An End-to-End PyTorch Interface for Differentiable PDE Solvers: A RANS Model-Correction Study
This work presents an end-to-end strategy for solving inverse problems constrained by Partial Differential Equations within a fully differentiable Machine Learning framework. The proposed formulation provides a unified and user-friendly methodology applicable to a wide range of problems, from data assimilation to closure modeling. Our approach combines a baseline differentiable PDE solver, which predicts the state w from the nonlinear system $R(w) = 0$, with a generic additive, parametrized, and differentiable correction $f_φ(w)$, with trainable parameters $φ$. We show how to optimize phi within a fully differentiable Python workflow by reformulating the PDE as an implicit layer, enabling...
| Authors | Luca Saverio, Michele Alessandro Bucci, Gianmarco Farro et al. |
|---|---|
| Primary category | cs.CE |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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