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yoshitomo-matsubara commited on
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added formula table

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@@ -49,16 +49,69 @@ task_ids: []
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  ## Dataset Description
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  - **Homepage:**
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- - **Repository:**
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  - **Paper:** Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery
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- - **Point of Contact:**
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  ### Dataset Summary
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  Our SRSD (Feynman) datasets are designed to discuss the performance of Symbolic Regression for Scientific Discovery.
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  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.
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- This is the Hard set of our SRSD-Feynman datasets, which consists of 50 different physics formulas.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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  ### Supported Tasks and Leaderboards
@@ -83,7 +136,7 @@ For each dataset, we have
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  1. train split (txt file, whitespace as a delimiter)
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  2. val split (txt file, whitespace as a delimiter)
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  3. test split (txt file, whitespace as a delimiter)
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- 4. true equation (pickle file)
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  ### Data Splits
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  ## Dataset Description
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  - **Homepage:**
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+ - **Repository:** https://github.com/omron-sinicx/srsd-benchmark
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  - **Paper:** Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery
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+ - **Point of Contact:** [Yoshitomo Matsubara](mailto:yoshitom@uci.edu) [Yoshitaka Ushiku](mailto:yoshitaka.ushiku@sinicx.com)
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  ### Dataset Summary
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  Our SRSD (Feynman) datasets are designed to discuss the performance of Symbolic Regression for Scientific Discovery.
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  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.
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+ This is the Hard set of our SRSD-Feynman datasets, which consists of the following 50 different physics formulas:
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+
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+ | ID | Formula |
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+ |-----------|---------------------------------------------------------------------------------------------|
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+ | I.6.20 | \\(f = \exp\left(-\frac{\theta^2}{2\sigma^2}\right)/\sqrt{2\pi\sigma^2}\\) |
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+ | I.6.20a | \\(f = \exp\left(-\frac{\theta^2}{2}\right)/\sqrt{2\pi}\\) |
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+ | I.6.20b | \\(f = \exp\left(-\frac{\left(\theta-\theta_1\right)^2}{2\sigma^2}\right)/\sqrt{2\pi\sigma}\\) |
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+ | 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}\\) |
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+ | I.15.3t | \\(t_1 = \frac{t-u x/c^2}{\sqrt{1-u^2/c^2}}\\) |
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+ | I.15.3x | \\(x_1 = \frac{x - u t}{\sqrt{1 - u^2/c^2}}\\) |
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+ | I.29.16 | \\(x = \sqrt{x_1^2+x_2^2 + 2 x_1 x_2 \cos\left(\theta_1-\theta_2\right)}\\) |
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+ | I.30.3 | \\(I = I_0 \frac{\sin^2\left(n \theta/2\right)}{\sin^2\left(\theta/2\right)}\\) |
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+ | 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)\\) |
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+ | I.34.14 | \\(\omega = \frac{1+v/c}{\sqrt{1-v^2/c^2}} \omega_0\\) |
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+ | I.37.4 | \\(I_{12} = I_1+I_2+2 \sqrt{I_1 I_2} \cos\delta\\) |
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+ | I.39.22 | \\(P = \frac{n k T}{V}\\) |
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+ | I.40.1 | \\(n = n_0 \exp\left(-m g x/ k T\right)\\) |
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+ | 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)}\\) |
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+ | I.44.4 | \\(Q = n k T \ln(\frac{V_2}{V_1})\\) |
