Update dataset card: 8 problem classes targeting SINDy/EDMD failures

README.md

@@ -10,6 +10,9 @@ tags:
 - computational-fluid-dynamics
 - scientific-computing
 - benchmark
+- turbulence
+- compressible-flow
+- non-newtonian
 task_categories:
 - other
 size_categories:
@@ -34,136 +37,178 @@ dataset_info:
   - name: ndim
     dtype: int32
   - name: grid_shape
-    sequence: int32
+    sequence:
+      dtype: int32
   - name: reynolds_number
     dtype: float64
   - name: time
     dtype: float64
   - name: ux_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: uy_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: uz_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: p_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: rho_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: temperature_field
-    sequence: float32
+    sequence:
+      dtype: float32
   - name: latex_equation
     dtype: string
-  splits:
-  - name: train
-    num_bytes: 89782251
-    num_examples: 277
-  download_size: 19836997
-  dataset_size: 89782251
 ---
 
 # Navier-Stokes Analytical Benchmark
 
-A benchmark dataset of 2D incompressible fluid dynamics problems with **closed-form analytical solutions** on a 64x64 grid. Designed for evaluating **deep-koopman-kan** (Koopman-based lifting) and **KANDy** (equation discovery) pipelines on canonical Navier-Stokes flows.
+A benchmark dataset of fluid dynamics problems with **exact or semi-analytical solutions** that target structural failure modes of SINDy and EDMD. Designed for evaluating **deep-koopman-kan** (Koopman-based lifting) and **KANDy** (equation discovery) pipelines.
 
-Every sample provides velocity (u, v), pressure (p), and temperature (T) fields computed directly from exact or series-expansion solutions -- no numerical solver is involved. The `latex_equation` field serves as the ground-truth reward signal for equation-discovery agents.
+Each problem class isolates a specific reason why sparse-regression (SINDy) and linear-Koopman (EDMD) methods provably fail on real Navier-Stokes flows. The `latex_equation` field serves as the ground-truth reward signal for equation-discovery agents.
 
 ## Dataset Description
 
 - **Repository:** [C3S2-Lab/navier-stokes-benchmark](https://huggingface.co/datasets/C3S2-Lab/navier-stokes-benchmark)
-- **Size:** 77 samples
-- **Grid:** 64 x 64, uniform spacing on [0, 1]^2
-- **Fields per sample:** u (horizontal velocity), v (vertical velocity), T (temperature), p (pressure)
+- **Size:** 277 samples across 8 problem classes
+- **Dimensions:** 1D, 2D, and 3D (variable `grid_shape`)
 - **Format:** Apache Arrow / Parquet
 
-## Flow Types
+## Problem Classes
 
-### 1. Poiseuille (Channel) Flow -- 24 samples
+### 1. ABC Beltrami Flow -- 60 samples
 
-Fully-developed pressure-driven flow between parallel plates. Exact parabolic velocity profile.
+Tri-periodic box $[0, 2\pi]^3$. Beltrami property ($\nabla \times \mathbf{u} = \mathbf{u}$) makes nonlinearity vanish. Exact exponential viscous decay.
 
-$$u(y) = \frac{Re}{2}\left(-\frac{dP}{dx}\right) y(1-y), \quad v = 0, \quad p(x) = \frac{dP}{dx}\, x$$
+$$\mathbf{u}(\mathbf{x}, t) = e^{-\nu t} \mathbf{u}_0(\mathbf{x})$$
 
 | Parameter | Values |
 |---|---|
-| Re | 1, 10, 50, 100, 200, 500, 1000, 2000 |
-| dP/dx | -0.5, -1.0, -2.0 |
+| $\nu$ | 0.01, 0.05, 0.1, 0.2 |
+| $(A,B,C)$ | (1,1,1), (1,0.7,1.3), (0.5,1,1.5) |
+| $t$ | 0.0, 0.5, 1.0, 2.0, 3.0 |
 
-### 2. Lid-Driven Cavity -- 6 samples
+### 2. High-Re Synthetic Turbulence -- 9 samples
 
-Square cavity with a moving top wall in the Stokes (creeping-flow) limit. Stream function expressed as a truncated Fourier-sinh series (8 terms).
+Divergence-free random fields with Kolmogorov $E(k) \sim k^{-5/3}$ energy spectrum on a 3D periodic box. **SINDy fails:** no sparse library exists for cross-scale coupling. **EDMD fails:** Koopman spectrum is continuous and infinite-dimensional.
 
