added formula table

README.md

@@ -49,16 +49,69 @@ task_ids: []
 ## Dataset Description
 
 - **Homepage:**
-- **Repository:**
+- **Repository:** https://github.com/omron-sinicx/srsd-benchmark
 - **Paper:** Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery
-- **Point of Contact:**
+- **Point of Contact:** [Yoshitomo Matsubara](mailto:[email protected]) [Yoshitaka Ushiku](mailto:[email protected])
 
 ### Dataset Summary
 
 Our SRSD (Feynman) datasets are designed to discuss the performance of Symbolic Regression for Scientific Discovery.
 We carefully reviewed the properties of each formula and its variables in [the Feynman Symbolic Regression Database](https://space.mit.edu/home/tegmark/aifeynman.html) to design reasonably realistic sampling range of values so that our SRSD datasets can be used for evaluating the potential of SRSD such as whether or not a SR method con (re)discover physical laws from such datasets.
 
-This is the Hard set of our SRSD-Feynman datasets, which consists of 50 different physics formulas.
+This is the Hard set of our SRSD-Feynman datasets, which consists of the following 50 different physics formulas:
+
+| ID        | Formula                                                                                     |
+|-----------|---------------------------------------------------------------------------------------------|
+| I.6.20    | \\(f = \exp\left(-\frac{\theta^2}{2\sigma^2}\right)/\sqrt{2\pi\sigma^2}\\) |
+| I.6.20a   | \\(f = \exp\left(-\frac{\theta^2}{2}\right)/\sqrt{2\pi}\\) |
+| I.6.20b   | \\(f = \exp\left(-\frac{\left(\theta-\theta_1\right)^2}{2\sigma^2}\right)/\sqrt{2\pi\sigma}\\) |
+| I.9.18    | \\(F = \frac{G m_1 m_2}{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\\) |
+| I.15.3t   | \\(t_1 = \frac{t-u x/c^2}{\sqrt{1-u^2/c^2}}\\) |
+| I.15.3x   | \\(x_1 = \frac{x - u t}{\sqrt{1 - u^2/c^2}}\\) |
+| I.29.16   | \\(x = \sqrt{x_1^2+x_2^2 + 2 x_1 x_2 \cos\left(\theta_1-\theta_2\right)}\\) |
+| I.30.3    | \\(I = I_0 \frac{\sin^2\left(n \theta/2\right)}{\sin^2\left(\theta/2\right)}\\) |
+| I.32.17   | \\(P = \left(\frac{1}{2} \epsilon c E^2\right) \left(\frac{8 \pi r^2}{3}\right) \left(\frac{\omega^4}{\left(\omega^2-\omega_0^2\right)^2}\right)\\) |
+| I.34.14   | \\(\omega = \frac{1+v/c}{\sqrt{1-v^2/c^2}} \omega_0\\) |
+| I.37.4    | \\(I_{12} = I_1+I_2+2 \sqrt{I_1 I_2} \cos\delta\\) |
+| I.39.22   | \\(P = \frac{n k T}{V}\\) |
+| I.40.1    | \\(n = n_0 \exp\left(-m g x/ k T\right)\\) |
+| I.41.16   | \\(L_\text{rad} = \frac{h}{2 \pi} \frac{\omega^3}{\pi^2 c^2 (\exp(h \omega/2 \pi k T)-1)}\\) |
+| I.44.4    | \\(Q = n k T \ln(\frac{V_2}{V_1})\\) |
+| I.50.26   | \\(x = K \left(\cos\omega t + \epsilon \cos^2 \omega t\right)\\) |
+| II.6.15a  | \\(E = \frac{p}{4 \pi \epsilon} \frac{3 z}{r^5} \sqrt{x^2+y^2}\\) |
+| II.6.15b  | \\(E = \frac{p}{4 \pi \epsilon} \frac{3 \cos\theta \sin\theta}{r^3}\\) |
+| II.11.17  | \\(n = n_0 \left(1 + \frac{p_0 E \cos\theta}{k T}\right)\\) |
+| II.11.20  | \\(P = \frac{n_0 p_0^2 E}{3 k T}\\) |
+| II.11.27  | \\(P = \frac{N \alpha}{1-(n \alpha/3)} \epsilon E\\) |
