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[2509.00663] Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networks
Summary
Morephy-Net introduces an evolutionary multi-objective optimization method for physics-informed neural operator learning networks, enhancing accuracy and robustness in solving parametric PDEs under noisy conditions.
Why It Matters
This research addresses critical challenges in physics-informed neural networks, particularly in noisy data environments. By improving accuracy and uncertainty quantification, Morephy-Net has significant implications for fields relying on predictive modeling and data analysis, such as engineering and physical sciences.
Key Takeaways
- Morephy-Net employs evolutionary multi-objective optimization to balance data and physics residual losses.
- The method enhances robustness against noise and sparse observations in data.
- Bayesian uncertainty quantification is integrated for reliable predictions.
- Validation on PDEs shows improved accuracy and noise resilience.
- This approach avoids ad hoc loss weighting by exploring the Pareto front.
Computer Science > Machine Learning arXiv:2509.00663 (cs) [Submitted on 31 Aug 2025 (v1), last revised 17 Feb 2026 (this version, v2)] Title:Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networks Authors:Binghang Lu, Changhong Mou, Guang Lin View a PDF of the paper titled Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networks, by Binghang Lu and 2 other authors View PDF HTML (experimental) 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 ...