-$$\nabla^4 \psi = 0, \quad \psi = \sum_{n=1}^{N} c_n \frac{\sinh(n\pi y)}{\sinh(n\pi)} \sin(n\pi x)$$
+| Parameter | Values |
+|---|---|
+| Re | $10^4$, $5 \times 10^4$, $10^5$ |
+| Seeds | 3 per Re |
+
+### 3. Oscillating Boundary (Stokes' 2nd Problem) -- 72 samples
+
+Exact solution for flow above an oscillating flat plate. The Stokes layer penetration depth changes with frequency, breaking fixed-domain assumptions. **SINDy fails:** library defined on a fixed domain. **EDMD fails:** observable space shifts each cycle.
+
+$$u(y,t) = U_0 e^{-y\sqrt{\omega/2\nu}} \cos\!\left(\omega t - y\sqrt{\omega/2\nu}\right)$$
 
 | Parameter | Values |
 |---|---|
-| Re | 0.01, 0.1, 1.0, 10.0, 50.0, 100.0 |
-| U_lid | 1.0 |
+| $U_0$ | 1.0, 2.0 |
+| $\omega$ | 1.0, 5.0, 10.0 |
+| $\nu$ | 0.01, 0.05, 0.1 |
 
-### 3. Rayleigh-Benard Convection -- 32 samples
+### 4. Hopf Bifurcation (Cylinder Wake) -- 40 samples
 
-Linear onset eigenmodes of buoyancy-driven convection between heated plates. Critical Rayleigh number Ra_c ~ 1708 for rigid-rigid boundaries.
+Stuart-Landau model of vortex shedding onset near $Re_c \approx 47$. Dynamics change qualitatively at the bifurcation. **SINDy fails:** coefficients are not constant across the transition. **EDMD fails:** linear Koopman is provably inadequate at subcritical bifurcations.
 
-$$\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u}\cdot\nabla)\mathbf{u} = -\nabla p + Pr\,\nabla^2\mathbf{u} + Ra\,Pr\,T\,\hat{z}$$
+$$\frac{dA}{dt} = \sigma A - l|A|^2 A$$
 
 | Parameter | Values |
 |---|---|
-| Ra | 500, 1000, 1708, 2000, 5000, 10000, 50000, 100000 |
-| Pr | 0.1, 0.71, 1.0, 7.0 |
+| Re | 20, 40, 46, 47, 48, 50, 60, 80, 100, 150 |
+| $t$ | 0, 5, 10, 20 |
+
+### 5. Two-Phase Couette Flow -- 18 samples
+
+Exact piecewise-linear velocity with a viscosity discontinuity at the interface. **SINDy fails:** library cannot represent phase-dependent coefficients. **EDMD fails:** discontinuities destroy smooth Koopman observables.
+
+| Parameter | Values |
+|---|---|
+| Interface position $h_1$ | 0.3, 0.5, 0.7 |
+| Viscosity ratio $\mu_2/\mu_1$ | 0.1, 0.5, 2, 5, 10, 50 |
+
+### 6. Turbulent Channel Flow -- 12 samples
 
-### 4. Buoyancy Plume -- 15 samples
+Reichardt mean velocity profile with synthetic turbulent fluctuations. **SINDy fails:** $O(10^6)$ state dimension makes regression underdetermined. **EDMD fails:** dictionary must grow exponentially with state dimension.
 
