Self-adaptive physics-informed neural network for forward and inverse problems in heterogeneous porous flow
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| Format: | Preprint |
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2025
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| _version_ | 1866909965514440704 |
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| author | Aziz, Md. Abdul Strauss, Thilo Mohebujjaman, Muhammad Khan, Taufiquar |
| author_facet | Aziz, Md. Abdul Strauss, Thilo Mohebujjaman, Muhammad Khan, Taufiquar |
| contents | We develop a self-adaptive physics-informed neural network (PINN) framework that reliably solves forward Darcy flow and performs accurate permeability inversion in heterogeneous porous media. In the forward setting, the PINN predicts velocity and pressure for discontinuous, piecewise-constant permeability; in the inverse setting, it identifies spatially varying permeability directly from indirect flow observations. Both models use a region-aware permeability parameterization with binary spatial masks, which preserves sharp permeability jumps and avoids the smoothing artifacts common in standard PINNs. To stabilize training, we introduce self-learned loss weights that automatically balance PDE residuals, boundary constraints, and data mismatch, eliminating manual tuning and improving robustness, particularly for inverse problems. An interleaved AdamW-L-BFGS optimization strategy further accelerates and stabilizes convergence. Numerical results demonstrate accurate forward surrogates and reliable inverse permeability recovery, establishing the method as an effective mesh-free solver and data-driven inversion tool for porous-media systems governed by partial differential equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-adaptive physics-informed neural network for forward and inverse problems in heterogeneous porous flow Aziz, Md. Abdul Strauss, Thilo Mohebujjaman, Muhammad Khan, Taufiquar Fluid Dynamics Numerical Analysis 65N22, 65N30, 76S05, 35R30, 68T07 We develop a self-adaptive physics-informed neural network (PINN) framework that reliably solves forward Darcy flow and performs accurate permeability inversion in heterogeneous porous media. In the forward setting, the PINN predicts velocity and pressure for discontinuous, piecewise-constant permeability; in the inverse setting, it identifies spatially varying permeability directly from indirect flow observations. Both models use a region-aware permeability parameterization with binary spatial masks, which preserves sharp permeability jumps and avoids the smoothing artifacts common in standard PINNs. To stabilize training, we introduce self-learned loss weights that automatically balance PDE residuals, boundary constraints, and data mismatch, eliminating manual tuning and improving robustness, particularly for inverse problems. An interleaved AdamW-L-BFGS optimization strategy further accelerates and stabilizes convergence. Numerical results demonstrate accurate forward surrogates and reliable inverse permeability recovery, establishing the method as an effective mesh-free solver and data-driven inversion tool for porous-media systems governed by partial differential equations. |
| title | Self-adaptive physics-informed neural network for forward and inverse problems in heterogeneous porous flow |
| topic | Fluid Dynamics Numerical Analysis 65N22, 65N30, 76S05, 35R30, 68T07 |
| url | https://arxiv.org/abs/2512.14610 |