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math.NA2026
TASE-Stabilized Time-Evolving Natural Gradient Methods for Diffusion-Dominated PDEs
Zihao Shi, Dongling Wang
The Time-Evolving Natural Gradient (TENG) method evolves neural approximations of time-dependent partial differential equations by projecting time-discrete target states onto the n…
math.NA2026
Preserving Conservation Laws in the Time-Evolving Natural Gradient Method via Relaxation and Projection Techniques
Zihao Shi, Dongling Wang
Neural networks have demonstrated significant potential in solving partial differential equations (PDEs). While global approaches such as Physics-Informed Neural Networks (PINNs) o…