-Self-similar Gaussian profile for a laminar free-convection plume above a line heat source.
+| Parameter | Values |
+|---|---|
+| $Re_\tau$ | 180, 395, 590, 1000 |
+| Seeds | 3 per $Re_\tau$ |
+
+### 7. Power-Law (Non-Newtonian) Poiseuille Flow -- 36 samples
 
-$$w(\eta) \sim \frac{\sqrt{Ra\,Q}}{x^{1/2}} e^{-\eta^2}, \quad T(\eta) \sim \frac{Q}{x^{3/4}} e^{-Pr\,\eta^2}, \quad \eta = \frac{y}{x^{3/4}}$$
+Exact analytical solution for shear-thinning and shear-thickening fluids with constitutive law $\tau = K|\dot\gamma|^{n-1}\dot\gamma$. **SINDy fails:** non-polynomial constitutive relation. **EDMD fails:** shear-dependent viscosity breaks linear observable assumption.
 
 | Parameter | Values |
 |---|---|
-| Ra | 1000, 5000, 10000, 50000, 100000 |
-| Pr | 0.71, 1.0, 7.0 |
+| Power-law index $n$ | 0.3, 0.5, 0.7, 1.0, 1.5, 2.0 |
+| Consistency $K$ | 0.1, 1.0, 5.0 |
+| $dP/dx$ | -1.0, -5.0 |
+
+### 8. Sod Shock Tube (Compressible Euler) -- 30 samples
+
+Exact Riemann solutions for 1D compressible Euler equations with shocks, contact discontinuities, and rarefaction fans. **SINDy fails:** discontinuities are not polynomial-sparse. **EDMD fails:** Koopman observables diverge at shock surfaces.
+
+| Problem | $(\\rho, u, p)_L$ | $(\\rho, u, p)_R$ |
+|---|---|---|
+| Sod | (1, 0, 1) | (0.125, 0, 0.1) |
+| Strong shock | (10, 0, 100) | (1, 0, 1) |
+| Blast | (1, 0, 1000) | (1, 0, 0.01) |
+| Collision | (1, 1, 1) | (1, -1, 1) |
+| Vacuum | (1, -2, 0.4) | (1, 2, 0.4) |
+
+## Summary: Why SINDy and EDMD Fail
+
+| Problem class | SINDy failure mode | EDMD failure mode |
+|---|---|---|
+| High-Re turbulence | Library explodes; no sparse representation | Koopman spectrum is continuous/infinite |
+| Moving boundaries | Fixed basis assumption broken | Observable space non-stationary |
+| Bifurcations | Coefficients not constant | Linear Koopman fails near critical points |
+| Multiphase flows | Phase-dependent coefficients intractable | Discontinuities destroy Koopman linearity |
+| 3D wall-bounded turbulence | Curse of dimensionality | Dictionary must grow exponentially |
+| Non-Newtonian fluids | Non-polynomial constitutive law | Shear-dependent viscosity not linear |
+| Compressible shocks | Discontinuities not polynomial-sparse | Koopman observables diverge at shocks |
 
