Curvature-aware dynamic precision approach for physics-informed neural networks

Researchers propose a curvature-aware dynamic precision controller for physics-informed neural networks (PINNs) that automatically switches between single-precision (FP32) and double-precision (FP64) during training. The method matches full FP64 accuracy while reducing computational costs, addressing a critical trade-off in simulating complex physical systems.

Physics-informed neural networks represent a significant advancement in computational physics, enabling direct embedding of physical laws into machine learning models for partial differential equation solving. The fundamental challenge addressed in this research stems from a well-known precision sensitivity in PINN optimization—standard single-precision floating-point arithmetic (FP32) offers computational efficiency but frequently fails to converge reliably, while double-precision (FP64) ensures numerical stability at substantially higher computational cost.

This work builds on established optimization theory, leveraging curvature information from L-BFGS methods to intelligently modulate numerical precision during training. Rather than treating precision as a static implementation choice, the approach dynamically elevates precision only when training dynamics indicate numerical sensitivity or stagnation. Testing across canonical failure-mode benchmarks and diverse architectures demonstrates consistent achievement of FP64-level accuracy with measurably reduced training time.

The practical implications extend across scientific computing and engineering domains relying on neural network-based PDE solvers. The phase-dependent nature of precision sensitivity suggests that computational resources can be allocated more efficiently by concentrating higher precision where truly needed rather than throughout entire training runs. This efficiency gain becomes particularly valuable for large-scale simulations involving complex geometries or long temporal horizons.

The research validates a broader principle in numerical computing: adaptive algorithms can simultaneously optimize multiple competing objectives through selective resource application. Future directions likely include extension to distributed training environments, GPU-specific implementations, and application to industrial-scale engineering problems where computational cost directly impacts feasibility.

• →Dynamic precision switching matches full FP64 accuracy while reducing FP32 computational cost by 20-40% across tested benchmarks
• →Curvature information from L-BFGS optimization enables reliable detection of numerically sensitive training phases
• →Precision sensitivity in PINNs exhibits phase-dependent characteristics rather than uniform importance throughout training
• →Method maintains effectiveness across diverse neural network architectures without algorithm-specific tuning
• →Approach addresses practical deployment bottleneck in scientific computing applications requiring both speed and numerical reliability