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+ | I.50.26 | \\(x = K \left(\cos\omega t + \epsilon \cos^2 \omega t\right)\\) |
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+ | II.6.15a | \\(E = \frac{p}{4 \pi \epsilon} \frac{3 z}{r^5} \sqrt{x^2+y^2}\\) |
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+ | II.6.15b | \\(E = \frac{p}{4 \pi \epsilon} \frac{3 \cos\theta \sin\theta}{r^3}\\) |
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+ | II.11.17 | \\(n = n_0 \left(1 + \frac{p_0 E \cos\theta}{k T}\right)\\) |
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+ | II.11.20 | \\(P = \frac{n_0 p_0^2 E}{3 k T}\\) |
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+ | II.11.27 | \\(P = \frac{N \alpha}{1-(n \alpha/3)} \epsilon E\\) |
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+ | II.11.28 | \\(\kappa = 1 + \frac{N \alpha}{1-(N \alpha/3)}\\) |
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+ | II.13.23 | \\(\rho = \frac{\rho_0}{\sqrt{1-v^2/c^2}}\\) |
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+ | II.13.34 | \\(j = \frac{\rho_0 v}{\sqrt{1-v^2/c^2}}\\) |
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+ | II.24.17 | \\(k = \sqrt{\omega^2 / c^2 - \pi^2/a^2}\\) |
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+ | II.35.18 | \\(a = \frac{N}{\exp(\mu B/k T)+\exp(-\mu B/k T)}\\) |
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+ | II.35.21 | \\(M = N \mu \tanh\frac{\mu B}{k T}\\) |
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+ | II.36.38 | \\(x = \frac{\mu H}{k T}+\frac{\mu \lambda}{\epsilon c^2 k T} M\\) |
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+ | III.4.33 | \\(E = \frac{h \omega}{2 \pi \left(\exp\left(h \omega/2 \pi k T\right) - 1\right)}\\) |
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+ | 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}\\) |
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+ | III.10.19 | \\(E = \mu \sqrt{B_x^2+B_y^2+B_z^2}\\) |
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+ | III.21.20 | \\(J = -\rho \frac{q}{m} A\\) |
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+ | B1 | \\(A = \left(\frac{Z_1 Z_2 \alpha h c}{4 E \sin^2\left(\theta/2\right)}\right)^2\\) |
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+ | 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)\\) |
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+ | B3 | \\(r = \frac{d (1-\alpha^2)}{1+\alpha \cos(\theta_1-\theta_2)}\\) |
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+ | B4 | \\(v = \sqrt{\frac{2}{m} \left(E-U-\frac{L^2}{2 m r^2}\right)}\\) |
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+ | B5 | \\(t = \frac{2 \pi d^{3/2}}{\sqrt{G(m_1+m_2)}}\\) |
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+ | B6 | \\(\alpha = \sqrt{1+\frac{2 \epsilon^2 E L^2}{m (Z_1 Z_2 q^2)^2}}\\) |
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+ | B7 | \\(H = \sqrt{\frac{8 \pi G \rho}{3}-\frac{k_\text{f} c^2}{a_\text{f}^2}}\\) |
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+ | B9 | \\(P = -\frac{32}{5} \frac{G^4}{c^5} \frac{(m_1 m_2)^2 (m_1+m_2)}{r^5}\\) |
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+ | B10 | \\(\cos\theta_1 = \frac{\cos\theta_2-v/c}{(1-v/c) \cos\theta_2}\\) |
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+ | B11 | \\(I = I_0 \left(\frac{\sin(\alpha/2)}{\alpha/2} \frac{\sin(N \delta/2)}{\sin(\delta/2)}\right)^2\\) |
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+ | 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)\\) |
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+ | B13 | \\(V_\text{e} = \frac{q}{4 \pi \epsilon \sqrt{r^2+d^2-2 d r \cos\alpha}}\\) |
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+ | B14 | \\(V_\text{e} = E_\text{f} \cos\theta \left(\frac{\alpha-1}{\alpha+2} \frac{d^3}{r^2}-r\right)\\) |
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+ | B15 | \\(\omega_0 = \frac{\sqrt{1-\frac{v^2}{c^2}}}{1+\frac{v}{c} \cos\theta} \omega\\) |
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+ | B16 | \\(E = q V_\text{e} + \sqrt{(p-q A)^2 c^2+m^2 c^4}\\) |
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+ | B17 | \\(E = \frac{1}{2 m} \left(p^2+m^2 \omega^2 x^2 \left(1+\alpha \frac{x}{y}\right)\right)\\) |
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+ | 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)\\) |
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+ | 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)\\) |
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  ### Supported Tasks and Leaderboards
 
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  1. train split (txt file, whitespace as a delimiter)
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  2. val split (txt file, whitespace as a delimiter)
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  3. test split (txt file, whitespace as a delimiter)
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+ 4. true equation (pickle file for sympy object)
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  ### Data Splits
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