发表机构
Imperial College London; New York University; Cornell University（帝国理工学院; 纽约大学; 康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究一次性系统识别问题，通过规定字典项线性参数化解析系统，证明零一律，将问题简化为关于退化输入的问题，能从单轨迹数据恢复多种系统并检测额外探测需求。
AI 中文摘要
我们研究由规定字典项（如偏微分算子和动力系统）组合进行线性参数化的解析系统。对于单个输入 - 响应对，当评估的字典项线性独立时恢复是可能的。我们证明了一个精确的零一律：要么没有输入能唯一确定系数，要么几乎每个从非退化高斯测度中采样的随机输入都能。这种二分法将一次性系统识别简化为关于退化输入的问题，并为任何恢复的模型提供后验证书。数值例子从单轨迹数据中恢复动力系统、非线性偏微分方程和结构化矩阵族，同时还能检测何时需要额外探测。
英文摘要
Can a model be identified from one experiment? We study analytic systems that are linearly parameterized by a combination of prescribed dictionary terms, such as partial differential operators and dynamical systems. For a single input-response pair, recovery is possible exactly when the evaluated dictionary terms are linearly independent. We prove a sharp zero-one law: either no input uniquely determines the coefficients, or almost every random input sampled from a nondegenerate Gaussian measure does. This dichotomy reduces one-shot system identification to a question about degenerate inputs and provides an a posteriori certificate for any recovered model. Numerical examples recover dynamical systems, nonlinear partial differential equations, and structured matrix families from single trajectory data, while also detecting when an extra probe is necessary.
Comments8 pages, 2 figures
