{"ID":2876138,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.00663","arxiv_id":"2509.00663","title":"Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networks","abstract":"We propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed operator-learning Networks (Morephy-Net) to solve parametric partial differential equations (PDEs) in noisy data regimes, for both forward prediction and inverse identification. Existing physics-informed neural networks and operator-learning models (e.g., DeepONets and Fourier neural operators) often face three coupled challenges: (i) balancing data/operator and physics residual losses, (ii) maintaining robustness under noisy or sparse observations, and (iii) providing reliable uncertainty quantification. Morephy-Net addresses these issues by integrating: (i) evolutionary multi-objective optimization that treats data/operator and physics residual terms as separate objectives and searches the Pareto front, thereby avoiding ad hoc loss weighting; (ii) replica-exchange stochastic gradient Langevin dynamics to enhance global exploration and stabilize training in non-convex landscapes; and (iii) Bayesian uncertainty quantification obtained from stochastic sampling. We validate Morephy-Net on representative forward and inverse problems, including the one-dimensional Burgers equation and the time-fractional mixed diffusion--wave equation. The results demonstrate consistent improvements in accuracy, noise robustness, and calibrated uncertainty estimates over standard operator-learning baselines.","short_abstract":"We propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed operator-learning Networks (Morephy-Net) to solve parametric partial differential equations (PDEs) in noisy data regimes, for both forward prediction and inverse identification. Existing physics-informed neural networks...","url_abs":"https://arxiv.org/abs/2509.00663","url_pdf":"https://arxiv.org/pdf/2509.00663v3","authors":"[\"Binghang Lu\",\"Changhong Mou\",\"Guang Lin\"]","published":"2025-08-31T02:17:59Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.NE\"]","methods":"[\"Diffusion Model\",\"LoRA\"]","has_code":false}