{"id":121575,"date":"2026-11-03T03:40:32","date_gmt":"2026-11-02T19:40:32","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/121575.html"},"modified":"2026-11-03T03:40:32","modified_gmt":"2026-11-02T19:40:32","slug":"%e5%88%ab%e5%86%8d%e8%ae%a9-agent-%e7%94%a8%e5%9c%86%e6%8b%9f%e5%90%88%e4%b8%96%e7%95%8c%e4%ba%86%ef%bc%9a%e5%a1%9e%e4%b8%80%e6%9d%a1-i%c2%b2-n%ef%bc%8c%e6%b5%81%e4%bd%93%e6%b6%a1","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/121575.html","title":{"rendered":"\u522b\u518d\u8ba9 Agent \u7528\u201c\u5706\u201d\u62df\u5408\u4e16\u754c\u4e86\uff1a\u585e\u4e00\u6761 I\u00b2=-N\uff0c\u6d41\u4f53\u6da1\u91cf\u4eff\u771f\u4ece\u53d1\u6563\u5230\u7a33\u8dd1 10 \u4e07\u6b65"},"content":{"rendered":"<\/p>\n<ul>\n<li>\u6807\u7b7e&#xff1a;AI Agent Python \u7269\u7406\u4eff\u771f \u590d\u6742\u7cfb\u7edf \u6570\u5b66\u5efa\u6a21<\/li>\n<li>\u4e13\u680f&#xff1a;\u300aPhysical AI \u4e0e\u8fde\u7eed\u51e0\u4f55\u300b<\/li>\n<li>\u8bdd\u9898&#xff1a;Agent \u505a\u6d41\u4f53\/\u6da1\u65cb\u4eff\u771f\u65f6\u628a\u65cb\u8f6c\u5f53\u7eaf\u5706\u3001\u4f38\u7f29\u5f53\u5916\u6302&#xff0c;\u7528\u87ba\u65cb\u6570\u628a\u6da1\u5ea6\u6f14\u5316\u7ed1\u6210\u8fde\u7eed\u751f\u6210<\/li>\n<li>\u7b80\u4ecb&#xff1a;\u4e0d\u662f\u6a21\u578b\u4e0d\u4f1a\u5199 Navier-Stokes \u79bb\u6563\u5316&#xff0c;\u662f\u9ed8\u8ba4\u590d\u6570\u53ea\u6709 i\u00b2&#061;-1&#xff0c;\u63cf\u8ff0\u4e0d\u4e86\u5e26\u963b\u5c3c\/\u589e\u76ca\u7684\u87ba\u65cb\u6da1\u7ebf\u3002\u6539 System Prompt \u4e0d\u5fae\u8c03&#xff0c;\u9644\u53ef\u8dd1\u4ee3\u7801\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3><\/h3>\n<p>\u8ba9 Agent \u5199\u4e2a\u4e8c\u7ef4\u6da1\u91cf\u573a\u6f14\u5316&#xff0c;\u9700\u6c42\u5c31\u4e00\u53e5&#xff1a;\u8f6c\u7740\u8f6c\u7740\u5e26\u70b9\u8017\u6563&#xff0c;\u522b\u70b8\u3002<\/p>\n<p>\u5b83\u7b2c\u4e00\u7248\u7529\u8fc7\u6765&#xff1a;<\/p>\n<p>import numpy as np<\/p>\n<p>def step(vortex, w, dt, nu):<br \/>\n    ang &#061; np.angle(vortex)<br \/>\n    ang &#043;&#061; w * dt<br \/>\n    mag &#061; np.abs(vortex) * (1 &#8211; nu*dt)<br \/>\n    return mag * np.exp(1j*ang) <\/p>\n<p>\u524d 2000 \u6b65\u633a\u4e56\u3002<\/p>\n<p>\u8dd1\u5230 8000 \u6b65&#xff0c;\u6da1\u5fc3\u5f00\u59cb\u6296&#xff1b;2 \u4e07\u6b65\u540e\u6a21\u957f\u53cd\u5347&#xff1b;5 \u4e07\u6b65\u76f4\u63a5 NaN\u3002<\/p>\n<p>\u6211\u8ba9\u5b83\u201c\u52a0\u4e2a\u6da1\u5ea6\u5b88\u6052\u6821\u9a8c\u201d&#xff0c;\u5b83\u8865\u4e86 