TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditions

• URL: http://arxiv.org/abs/2603.00397v1
• Date: Sat, 28 Feb 2026 01:03:22 GMT
• Title: TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditions
• Authors: Hongjie Jiang, Di Luo,
• Abstract summary: We introduce TENG-BC, a high-precision neural PDE solver based on the Time-Evolving Natural Gradient.<n>At each time step, TENG-BC performs a boundary-aware optimization that jointly enforces interior dynamics and boundary conditions.<n>This formulation admits a natural-gradient interpretation, enabling stable time evolution without delicate penalty tuning.
• Score: 6.258801939886893
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Accurately solving time-dependent partial differential equations (PDEs) with neural networks remains challenging due to long-time error accumulation and the difficulty of enforcing general boundary conditions. We introduce TENG-BC, a high-precision neural PDE solver based on the Time-Evolving Natural Gradient, designed to perform under general boundary constraints. At each time step, TENG-BC performs a boundary-aware optimization that jointly enforces interior dynamics and boundary conditions, accommodating Dirichlet, Neumann, Robin, and mixed types within a unified framework. This formulation admits a natural-gradient interpretation, enabling stable time evolution without delicate penalty tuning. Across benchmarks over diffusion, transport, and nonlinear PDEs with various boundary conditions, TENG-BC achieves solver-level accuracy under comparable sampling budgets, outperforming conventional solvers and physics-informed neural network (PINN) baselines.

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