【Hackathon 5th No.56】A Physics-Informed Neural Network to solve 2D steady-state heat equation #683
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HydrogenSulfate
requested changes
Oct 9, 2023
| f := u_{xx} + u_{yy} \tag{3} | ||
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| 然后通过深度神经网络对$u(x，y)$进行近似。采用Paddle API的$u(x，y)$定义如下： |
| 计算域为： | ||
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| $$ | ||
| D = \{(x, y)|-1\leq{x}\leq{+1},-1\leq{y}\leq{+1}\} |
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| $$ | ||
| T(-1, y) = 75.0 ^\circ{C} \\ | ||
| T(+1, y) = 0.0 ^\circ{C} \\ | ||
| T(x, -1) = 50.0 ^\circ{C} \\ | ||
| T(x, +1) = 0.0 ^\circ{C} | ||
| $$ |
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改为
$$
\begin{cases}
T(-1, y) = 75.0 ^\circ{C} \\
T(+1, y) = 0.0 ^\circ{C} \\
T(x, -1) = 50.0 ^\circ{C} \\
T(x, +1) = 0.0 ^\circ{C}
\end{cases}
$$
否则无法正常换行
| u(x,y) + \mathcal{N}[u] = 0 \tag{1} | ||
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| 由式（1）定义$f(x，y)$为： |
| f := u(x,y) + \mathcal{N}[u] \tag{2} | ||
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| $u(x，y)$可通过深度神经网络进行近似求解。这个假设与方程（2）一起得出了基于物理信息的神经网络$f(x，y)$。这个网络可以通过对组成函数应用链式规则进行自动微分而导出。 |
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| - 202309 : 调研 | ||
| - 202310 ：基于Paddle API的复现 | ||
| - 202311 ：基于PaddleScience的复现 | ||
| - 202312 ：整理项目产出，撰写案例文档 |
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这个模型看起来比较简单，按照正常模型复现进度，10月20日左右应该能完成基于PaddleAPI的复现，11月初应该能完成基于PaddleScience的复现；11月中旬完成案例文档。可以参考一下这个进度重新写一下排期规划
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辛苦大佬提交RFC文档，建议全文检查一下数学公式渲染的正确性。内联的数学公式两侧的美元符号 $ 均需要空一格（xxx空格$a+b$空格xxx），否则无法在github上正常渲染。
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已经有 RFC 合入了，如果需要更新和完善，可以在原来的 RFC 上进行修改，感谢！ |
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【Hackathon 5th No.56】A Physics-Informed Neural Network to solve 2D steady-state heat equation