Physics-Informed Multitask Neural Networks for solving Parametric Partial Differential Equations: Is Explicit Specialization necessary?
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Physics‑Informed Neural Networks (PINNs) embed the governing equations of physical systems into Neural Network (NN) training, enabling mesh‑free solution of forward and inverse PDE problems. Recent extensions address parametric PDEs, where solutions depend on additional parameters describing material, geometric, or operating conditions. By incorporating these parameters as inputs, PINNs can learn families of solutions across a continuous domain, as demonstrated in several applications. In parallel, growing evidence suggests that PINNs naturally align with Multitask Learning (MTL), since each component of the loss (PDE residuals, boundary conditions, data constraints) can be interpreted as a related task. When parametric PDEs are viewed through this lens, each parameter instance becomes a task within a shared physical structure, enabling improved generalization and more efficient training. This work investigates how MTL formulations can enhance PINNs for parametric PDEs. We analyze different architectures to show that explicit task‑specific heads are often unnecessary: specialization emerges organically when the loss is properly designed. Our results highlight how non-specialized heads cover more variability of the solution compared to explicitly specialized heads.
