# Datasets: yoshitomo-matsubara /srsd-feynman_hard

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 49 ## Dataset Description 50 51 - **Homepage:** 52 + - **Repository:** https://github.com/omron-sinicx/srsd-benchmark 53 - **Paper:** Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery 54 + - **Point of Contact:** [Yoshitomo Matsubara](mailto:yoshitom@uci.edu) [Yoshitaka Ushiku](mailto:yoshitaka.ushiku@sinicx.com) 55 56 ### Dataset Summary 57 58 Our SRSD (Feynman) datasets are designed to discuss the performance of Symbolic Regression for Scientific Discovery. 59 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. 60 61 + This is the Hard set of our SRSD-Feynman datasets, which consists of the following 50 different physics formulas: 62 + 63 + | ID | Formula | 64 + |-----------|---------------------------------------------------------------------------------------------| 65 + | I.6.20 | \$$f = \exp\left(-\frac{\theta^2}{2\sigma^2}\right)/\sqrt{2\pi\sigma^2}\$$ | 66 + | I.6.20a | \$$f = \exp\left(-\frac{\theta^2}{2}\right)/\sqrt{2\pi}\$$ | 67 + | I.6.20b | \$$f = \exp\left(-\frac{\left(\theta-\theta_1\right)^2}{2\sigma^2}\right)/\sqrt{2\pi\sigma}\$$ | 68 + | 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}\$$ | 69 + | I.15.3t | \$$t_1 = \frac{t-u x/c^2}{\sqrt{1-u^2/c^2}}\$$ | 70 + | I.15.3x | \$$x_1 = \frac{x - u t}{\sqrt{1 - u^2/c^2}}\$$ | 71 + | I.29.16 | \$$x = \sqrt{x_1^2+x_2^2 + 2 x_1 x_2 \cos\left(\theta_1-\theta_2\right)}\$$ | 72 + | I.30.3 | \$$I = I_0 \frac{\sin^2\left(n \theta/2\right)}{\sin^2\left(\theta/2\right)}\$$ | 73 + | 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)\$$ | 74 + | I.34.14 | \$$\omega = \frac{1+v/c}{\sqrt{1-v^2/c^2}} \omega_0\$$ | 75 + | I.37.4 | \$$I_{12} = I_1+I_2+2 \sqrt{I_1 I_2} \cos\delta\$$ | 76 + | I.39.22 | \$$P = \frac{n k T}{V}\$$ | 77 + | I.40.1 | \$$n = n_0 \exp\left(-m g x/ k T\right)\$$ | 78 + | 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)}\$$ | 79 + | I.44.4 | \$$Q = n k T \ln(\frac{V_2}{V_1})\$$ | 80 + | I.50.26 | \$$x = K \left(\cos\omega t + \epsilon \cos^2 \omega t\right)\$$ | 81 + | II.6.15a | \$$E = \frac{p}{4 \pi \epsilon} \frac{3 z}{r^5} \sqrt{x^2+y^2}\$$ | 82 + | II.6.15b | \$$E = \frac{p}{4 \pi \epsilon} \frac{3 \cos\theta \sin\theta}{r^3}\$$ | 83 + | II.11.17 | \$$n = n_0 \left(1 + \frac{p_0 E \cos\theta}{k T}\right)\$$ | 84 + | II.11.20 | \$$P = \frac{n_0 p_0^2 E}{3 k T}\$$ | 85 + | II.11.27 | \$$P = \frac{N \alpha}{1-(n \alpha/3)} \epsilon E\$$ | 86 + | II.11.28 | \$$\kappa = 1 + \frac{N \alpha}{1-(N \alpha/3)}\$$ | 87 + | II.13.23 | \$$\rho = \frac{\rho_0}{\sqrt{1-v^2/c^2}}\$$ | 88 + | II.13.34 | \$$j = \frac{\rho_0 v}{\sqrt{1-v^2/c^2}}\$$ | 89 + | II.24.17 | \$$k = \sqrt{\omega^2 / c^2 - \pi^2/a^2}\$$ | 90 + | II.35.18 | \$$a = \frac{N}{\exp(\mu B/k T)+\exp(-\mu B/k T)}\$$ | 91 + | II.35.21 | \$$M = N \mu \tanh\frac{\mu B}{k T}\$$ | 92 + | II.36.38 | \$$x = \frac{\mu H}{k T}+\frac{\mu \lambda}{\epsilon c^2 k T} M\$$ | 93 + | III.4.33 | \$$E = \frac{h \omega}{2 \pi \left(\exp\left(h \omega/2 \pi k T\right) - 1\right)}\$$ | 94 + | 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}\$$ | 95 + | III.10.19 | \$$E = \mu \sqrt{B_x^2+B_y^2+B_z^2}\$$ | 96 + | III.21.20 | \$$J = -\rho \frac{q}{m} A\$$ | 97 + | B1 | \$$A = \left(\frac{Z_1 Z_2 \alpha h c}{4 E \sin^2\left(\theta/2\right)}\right)^2\$$ | 98 + | 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)\$$ | 99 + | B3 | \$$r = \frac{d (1-\alpha^2)}{1+\alpha \cos(\theta_1-\theta_2)}\$$ | 100 + | B4 | \$$v = \sqrt{\frac{2}{m} \left(E-U-\frac{L^2}{2 m r^2}\right)}\$$ | 101 + | B5 | \$$t = \frac{2 \pi d^{3/2}}{\sqrt{G(m_1+m_2)}}\$$ | 102 + | B6 | \$$\alpha = \sqrt{1+\frac{2 \epsilon^2 E L^2}{m (Z_1 Z_2 q^2)^2}}\$$ | 103 + | B7 | \$$H = \sqrt{\frac{8 \pi G \rho}{3}-\frac{k_\text{f} c^2}{a_\text{f}^2}}\$$ | 104 + | B9 | \$$P = -\frac{32}{5} \frac{G^4}{c^5} \frac{(m_1 m_2)^2 (m_1+m_2)}{r^5}\$$ | 105 + | B10 | \$$\cos\theta_1 = \frac{\cos\theta_2-v/c}{(1-v/c) \cos\theta_2}\$$ | 106 + | B11 | \$$I = I_0 \left(\frac{\sin(\alpha/2)}{\alpha/2} \frac{\sin(N \delta/2)}{\sin(\delta/2)}\right)^2\$$ | 107 + | 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)\$$ | 108 + | B13 | \$$V_\text{e} = \frac{q}{4 \pi \epsilon \sqrt{r^2+d^2-2 d r \cos\alpha}}\$$ | 109 + | B14 | \$$V_\text{e} = E_\text{f} \cos\theta \left(\frac{\alpha-1}{\alpha+2} \frac{d^3}{r^2}-r\right)\$$ | 110 + | B15 | \$$\omega_0 = \frac{\sqrt{1-\frac{v^2}{c^2}}}{1+\frac{v}{c} \cos\theta} \omega\$$ | 111 + | B16 | \$$E = q V_\text{e} + \sqrt{(p-q A)^2 c^2+m^2 c^4}\$$ | 112 + | B17 | \$$E = \frac{1}{2 m} \left(p^2+m^2 \omega^2 x^2 \left(1+\alpha \frac{x}{y}\right)\right)\$$ | 113 + | 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)\$$ | 114 + | 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)\$$ | 115 116 117 ### Supported Tasks and Leaderboards 136 1. train split (txt file, whitespace as a delimiter) 137 2. val split (txt file, whitespace as a delimiter) 138 3. test split (txt file, whitespace as a delimiter) 139 + 4. true equation (pickle file for sympy object) 140 141 ### Data Splits 142