发表机构
Seymour Research Laboratories（西摩研究实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
受量化大语言模型启发，本文提出三值有限差分时域方法，通过噪声整形量化实现与Yee格式等价，可大幅降低存储与运算复杂度，适用于多种物理方程求解。
AI 中文摘要
受量化大语言模型快速发展的启发，这类模型大幅降低了计算成本，使资源受限及消费级硬件上的高效人工智能成为可能，本文证明有限差分时域（FDTD）动力学可通过限定于三值字母集{-1,0,+1}的场变量重现。所得更新无需运行时乘法或浮点运算，仅用log₂3≈1.58比特表示每个场分量；真实状态累加器执行积分，带独立误差寄存器的二阶噪声整形编码器执行量化。Courant数S同时作为精确定点比率和编码器的过采样比率，在小S极限下，三值FDTD收敛于标准Yee格式，同时大幅减少状态存储和算术复杂度；其向声学、Virieux型弹性动力学及薛定谔方程求解器的扩展，指向适用于资源受限和专用硬件的更广泛量化物理求解器类别。
英文摘要
I show that finite-difference time-domain (FDTD) dynamics can be reproduced using field variables restricted to the ternary alphabet ${-1,0,+1}$. The integration is carried out by a state accumulator, while quantisation is done by a second-order noise-shaped encoder with a separate error register. The Courant number $S$ plays two roles: it is the exact fixed-point ratio and also sets the encoder's oversampling ratio. When $S$ is chosen as a power of two, each cell update requires neither run-time multiplication nor floating-point arithmetic, and each emitted field symbol is represented by just two bits. The ternary scheme converges asymptotically to the standard Yee scheme as $S$ decreases towards zero. I report wall-clock and instruction counts relative to a floating-point reference, long-time energy integrations over $2\times10^{5}$ steps and the $S$ required to achieve a prescribed accuracy for the driven mode. Extending the approach to acoustics, Virieux-type elastodynamics and Schrodinger-equation solvers is a prospective direction towards a broader class of quantised physics solvers for resource-constrained and specialised hardware.
Comments5 figures, 2 tables