+| II.11.28  | \\(\kappa = 1 + \frac{N \alpha}{1-(N \alpha/3)}\\) |
+| II.13.23  | \\(\rho = \frac{\rho_0}{\sqrt{1-v^2/c^2}}\\) |
+| II.13.34  | \\(j = \frac{\rho_0 v}{\sqrt{1-v^2/c^2}}\\) |
+| II.24.17  | \\(k = \sqrt{\omega^2 / c^2 - \pi^2/a^2}\\) |
+| II.35.18  | \\(a = \frac{N}{\exp(\mu B/k T)+\exp(-\mu B/k T)}\\) |
+| II.35.21  | \\(M = N \mu \tanh\frac{\mu B}{k T}\\) |
+| II.36.38  | \\(x = \frac{\mu H}{k T}+\frac{\mu \lambda}{\epsilon c^2 k T} M\\) |
+| III.4.33  | \\(E = \frac{h \omega}{2 \pi \left(\exp\left(h \omega/2 \pi k T\right) - 1\right)}\\) |
+| III.9.52  | \\(P_{\text{I} \rightarrow \text{II}} = \left(\frac{2 \pi \mu E t}{h}\right)^2 \frac{\sin^2\left(\left(\omega-\omega_0\right) t/2\right)}{\left(\omega-\omega_0\right) t / 2)^2}\\) |
+| III.10.19 | \\(E = \mu \sqrt{B_x^2+B_y^2+B_z^2}\\) |
+| III.21.20 | \\(J = -\rho \frac{q}{m} A\\) |
+| B1        | \\(A = \left(\frac{Z_1 Z_2 \alpha h c}{4 E \sin^2\left(\theta/2\right)}\right)^2\\) |
+| B2        | \\(k = \frac{m k_G}{L^2} \left(1+\sqrt{1+\frac{2 E L^2}{m k_G^2}} \cos\left(\theta_1-\theta_2\right)\right)\\) |
+| B3        | \\(r = \frac{d (1-\alpha^2)}{1+\alpha \cos(\theta_1-\theta_2)}\\) |
+| B4        | \\(v = \sqrt{\frac{2}{m}  \left(E-U-\frac{L^2}{2 m r^2}\right)}\\) |
+| B5        | \\(t = \frac{2 \pi d^{3/2}}{\sqrt{G(m_1+m_2)}}\\) |
+| B6        | \\(\alpha = \sqrt{1+\frac{2 \epsilon^2 E L^2}{m (Z_1 Z_2 q^2)^2}}\\) |
+| B7        | \\(H = \sqrt{\frac{8 \pi G \rho}{3}-\frac{k_\text{f} c^2}{a_\text{f}^2}}\\) |
+| B9        | \\(P = -\frac{32}{5} \frac{G^4}{c^5} \frac{(m_1 m_2)^2 (m_1+m_2)}{r^5}\\) |
+| B10       | \\(\cos\theta_1 = \frac{\cos\theta_2-v/c}{(1-v/c) \cos\theta_2}\\) |
+| B11       | \\(I = I_0 \left(\frac{\sin(\alpha/2)}{\alpha/2} \frac{\sin(N \delta/2)}{\sin(\delta/2)}\right)^2\\) |
+| B12       | \\(F = \frac{q}{4 \pi \epsilon y^2} \left(4 \pi \epsilon V_\text{e} d - \frac{q d y^3}{(y^2-d^2)^2}\right)\\) |
+| B13       | \\(V_\text{e} = \frac{q}{4 \pi \epsilon \sqrt{r^2+d^2-2 d r \cos\alpha}}\\) |
+| B14       | \\(V_\text{e} = E_\text{f} \cos\theta \left(\frac{\alpha-1}{\alpha+2} \frac{d^3}{r^2}-r\right)\\) |
+| B15       | \\(\omega_0 = \frac{\sqrt{1-\frac{v^2}{c^2}}}{1+\frac{v}{c} \cos\theta} \omega\\) |
+| B16       | \\(E = q V_\text{e} + \sqrt{(p-q A)^2 c^2+m^2 c^4}\\) |
+| B17       | \\(E = \frac{1}{2 m} \left(p^2+m^2 \omega^2 x^2 \left(1+\alpha \frac{x}{y}\right)\right)\\) |
+| B19       | \\(p_\text{f} = -\frac{1}{8 \pi G} \left(\frac{c^4 k_\text{f}}{a_\text{f}^2}+c^2 H^2 \left(1-2 \alpha\right)\right)\\) |
+| B20       | \\(A = \frac{\alpha^2 h^2}{4 \pi m^2 c^2} \left(\frac{\omega_0}{\omega}\right)^2 \left(\frac{\omega_0}{\omega}+\frac{\omega}{\omega_0}-\sin^2\theta\right)\\) |
 
 
 ### Supported Tasks and Leaderboards
@@ -83,7 +136,7 @@ For each dataset, we have
 1. train split (txt file, whitespace as a delimiter)
 2. val split (txt file, whitespace as a delimiter)
 3. test split (txt file, whitespace as a delimiter)
-4. true equation (pickle file)
+4. true equation (pickle file for sympy object)
 
 ### Data Splits