Adjoint vs PINNs: Performance Compared for PDE Inverse Problems

A new research paper compares the performance of adjoint optimization and physics-informed neural networks (PINNs) for solving inverse problems governed by partial differential equations (PDEs). The study found that the choice of method depends on how the unknown parameters are represented, with grid-based fields favoring adjoint methods and neural representations suiting PINNs. For time-dependent problems, PINNs offered comparable reconstructions at a lower cost than adjoint inversion, and a hybrid PINN-warm-started adjoint strategy achieved adjoint-level accuracy more efficiently. AI

IMPACT Provides a comparative analysis of PINNs against traditional methods, informing practitioners on optimal strategy selection for PDE-constrained inverse problems.

RANK_REASON Academic paper comparing two computational methods for solving PDE-constrained inverse problems. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• arXiv
• Partial Differential Equations
• Physics-Informed Neural Networks

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