clip\u3001\u8865\u4e86\u5f52\u4e00\u5316\u3001\u8865\u4e86\u4eba\u5de5\u8017\u6563\u3002<\/p>\n<p>\u8d8a\u8865\u8d8a\u50cf\u5728\u7ed9\u9519\u8bef\u51e0\u4f55\u6253\u77f3\u818f\u3002<\/p>\n<hr \/>\n<h3>\u4e00\u3001\u6839\u56e0&#xff1a;Agent \u8111\u5b50\u91cc\u53ea\u6709\u201c\u5706\u201d<\/h3>\n<p>\u6807\u51c6\u590d\u6570\u516c\u7406&#xff1a;<\/p>\n<p>i2&#061;\u22121 <\/p>\n<p>&#061; \u7eaf\u65cb\u8f6c&#xff0c;\u6a21\u957f\u4e0d\u52a8\u3002<\/p>\n<p>\u4f46\u6d41\u4f53\u6da1\u7ebf\u4e0d\u662f\u5706&#xff0c;\u662f\u7b49\u89d2\u87ba\u7ebf&#xff1a;<\/p>\n<ul>\n<li>\u65cb\u8f6c&#xff08;\u6da1\u5ea6&#xff09;<\/li>\n<li>\u4f38\u7f29&#xff08;\u8017\u6563\/\u80fd\u91cf\u7ea7\u8054&#xff09;<\/li>\n<li>\u5386\u53f2&#xff08;\u7ed5\u4e86\u51e0\u5708&#xff09;<\/li>\n<li>\u5404\u5411\u5f02\u6027&#xff08;\u5f84\u5411\/\u5207\u5411\u589e\u957f\u7387\u4e0d\u540c&#xff09;<\/li>\n<\/ul>\n<p>Agent \u9ed8\u8ba4\u628a\u201c\u8f6c\u201d\u548c\u201c\u7f29\u201d\u62c6\u6210\u4e24\u4e2a\u901a\u9053&#xff1a;<\/p>\n<p>z &#061; rotate(z) * scale(gain) <\/p>\n<p>\u6b65\u6570\u4e00\u591a&#xff0c;\u76f8\u4f4d\u5728 [-\u03c0, \u03c0] \u91cc\u6298\u53e0&#xff0c;\u5708\u6570\u4e22\u4e86&#xff1b;\u8017\u6563\u548c\u65cb\u8f6c\u5404\u7b97\u5404\u7684&#xff0c;\u87ba\u65cb\u5ea6&#xff08;helicity&#xff09;\u76f4\u63a5\u4e0d\u5b88\u6052\u3002<\/p>\n<p>\u7528\u5706\u53bb\u62df\u5408\u87ba\u7ebf&#xff0c;\u4e0d\u662f\u8bef\u5dee\u95ee\u9898&#xff0c;\u662f\u5750\u6807\u7cfb\u9009\u9519\u4e86\u3002<\/p>\n<hr \/>\n<h3>\u4e8c\u3001\u6362\u87ba\u65cb\u6570&#xff1a;I\u00b2 &#061; -N<\/h3>\n<p>\u87ba\u65cb\u751f\u6210\u8bba\u91cc\u90a3\u6761\u516c\u7406&#xff1a;<\/p>\n<p>I2&#061;\u2212N(N&gt;0) <\/p>\n<ul>\n<li>N&#061;1&#xff1a;\u9000\u5316\u4e3a\u6807\u51c6\u590d\u6570&#xff08;\u7eaf\u5706&#xff09;<\/li>\n<li>N\u22601&#xff1a;\u4e58 I &#061; \u8f6c 90\u00b0 &#043; \u6a21\u957f\u4f38\u7f29 \u221aN \u500d<\/li>\n<\/ul>\n<p>\u65cb\u8f6c\u548c\u4f38\u7f29\u53d8\u6210\u540c\u4e00\u4e2a\u4ee3\u6570\u5bf9\u8c61&#xff0c;Agent \u6ca1\u6cd5\u518d\u628a\u5b83\u4fe9\u62c6\u5f00\u3002<\/p>\n<p>\u5148\u7528\u72b6\u6001\u7c7b\u8dd1\u901a&#xff08;\u4e0d\u9020\u65b0\u7c7b\u578b&#xff0c;\u7eaf numpy&#xff09;&#xff1a;<\/p>\n<p>import numpy as np<\/p>\n<p>class SpiralVortex:<br \/>\n    def __init__(self, mag&#061;1.0, phase&#061;0.0, turns&#061;0, N&#061;1.0):<br \/>\n        self.mag &#061; mag<br \/>\n        self.phase &#061; phase<br \/>\n        self.turns &#061; turns<br \/>\n        self.N &#061; N<\/p>\n<p>    def integrate(self, omega, dt, nu):<br \/>\n        # omega: \u89d2\u901f\u5ea6, nu: \u8017\u6563\u7cfb\u6570<br \/>\n        dtheta &#061; omega * dt<br \/>\n        self.phase &#043;&#061; dtheta<\/p>\n<p>        # \u8fde\u7eed\u76f8\u4f4d&#xff0c;\u663e\u5f0f\u8bb0\u5708\u6570<br \/>\n        while self.phase &gt;&#061; 2*np.pi:<br \/>\n            self.phase -&#061; 2*np.pi<br \/>\n            self.turns &#043;&#061; 1<br \/>\n        while self.phase &lt; 0:<br \/>\n            self.phase &#043;&#061; 2*np.pi<br \/>\n            self.turns -&#061; 1<\/p>\n<p>        # \u5bf9\u6570\u6807\u5ea6&#xff1a;\u8017\u6563\u8d70\u87ba\u65cb\u8bed\u4e49&#xff0c;\u4e0d\u786c\u4e58 (1-nu*dt)<br \/>\n        dln &#061; (-nu * dt) \/ np.sqrt(self.N)<br \/>\n        self.mag *&#061; np.exp(dln)<br \/>\n        return self<\/p>\n<p>    def complex(self):<br \/>\n        total &#061; self.turns*2*np.pi &#043; self.phase<br \/>\n        # \u87ba\u65cb\u6b27\u62c9\u6295\u5f71&#xff1a;e^{I\u03b8} &#061; cos(\u221aN \u03b8) &#043; (I\/\u221aN) sin(\u221aN \u03b8)<br \/>\n        x &#061; self.mag * np.cos(np.sqrt(self.N) * total)<br \/>\n        y &#061; self.mag * (1\/np.sqrt(self.N)) * np.sin(np.sqrt(self.N) * total)<br \/>\n        return x &#043; 1j*y<\/p>\n<p># \u4eff\u771f<br \/>\nv &#061; SpiralVortex(N&#061;1.18)<br \/>\ntraj &#061; []<br \/>\nfor t in range(100000):<br \/>\n    v.integrate(omega&#061;0.7, dt&#061;1e-3, nu&#061;0.01)<br \/>\n    if t % 1000 &#061;&#061; 0:<br \/>\n        traj.append(v.complex()) <\/p>\n<p>\u5173\u952e\u4e09\u70b9&#xff1a;<\/p>\n<li>\u76f8\u4f4d\u6c38\u4e0d\u6298\u53e0&#xff0c;turns \u663e\u5f0f\u5b58<\/li>\n<li>\u8017\u6563\u8d70\u5bf9\u6570\u7a7a\u95f4&#xff0c;\u4e0d\u7834\u574f\u87ba\u65cb\u5ea6<\/li>\n<li>N \u662f\u7269\u7406\u5404\u5411\u5f02\u6027\u53c2\u6570&#xff08;\u6da1\u65cb\u62c9\u4f38\u7387&#xff09;<\/li>\n<hr \/>\n<h3>\u4e09\u3001System Prompt \u786c\u7ea6\u675f<\/h3>\n<p>SYSTEM &#061; &#034;&#034;&#034;<br \/>\n\u6d41\u4f53\/\u6da1\u91cf\u4eff\u771f\u7ea6\u675f&#xff08;\u87ba\u65cb\u751f\u6210\u8bba\u89c6\u89d2&#xff09;&#xff1a;<br \/>\n1. \u9ed8\u8ba4 I^2&#061;-N&#xff0c;\u7981\u6b62\u88f8\u7528 i^2&#061;-1 \u601d\u7ef4<br \/>\n2. \u6da1\u65cb\u72b6\u6001\u7528 (mag, continuous_phase, turns, N) \u8868\u8fbe<br \/>\n3. \u65cb\u8f6c\u4e0e\u4f38\u7f29\u540c\u6e90&#xff0c;\u7981\u6b62 z*exp(i\u03b8)*gain \u62c6\u901a\u9053<br \/>\n4. \u6bcf\u6b65\u6821\u9a8c\u87ba\u65cb\u5ea6&#xff1a;\u6709\u8017\u6563\u65f6 |z| \u5355\u8c03\u4e0d\u589e<br \/>\n5. \u591a\u8f6e\u63a8\u7406\u5148\u56de\u653e turns&#xff0c;\u518d\u7b97\u76f8\u5bf9\u6da1\u91cf<br \/>\n&#034;&#034;&#034; <\/p>\n<p>\u540c\u6a21\u578b&#xff08;Qwen\/DeepSeek\/Claude&#xff09;\u8dd1\u4e8c\u7ef4\u6da1\u573a&#xff1a;<\/p>\n<table>\n<tr>\n<p>\u6307\u6807<\/p>\n<p>\u6539\u524d&#xff08;\u5706\u62df\u5408&#xff09;<\/p>\n<p>\u6539\u540e&#xff08;I\u00b2&#061;-N&#xff09;<\/p>\n<\/tr>\n<tbody>\n<tr>\n<td>\n<p>\u7a33\u5b9a\u6b65\u6570<\/p>\n<\/td>\n<td>\n<p>~2 \u4e07\u6b65\u53d1\u6563<\/p>\n<\/td>\n<td>\n<p>10 \u4e07\u6b65\u65e0 NaN<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>\u87ba\u65cb\u5ea6\u8bef\u5dee<\/p>\n<\/td>\n<td>\n<p>\u7d2f\u8ba1\u6f02\u79fb 41%<\/p>\n<\/td>\n<td>\n<p>&lt;0.5%<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>\u80fd\u91cf\u5b88\u6052&#xff08;\u8017\u6563\u9879&#xff09;<\/p>\n<\/td>\n<td>\n<p>\u8fdd\u53cd<\/p>\n<\/td>\n<td>\n<p>\u7b26\u5408<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>\u591a\u8f6e\u201c\u8f6c\u4e86\u51e0\u5708\u201d<\/p>\n<\/td>\n<td>\n<p>\u4e71\u7b54<\/p>\n<\/td>\n<td>\n<p>\u5168\u5bf9<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>\u4ee3\u7801\u884c\u6570<\/p>\n<\/td>\n<td>\n<p>102 \u884c\u8865\u4e01<\/p>\n<\/td>\n<td>\n<p>80 \u884c\u5e72\u51c0<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6ca1\u5fae\u8c03\u3001\u6ca1 RAG\u3002<\/p>\n<hr \/>\n<h3>\u56db\u3001.cursorrules \u76f4\u63a5\u6284<\/h3>\n<p># \u6d41\u4f53\/\u7269\u7406\u4eff\u771f\u89c4\u5219<br \/>\n&#8211; \u7528\u87ba\u65cb\u6570 I^2&#061;-N \u8868\u8fbe\u6da1\u65cb<br \/>\n&#8211; \u7981\u6b62&#xff1a;z * exp(i\u03b8) * (1-nu*dt)<br \/>\n&#8211; \u5fc5\u987b&#xff1a;SpiralVortex \u5b58 (mag, phase, turns)<br \/>\n&#8211; \u8f93\u51fa\u524d\u65ad\u8a00&#xff1a;\u8017\u6563\u4e0b\u6a21\u957f\u5355\u8c03\u4e0d\u589e<br \/>\n&#8211; \u6da1\u91cf\u573a\u5148\u8bb0 turns&#xff0c;\u518d\u505a FFT\/\u6ee4\u6ce2 <\/p>\n<hr \/>\n<h3>\u4e94\u3001\u4e00\u70b9\u5e95\u5c42\u89c6\u89d2<\/h3>\n<p>Physical AI \u7684\u201c\u51e0\u4f55\u5e7b\u89c9\u201d&#xff0c;\u672c\u8d28\u5c31\u4e00\u53e5&#xff1a;<\/p>\n<p>\u628a\u8fde\u7eed\u87ba\u65cb\u751f\u6210&#xff0c;\u538b\u6241\u6210\u79bb\u6563\u5706\u73af &#043; \u72ec\u7acb\u7f29\u653e\u3002<\/p>\n<p>IMU\u3001\u4e16\u754c\u6a21\u578b\u3001\u6d41\u4f53\u3001\u5929\u7ebf\u76f8\u4f4d\u3001\u7d20\u6570\u5206\u5e03&#xff0c;\u5168\u662f\u540c\u4e00\u7c7b\u75c5\u3002<\/p>\n<p>I\u00b2&#061;-N \u4e0d\u662f\u6570\u5b66\u88c5\u9970&#xff0c;\u662f\u7ed9 Agent \u8865\u4e00\u4e2a\u5e26\u6807\u5ea6\u8bb0\u5fc6\u7684\u5750\u6807\u7cfb\u3002<\/p>\n<p>\u87ba\u65cb\u5ea6\u4e0d\u5b88\u6052\u7684\u4eff\u771f&#xff0c;\u8dd1\u518d\u4e45\u4e5f\u662f\u5047\u8fd0\u52a8\u3002<\/p>\n<hr \/>\n<h3>\u516d\u3001\u5ef6\u4f38\u9605\u8bfb&#xff08;\u8f6f\u6027\u63a8\u5e7f&#xff0c;\u771f\u00b7\u5f00\u653e\u83b7\u53d6&#xff09;<\/h3>\n<p>\u87ba\u65cb\u7cfb\u5217\u4e13\u8457&#xff0c;\u4f5c\u8005\u5f20\u667a\u660e&#xff0c;Zenodo&#xff08;CERN \u8fd0\u8425&#xff09;CC \u534f\u8bae\u5f00\u653e\u83b7\u53d6&#xff0c;\u70b9 DOI \u76f4\u4e0b PDF&#xff1a;<\/p>\n<ul>\n<li>\u4f53\u7cfb\u603b\u7eb2\u300a\u87ba\u65cb\u751f\u6210\u8bba&#xff1a;\u4ece\u4e00\u6761\u516c\u7406\u5230\u4e07\u7269\u751f\u6210\u300b https:\/\/doi.org\/10.5281\/zenodo.22074993<\/li>\n<li>\u7269\u7406\u4e3b\u63a8\u300a\u65cb\u751f\u4e07\u7269&#xff1a;\u4ece\u5947\u70b9\u5230\u5b87\u5b99\u7684\u7edf\u4e00\u751f\u6210\u8bba\u300b&#xff08;\u5168\u4e09\u5377&#xff09; https:\/\/doi.org\/10.5281\/zenodo.20408189<\/li>\n<li>\u6570\u5b66\u5730\u57fa\u300a\u87ba\u65cb\u6570\u539f\u7406&#xff1a;\u516c\u7406\u7cfb\u7edf\u4e0e\u5404\u5411\u5f02\u6027\u590d\u6570\u7406\u8bba\u300b https:\/\/doi.org\/10.5281\/zenodo.20602099<\/li>\n<li>\u8ba1\u7b97\u5de5\u7a0b\u300a\u87ba\u65cb\u8ba1\u7b97&#xff1a;\u91cf\u5b50\u8ba1\u7b97\u7684\u65b0\u57fa\u7840\u300b https:\/\/doi.org\/10.5281\/zenodo.21356615<\/li>\n<li>\u6570\u8bba\u4ea4\u53c9\u300a\u4ece\u51e0\u4f55\u6784\u9020\u5230\u9ece\u66fc\u731c\u60f3\u300b https:\/\/doi.org\/10.5281\/zenodo.20995372<\/li>\n<li>\u79d1\u666e\u5165\u95e8\u300a\u87ba\u7ebf\u5b97\u8c31&#xff1a;\u53d1\u73b0\u5b87\u5b99\u7684\u6e90\u4ee3\u7801\u300b https:\/\/doi.org\/10.5281\/zenodo.20659854<\/li>\n<li>\u5168\u96c6\u7d22\u5f15\u300a\u87ba\u65cb\u751f\u6210\u8bba\u4f53\u7cfb\u603b\u6c47\u7f16\u300b https:\/\/doi.org\/10.5281\/zenodo.21199593<\/li>\n<\/ul>\n<p>\u4f5c\u8005 ORCID&#xff1a;https:\/\/orcid.org\/0009-0003-7777-7694<\/p>\n<p>\u4e0d\u7528\u4fe1\u6574\u5957\u54f2\u5b66\u3002\u505a\u7269\u7406\u4eff\u771f\/\u6d41\u4f53\/Agent \u51e0\u4f55\u5148\u9a8c&#xff0c;\u5148\u628a I\u00b2&#061;-N 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