Meta Pareto Flow Learning with Ordinary Differential Equation Residual Supervision

Pareto set learning (PSL) amortizes multiobjective optimization by learning a continuous mapping from objective preferences to solutions. However, existing PSL methods mainly model task-specific Pareto sets, whose terminal solution manifolds can be geometrically misaligned across related tasks, making shared transferable structure difficult to capture from these mappings alone. We propose Pareto Flow Learning (PFL), which formulates each preference-conditioned scalarized problem as a continuous-time Pareto gradient flow and trains a neural model to approximate the resulting flows through ordinary differential equation (ODE) residual supervision. The learned model represents optimization dynamics in addition to Pareto-optimal solutions, providing complementary process-level information for transfer. We further extend PFL to meta-learning by learning shared structure across source-task Pareto flows and adapting the resulting meta Pareto flow model (mPFM) to unseen targets. Integrating mPFM with multiobjective Bayesian optimization yields mPFM-MOBO for search under limited evaluation budgets. Experiments on synthetic benchmarks and engineering design problems show improved early-stage convergence and competitive or better final performance on most target tasks, including under distribution shift. Ablation studies further indicate that Pareto-flow ODE supervision provides useful transferable information beyond terminal Pareto-set mappings alone.