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Update README.md
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README.md
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@@ -53,14 +53,14 @@ The physical quantities are also distributed in seven orders of magnitude, which
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**Equation**:
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-
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\begin{align}
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P&=(\gamma-1) \rho u \\
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\frac{d \rho}{dt} &= -\rho \nabla \cdot \mathbf{v} \\
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\frac{d^2 \mathbf{r}}{dt^2} &= -\frac{\nabla P}{\rho} + \mathbf{a}_{\rm visc}-\nabla \Phi \\
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\frac{d u}{dt} &= -\frac{P}{\rho} \nabla \cdot \mathbf{v} + \frac{\Gamma-\Lambda}{\rho}
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\end{align}
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where \\(P\\), \\(\rho\\), and \\(u\\) are the pressure. \\(r\\) is the position, \\(a_{\rm visc}\\) is the acceleration generated by the viscosity, \\(\Phi\\) is the gravitational potential, \\(\Gamma\\) is the radiative heat influx per unit volume, and \\(\Lambda\\) is the radiative heat outflux per unit volume.
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@@ -68,7 +68,7 @@ where \\(P\\), \\(\rho\\), and \\(u\\) are the pressure. \\(r\\) is the position
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| Dataset | FNO | TFNO | Unet | CNextU-net
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|:-:|:-:|:-:|:-:|:-:|
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| `supernova_explosion_64` | 0.3783 | 0.3785
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Table: VRMSE metrics on test sets (lower is better). Best results are shown in bold. VRMSE is scaled such that predicting the mean value of the target field results in a score of 1.
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@@ -89,11 +89,11 @@ Pressure (scalar field), density (scalar field), temperature(scalar field), velo
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**Boundary conditions:** open.
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**Data are stored separated by (\\(\Delta t\\)):** \\(100\\) ~ \\(10\,000\\) years (variable timesteps).
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**Total time range (\\(t_{min}\\) to \\(t_{max}\\)):** \\(0\\) yr to \\(0.2\\) Myr.
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**Spatial domain size (\\(L_x\\), \\(L_y\\), \\(L_z\\)):** 60 pc.
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**Set of coefficients or non-dimensional parameters evaluated:** Initial temperature \\(T_0\\)=\{100K\}, Initial number density of hydrogen \\(\rho_0=\\)\{44.5/cc\}, metallicity (effectively strength of cooling) \\(Z=\{Z_0\}\\).
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**Equation**:
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$$
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\begin{align}
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P&=(\gamma-1) \rho u \\
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\frac{d \rho}{dt} &= -\rho \nabla \cdot \mathbf{v} \\
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\frac{d^2 \mathbf{r}}{dt^2} &= -\frac{\nabla P}{\rho} + \mathbf{a}_{\rm visc}-\nabla \Phi \\
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\frac{d u}{dt} &= -\frac{P}{\rho} \nabla \cdot \mathbf{v} + \frac{\Gamma-\Lambda}{\rho}
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\end{align}
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+
$$
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where \\(P\\), \\(\rho\\), and \\(u\\) are the pressure. \\(r\\) is the position, \\(a_{\rm visc}\\) is the acceleration generated by the viscosity, \\(\Phi\\) is the gravitational potential, \\(\Gamma\\) is the radiative heat influx per unit volume, and \\(\Lambda\\) is the radiative heat outflux per unit volume.
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| Dataset | FNO | TFNO | Unet | CNextU-net
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|:-:|:-:|:-:|:-:|:-:|
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+
| `supernova_explosion_64` | 0.3783 | 0.3785 | \\(\mathbf{0.3063}\\)|0.3181|
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Table: VRMSE metrics on test sets (lower is better). Best results are shown in bold. VRMSE is scaled such that predicting the mean value of the target field results in a score of 1.
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**Boundary conditions:** open.
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+
**Data are stored separated by ( \\(\Delta t\\)):** \\(100\\) ~ \\(10\,000\\) years (variable timesteps).
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+
**Total time range ( \\(t_{min}\\) to \\(t_{max}\\)):** \\(0\\) yr to \\(0.2\\) Myr.
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+
**Spatial domain size ( \\(L_x\\), \\(L_y\\), \\(L_z\\)):** 60 pc.
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**Set of coefficients or non-dimensional parameters evaluated:** Initial temperature \\(T_0\\)=\{100K\}, Initial number density of hydrogen \\(\rho_0=\\)\{44.5/cc\}, metallicity (effectively strength of cooling) \\(Z=\{Z_0\}\\).
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