……这些函数具备一些很好的理论性质，在拟合某些复杂数据时非常有用；比如我没记错的话，MIT 的 D. Bertsekas 就曾用这种拟合来近似随机最优控制中的最优价值函数。或者说，如果你手里有海量数据和大量的计算算力？消耗它们的一个路子就是随机最优控制，说不定还能结合一些 sigmoid 拟合。在我看来，这比……更具未来前景。
…functions have some nice theoretical properties and can be useful in approximating some complicated data; e.g., IIRC D. Bertsekas at MIT used such fitting to approxmate the optimal value functions in stochastic optimal control. Or, have some big data and a lot of computing cycles? One way to soak them up is stochastic optimal control, possibly with some sigmoid fitting. To me, that's more promising for the future than what…
……其他地方。对于物理学来说，是的，确定性最优控制理论已经被视作取代了源自牛顿的传统变分法。我参考的文献都比较老了。华盛顿大学的 R. T. Rockafellar 在随机最优控制领域做了比较新的工作。关于 Stuart E. Dreyfus 和 Averill M. Law 的《The Art and Theory of Dynamic Programming》（ISBN 0-12-221860-4，纽约 Academic Press）。“dynamic……
…elsewhere. For physics, yes, the deterministic theory of optimal control has been seen as replacing the older calculus of variations which goes back to Newton. My references are old. More recent work on stochastic optimal control has been by R. T. Rockafellar at University of Washington. For Stuart E. Dreyfus and Averill M. Law, 'The Art and Theory of Dynamic Programming', ISBN 0-12-221860-4, Academic Press, New York. 'dynamic…
…then go nearly vertical, all supersonic, directly to 100,000 feet. For neural networks, IIRC there is some nice math that shows how general those can be for representing functions, and for some parts of stochastic optimal control Bertsekas proposed such a use for neural networks. There he, as usual, was being mathematical.
…physics, especially Maxwell's equations. For stochastic processes, Doob, Karatsas and Shreve. For Princeton and its department of Operations Research and Financial Engineering, the more elementary parts of stochastic optimal control via, say, Nemhauser, Dreyfus and Law, Bertsekas and Shreve, Dynkin and Yushkevich, etc.
……这些函数具备一些很好的理论性质，在拟合某些复杂数据时非常有用；比如我没记错的话，MIT 的 D. Bertsekas 就曾用这种拟合来近似随机最优控制中的最优价值函数。或者说，如果你手里有海量数据和大量的计算算力？消耗它们的一个路子就是随机最优控制，说不定还能结合一些 sigmoid 拟合。在我看来，这比……更具未来前景。
…functions have some nice theoretical properties and can be useful in approximating some complicated data; e.g., IIRC D. Bertsekas at MIT used such fitting to approxmate the optimal value functions in stochastic optimal control. Or, have some big data and a lot of computing cycles? One way to soak them up is stochastic optimal control, possibly with some sigmoid fitting. To me, that's more promising for the future than what…
……其他地方。对于物理学来说，是的，确定性最优控制理论已经被视作取代了源自牛顿的传统变分法。我参考的文献都比较老了。华盛顿大学的 R. T. Rockafellar 在随机最优控制领域做了比较新的工作。关于 Stuart E. Dreyfus 和 Averill M. Law 的《The Art and Theory of Dynamic Programming》（ISBN 0-12-221860-4，纽约 Academic Press）。“dynamic……
…elsewhere. For physics, yes, the deterministic theory of optimal control has been seen as replacing the older calculus of variations which goes back to Newton. My references are old. More recent work on stochastic optimal control has been by R. T. Rockafellar at University of Washington. For Stuart E. Dreyfus and Averill M. Law, 'The Art and Theory of Dynamic Programming', ISBN 0-12-221860-4, Academic Press, New York. 'dynamic…
……然后几乎垂直爬升，全超音速，直冲 10 万英尺。关于神经网络，我没记错的话，有一些很精妙的数学证明展示了它们在表示函数方面有多强大，而且针对随机最优控制的某些部分，Bertsekas 曾提议将神经网络用于此类场景。在那里，他一如既往地展现了极强的数学风格。
…then go nearly vertical, all supersonic, directly to 100,000 feet. For neural networks, IIRC there is some nice math that shows how general those can be for representing functions, and for some parts of stochastic optimal control Bertsekas proposed such a use for neural networks. There he, as usual, was being mathematical.
……物理学，尤其是麦克斯韦方程组。至于随机过程，可以看 Doob，以及 Karatsas 和 Shreve。关于普林斯顿及其运筹与金融工程系，随机最优控制中更基础的部分可以参考比如 Nemhauser、Dreyfus 和 Law、Bertsekas 和 Shreve、Dynkin 和 Yushkevich 等人的著作。
…physics, especially Maxwell's equations. For stochastic processes, Doob, Karatsas and Shreve. For Princeton and its department of Operations Research and Financial Engineering, the more elementary parts of stochastic optimal control via, say, Nemhauser, Dreyfus and Law, Bertsekas and Shreve, Dynkin and Yushkevich, etc.