuning achieves competitive accuracy without requiring PDE solutions for training. Furthermore, a hybrid fine-tuning strategy yields superior generalization to out-of-distribution scenarios when only minimal training data is available. These findings establish physics-informed fine-tuning as a scalable and data-efficient paradigm, providing a physically interpretable pathway for adapting foundation models in scientific machine learning. |
| title | Physics-informed fine-tuning of foundation models for partial differential equations |
| topic | Machine Learning Artificial Intelligence Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2603.15431 |