End-to-End Probabilistic Framework for Learning with Hard Constraints
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917057550876672 |
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| author | Utkarsh, Utkarsh Maddix, Danielle C. Ma, Ruijun Mahoney, Michael W. Wang, Yuyang |
| author_facet | Utkarsh, Utkarsh Maddix, Danielle C. Ma, Ruijun Mahoney, Michael W. Wang, Yuyang |
| contents | We present ProbHardE2E, a probabilistic forecasting framework that incorporates hard operational/physical constraints, and provides uncertainty quantification. Our methodology uses a novel differentiable probabilistic projection layer (DPPL) that can be combined with a wide range of neural network architectures. DPPL allows the model to learn the system in an end-to-end manner, compared to other approaches where constraints are satisfied either through a post-processing step or at inference. ProbHardE2E optimizes a strictly proper scoring rule, without making any distributional assumptions on the target, which enables it to obtain robust distributional estimates (in contrast to existing approaches that generally optimize likelihood-based objectives, which are heavily biased by their distributional assumptions and model choices); and it can incorporate a range of non-linear constraints (increasing the power of modeling and flexibility). We apply ProbHardE2E in learning partial differential equations with uncertainty estimates and to probabilistic time-series forecasting, showcasing it as a broadly applicable general framework that connects these seemingly disparate domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | End-to-End Probabilistic Framework for Learning with Hard Constraints Utkarsh, Utkarsh Maddix, Danielle C. Ma, Ruijun Mahoney, Michael W. Wang, Yuyang Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science We present ProbHardE2E, a probabilistic forecasting framework that incorporates hard operational/physical constraints, and provides uncertainty quantification. Our methodology uses a novel differentiable probabilistic projection layer (DPPL) that can be combined with a wide range of neural network architectures. DPPL allows the model to learn the system in an end-to-end manner, compared to other approaches where constraints are satisfied either through a post-processing step or at inference. ProbHardE2E optimizes a strictly proper scoring rule, without making any distributional assumptions on the target, which enables it to obtain robust distributional estimates (in contrast to existing approaches that generally optimize likelihood-based objectives, which are heavily biased by their distributional assumptions and model choices); and it can incorporate a range of non-linear constraints (increasing the power of modeling and flexibility). We apply ProbHardE2E in learning partial differential equations with uncertainty estimates and to probabilistic time-series forecasting, showcasing it as a broadly applicable general framework that connects these seemingly disparate domains. |
| title | End-to-End Probabilistic Framework for Learning with Hard Constraints |
| topic | Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2506.07003 |