{"ID":3053374,"CreatedAt":"2026-06-04T04:41:36.695875263Z","UpdatedAt":"2026-06-06T03:31:06.711308811Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04420","arxiv_id":"2606.04420","title":"Loss-Conditional PINNs for Parametric PDE Families","abstract":"Physics-informed neural networks (PINNs) approximate solutions of ODEs and PDEs by minimising a weighted combination of residual, boundary, initial, and data losses. Their performance is often dominated by the choice of loss weights: a poor weighting can drive training to a degenerate solution in which one physical constraint is satisfied while another is ignored. Existing methods select or adapt a single good set of weights. We take a different view: instead of tuning one weight vector, we explore the entire weight space during training. We introduce LC-PINN, which adapts the loss-conditional training of Dosovitskiy and Djolonga (2020) to the PDE-residual setting: the conditioning vector (either the loss weights or a scalar physical coefficient) is treated as a network input and sampled from a simple prior at every optimisation step. This turns PINN training into learning a continuous family of solutions indexed by that vector, with no solver-generated paired data. LC-PINN thus lies between classical PINNs and operator learning: it stays fully physics-informed but amortises training over a parametric family. Our contribution is not the loss-conditional construction itself, but its extension to PINNs, the unification of the loss-weight and parametric-coefficient regimes under one architecture (concatenation for loss weights, FiLM for coefficients), and a fixed-quadrature L-BFGS finishing protocol that makes the parametric-coefficient regime trainable. We give a lambda-invariance result for the conditional optimum and study LC-PINN on parametric Helmholtz, Schrodinger, viscous Burgers, and Buckley-Leverett equations. A single LC-PINN matches or improves retrained per-weight PINN baselines while parameterising the full family in one model, at a total cost that amortises favourably against per-instance retraining.","short_abstract":"Physics-informed neural networks (PINNs) approximate solutions of ODEs and PDEs by minimising a weighted combination of residual, boundary, initial, and data losses. Their performance is often dominated by the choice of loss weights: a poor weighting can drive training to a degenerate solution in which one physical con...","url_abs":"https://arxiv.org/abs/2606.04420","url_pdf":"https://arxiv.org/pdf/2606.04420v1","authors":"[\"Anna Lazareva\",\"Alexander Tarakanov\"]","published":"2026-06-03T04:02:10Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}