arXiv:2611.12954v1 Announce Type: new
Abstract: Recent advances in large language models (LLMs) have enabled weight-space programming (WSP), which directly generates neural network weights without gradient-based optimization. However, extending WSP to physical problems remains challenging, particularly in achieving both solution accuracy and physical consistency. In this paper, we propose Physics2Weight (PtW), a framework that extends WSP to solving partial differential equations by directly generating neural network weights and editing architectures based on governing equations and initial and boundary conditions. PtW introduces physics-constrained prompting and physics-guided architecture editing, combined with iterative weight refinement from WSP, to improve solution accuracy and physical consistency without gradient-based optimization. Experiments on four PDEs, namely the heat, advection, Burgers', and Allen–Cahn equations, demonstrate lower solution errors than conventional physics-informed neural networks, while revealing limitations in satisfying the governing equations for nonlinear PDEs.
Abstract: Recent advances in large language models (LLMs) have enabled weight-space programming (WSP), which directly generates neural network weights without gradient-based optimization. However, extending WSP to physical problems remains challenging, particularly in achieving both solution accuracy and physical consistency. In this paper, we propose Physics2Weight (PtW), a framework that extends WSP to solving partial differential equations by directly generating neural network weights and editing architectures based on governing equations and initial and boundary conditions. PtW introduces physics-constrained prompting and physics-guided architecture editing, combined with iterative weight refinement from WSP, to improve solution accuracy and physical consistency without gradient-based optimization. Experiments on four PDEs, namely the heat, advection, Burgers', and Allen–Cahn equations, demonstrate lower solution errors than conventional physics-informed neural networks, while revealing limitations in satisfying the governing equations for nonlinear PDEs.
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