# Datasets: yoshitomo-matsubara /srsd-feynman_hard

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yoshitomo-matsubara commited on
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 @@ -60,61 +60,10 @@ We carefully reviewed the properties of each formula and its variables in [the F 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 - More details of these datasets such as variables and sampling ranges are provided in [the paper and its supplementary material](https://arxiv.org/abs/2206.10540). 118 119 120 ### Supported Tasks and Leaderboards @@ -210,7 +159,7 @@ MIT License 210 bibtex 211 @article{matsubara2022rethinking, 212 title={Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery}, 213 - author={Matsubara, Yoshitomo and Chiba, Naoya and Igarashi, Ryo and Tatsunori, Taniai and Ushiku, Yoshitaka}, 214 journal={arXiv preprint arXiv:2206.10540}, 215 year={2022} 216 } @@ -222,7 +171,6 @@ Authors: 222 - Yoshitomo Matsubara (@yoshitomo-matsubara) 223 - Naoya Chiba (@nchiba) 224 - Ryo Igarashi (@rigarash) 225 - - Tatsunori Taniai 226 - Yoshitaka Ushiku (@yushiku) 227 228
 60 61 This is the ***Hard set*** of our SRSD-Feynman datasets, which consists of the following 50 different physics formulas: 62 63 + [![Click here to open a PDF file](problem_table.png)](https://huggingface.co/datasets/yoshitomo-matsubara/srsd-feynman_hard/resolve/main/problem_table.pdf) 64 + 65 + 66 + More details of these datasets are provided in [the paper and its supplementary material](https://arxiv.org/abs/2206.10540). 67 68 69 ### Supported Tasks and Leaderboards 159 bibtex 160 @article{matsubara2022rethinking, 161 title={Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery}, 162 + author={Matsubara, Yoshitomo and Chiba, Naoya and Igarashi, Ryo and Ushiku, Yoshitaka}, 163 journal={arXiv preprint arXiv:2206.10540}, 164 year={2022} 165 } 171 - Yoshitomo Matsubara (@yoshitomo-matsubara) 172 - Naoya Chiba (@nchiba) 173 - Ryo Igarashi (@rigarash) 174 - Yoshitaka Ushiku (@yushiku) 175 176