This article by Max Slater on differential programming does this particularly well.

马克斯·斯莱特这关于微分编文章做得特别好。

Many differential equations students among you might enjoy thinking about how you solve this.

许多学习微分方学生可能会喜欢思考如何解决这个问题。

So you're just explicitly solving the differential equations that describe the circuit elements.

所以你只是显式地求解描述电路元件微分方。

So it results in a lot of differential equations that need to be solved simultaneously.

因此，这导致了大量需要同时求解微分方。

They derived and solved the differential equation of pipeline deformation under high-fill conditions.

推导并求解了高填充条件下管道变形微分方。

And the best paper at this year's symposium was this thing called Neural Ordinary Differential Equations.

今年研讨会最佳论文是这《神经常微分方》文章。

They're not into complex differential equations.

不擅长复杂微分方。

So what we found is that the action is minimal for the path that satisfies this curious differential equation.

因此我发现，对于满足这个奇怪微分方路径，作用量是最小。

I saw the differential equations you listed, and I don't think an analytical solution is possible, only a numerical one.

我看了你列出微分方，我认不可能有解析解，只能有数值解。

But we are much better at learning differentiable models of the world.

但我更擅长学习世界可微分模型。

To obtain the governing differential equations for the actual nodes near circumferential joints, virtual nodes are specially added near the joints.

了获得圆周关节附近实际节点控制微分方，在关节附近专门添加了虚拟节点。

So it's different than the, optimization over differentiable functions.

这与通过可微分函数进行优化不同。

Like I didn't have an ordinary differential equation solver I could just call.

就像我没有一个可以直接调用常微分方求解器。

Combining Equations (8), (9), and (17a, 17b, 17c, 17d), the governing differential equations of all actual nodes of the tunnel can be obtained.

结合方 （8）、（9） 和 （17a， 17b， 17c， 17d），可以得到隧道所有实际节点控制微分方。

This system will then be able to carry out the calculations we need and work out those differential equations for predicting the suns' movements.

这个系统将能够执行我需要计算，并解决那些用于预测太阳运动微分方。

And now what you have is a differentiable model of, let's say, drag and lift as a function of the shape of that solid.

你现在拥有是一个可微分模型，可以说这个模型描述了阻力和升力作该固体形状函数。

Yeah, all of that needs to be somewhat differentiable so that you can apply sort of gradient-based learning, which is really what deep learning is about.

嗯， 所有这些都需要有一定可微分性， 以便你可以应用基于梯度学习，而这正是深度学习核心。

An ordinary differential equation for the longitudinal deformation of an existing tunnel subjected to ground surcharge was established, and the analytical solution of the longitudinal deformation was obtained.

建立了地基附加作用下既有隧道纵向变形常微分方，得到了纵向变形解析解。

Fetched and far in the future to be calling or to be thinking, well, this mathematical function that is differentiable is in fact sentient and so on.

遥不可及且远在未来， 以至于我难以称之或思考，好吧， 这个可微分数学函数实际上是有感知能力等等。

So it's background knowledge, ability to reason in a way that's differentiable, that is somehow connected, deeply integrated with that background knowledge, or builds on top of that background knowledge.

所以这是背景知识， 能够以可微分方式进行推理，这种推理与背景知识在某种度上是相连， 深度集成，或者是在背景知识之上构建。