无需训练即可快速预测物理系统状态，且精度媲美神经网络。
Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures
- 用泰勒展开建模，直接计算预测点的值与导数、曲率。
- 在反应-扩散系统上预测精度接近神经网络，但无需训练。
- 支持任意采样布局，适合实时或动态场景下的物理建模。
我们重新审视了物理信息回归问题，提出一种方法：在预测点直接计算状态值，同时获取现有样本的导数与曲率信息。将每个预测建模为约束优化问题，利用多变量泰勒展开并显式施加物理定律。相比基于全局函数逼近器（如神经网络）的方案，该方法无需预训练或重训练，单次查询计算成本极低。在反应-扩散系统上的对比实验表明，其预测精度可媲美神经网络方法，完全避免长周期训练，并对采样布局变化保持鲁棒性。
原文摘要 · Abstract (English)
We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each prediction as a constrained optimisation problem, leveraging multivariate Taylor series expansions and explicitly enforcing physical laws. Each individual query can be processed with low computational cost without any pre- or re-training, in contrast to global function approximator-based solutions such as neural networks. Our comparative benchmarks on a reaction-diffusion system show competitive predictive accuracy relative to a neural network-based solution, while completely eliminating the need for long training loops, and remaining robust to changes in the sampling layout.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。