Chebyshev Center-Based Direction Selection for Multi-Objective Optimization and Training PINNs
Physics-informed neural networks (PINNs) are a promising approach for solving partial differential equations (PDEs). Their training, however, is often difficult because multiple loss terms induced by PDE residuals and boundary or initial conditions must be optimized simultaneously. To address this difficulty, existing approaches often construct update directions by explicitly enforcing particular desirable properties, such as scale robustness and simultaneous descent. While effective in many cases, such property-by-property designs can make it unclear which conditions are essential, what geometric principle determines the selected update direction, and how different methods are structural...
| Authors | Hoyeol Yoon, Seoungbin Bae, Nam Ho-Nguyen et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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