From c43e1b0faf95f816586315bf8a752c44d3075b7f Mon Sep 17 00:00:00 2001
From: Peter Sharpe <pds@mit.edu>
Date: Mon, 13 Jan 2025 09:25:36 -0500
Subject: [PATCH] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 8844639..8fc1653 100644
--- a/README.md
+++ b/README.md
@@ -120,7 +120,7 @@ This table details both of these considerations. The first few columns show the
 
 <table><thead><tr><th>Aerodynamics Model</th><th colspan="4">Mean Absolute Error (MAE) of Given Metric, on the Test Dataset, with respect to XFoil</th><th colspan="2">Computational Cost to Run</th></tr></thead><tbody><tr><td></td><td>Lift Coeff.<br>$C_L$</td><td>Fractional Drag Coeff.<br>$\ln(C_D)$&nbsp;&nbsp;&nbsp;†</td><td>Moment Coeff.<br>$C_M$</td><td>Transition Locations<br>$x_{tr}/c$</td><td>Runtime<br>(1 run)</td><td>Total Runtime<br>(100,000 runs)</td></tr><tr><td>NF "xxsmall"</td><td>0.040</td><td>0.078</td><td>0.007</td><td>0.044</td><td>4 ms</td><td>0.85 sec</td></tr><tr><td>NF "xsmall"</td><td>0.030</td><td>0.057</td><td>0.005</td><td>0.033</td><td>4 ms</td><td>0.96 sec</td></tr><tr><td>NF "small"</td><td>0.027</td><td>0.050</td><td>0.005</td><td>0.027</td><td>5 ms</td><td>1.08 sec</td></tr><tr><td>NF "medium"</td><td>0.020</td><td>0.039</td><td>0.003</td><td>0.020</td><td>5 ms</td><td>1.29 sec</td></tr><tr><td>NF "large"</td><td>0.016</td><td>0.030</td><td>0.003</td><td>0.014</td><td>8 ms</td><td>2.23 sec</td></tr><tr><td>NF "xlarge"</td><td>0.013</td><td>0.024</td><td>0.002</td><td>0.010</td><td>13 ms</td><td>4.21 sec</td></tr><tr><td>NF "xxlarge"</td><td>0.012</td><td>0.022</td><td>0.002</td><td>0.009</td><td>16 ms</td><td>5.16 sec</td></tr><tr><td>NF "xxxlarge"</td><td>0.012</td><td>0.020</td><td>0.002</td><td>0.007</td><td>56 ms</td><td>13.6 sec</td></tr><tr><td>XFoil</td><td>0</td><td>0</td><td>0</td><td>0</td><td>73 ms</td><td>42 min</td></tr></tbody></table>
 
-> † The deviation of $\ln(C_D)$ can be thought of as "the typical relative error in $C_D$". For example, if the mean absolute error ("MAE", or $L^1$ norm) of $\ln(C_D)$ is 0.020, you can think of it as "typically, drag is accurate to within 2.0% of XFoil." Note that this doesn't necessarily mean that NeuralFoil is *less* accurate than XFoil - although XFoil is quite accurate, it is clearly not a perfect "ground truth" in all cases (see $Re=\mathrm{80k}$ in the [figure above](#clcd-polar)). So, NeuralFoil's true accuracy compared to experiment may differ (in either direction) from the numbers in this table.
+> † The deviation of $\ln(C_D)$ can be thought of as "the typical relative error in $C_D$". For example, if the mean absolute error ("MAE", or $L^1$ norm) of $\ln(C_D)$ is 0.020, you can think of it as "typically, drag is accurate to within 2.0% of XFoil."
 
 A better way to look at this tradeoff against XFoil is to assess speedup *while controlling for equivalent accuracy*. (After all, [it is usually trivial to get a speedup if you don't care about accuracy - just use a coarser discretization](https://x.com/shoyer/status/1362301955243057154).) This is shown in the plot below, where we vary the accuracy "knobs" for both XFoil and NeuralFoil - discretization resolution for XFoil, and model size for NeuralFoil. As shown here, NeuralFoil achieves a ~8x speedup over XFoil for a given level of accuracy, if a single analysis is run. For batched analyses, the vectorization advantage of NeuralFoil can result in speedups of nearly 1,000x at the same accuracy. More details on this benchmark setup are available in the [NeuralFoil whitepaper](./paper/out/main.pdf).