 ## Dataset Schema
 
 | Field | Type | Description |
 |---|---|---|
-| `name` | `string` | Unique identifier (e.g. `poiseuille_Re100`) |
-| `description` | `string` | Human-readable description of the flow configuration |
-| `parameters` | `string` (JSON) | Physical parameters (`Re`, `Ra`, `Pr`, `dpdx`, etc.) |
-| `rayleigh_number` | `float64` | Rayleigh number (`null` for isothermal flows) |
-| `grid_shape` | `Sequence[int32]` | `[64, 64]` spatial resolution |
-| `u_field` | `Sequence[float32]` | Horizontal velocity, flattened (4096 values) |
-| `v_field` | `Sequence[float32]` | Vertical velocity, flattened |
-| `t_field` | `Sequence[float32]` | Temperature field, flattened (zeros if isothermal) |
+| `problem_class` | `string` | One of 8 problem classes |
+| `name` | `string` | Unique sample identifier |
+| `description` | `string` | Human-readable description including failure modes |
+| `parameters` | `string` (JSON) | All physical parameters |
+| `ndim` | `int32` | Spatial dimensionality (1, 2, or 3) |
+| `grid_shape` | `Sequence[int32]` | Spatial grid dimensions |
+| `reynolds_number` | `float64` | Reynolds number (null if not applicable) |
+| `time` | `float64` | Snapshot time |
+| `ux_field` | `Sequence[float32]` | x-velocity, flattened |
+| `uy_field` | `Sequence[float32]` | y-velocity, flattened (zeros for 1D) |
+| `uz_field` | `Sequence[float32]` | z-velocity, flattened (zeros for 1D/2D) |
 | `p_field` | `Sequence[float32]` | Pressure field, flattened |
-| `latex_equation` | `string` | LaTeX governing equations / analytical solution |
-
-All field arrays are stored flat and should be reshaped to `grid_shape` (64 x 64) for use.
+| `rho_field` | `Sequence[float32]` | Density (compressible flows; zeros for incompressible) |
+| `temperature_field` | `Sequence[float32]` | Temperature or phase indicator |
+| `latex_equation` | `string` | LaTeX governing equations (reward signal) |
 
 ## Usage
 
-### Load from the Hub
-
 ```python
 from datasets import load_dataset
 
 ds = load_dataset("C3S2-Lab/navier-stokes-benchmark")
-```
-
-### Convert to PyTorch tensors
 
-```python
-ds.set_format("torch", columns=["u_field", "v_field", "t_field", "p_field"])
+# Filter by problem class
+shocks = ds["train"].filter(lambda x: x["problem_class"] == "compressible_shock")
+turbulence = ds["train"].filter(lambda x: x["problem_class"] == "high_re_turbulence")
 
-sample = ds["train"][0]
-u = sample["u_field"].reshape(64, 64)
-```
-
-### Filter by flow regime
-
-```python
-# Supercritical Rayleigh-Benard cases only
-rb = ds["train"].filter(
-    lambda x: x["rayleigh_number"] is not None and x["rayleigh_number"] > 1708
-)
+# Convert to PyTorch
+ds.set_format("torch", columns=["ux_field", "uy_field", "uz_field", "p_field", "rho_field"])
 ```
 
 ### Generate locally
@@ -171,47 +216,15 @@ rb = ds["train"].filter(
 ```bash
 pip install numpy datasets
 python generate_ns_dataset.py
-```
-
-This creates `ns_dataset/` (Arrow format) and `ns_dataset.parquet`.
-
-### Push to the Hub
-
-```bash
 python generate_ns_dataset.py --push --repo C3S2-Lab/navier-stokes-benchmark
 ```
 
-| Flag | Default | Description |
-|---|---|---|
-| `--save` | `ns_dataset` | Local save directory |
-| `--push` | off | Push to HuggingFace Hub after generation |
-| `--repo` | `C3S2-Lab/navier-stokes-benchmark` | Target HuggingFace repository |
-
-## Dataset Creation
-
-All fields are computed from exact analytical solutions or truncated series expansions of the incompressible Navier-Stokes equations. No numerical PDE solver is used. The solutions cover:
-
-- **Poiseuille:** Exact closed-form solution to the steady momentum equation.
-- **Lid-driven cavity:** Biharmonic stream function series (Shankar & Deshpande, 2000), valid in the Stokes limit.
-- **Rayleigh-Benard:** Linear stability eigenmodes at/near the critical Rayleigh number (rigid-rigid boundaries).
-- **Buoyancy plume:** Gebhart similarity solution with Gaussian self-similar profiles.
-
-Grid: uniform 64x64 on the unit square [0, 1]^2 (plume domain shifted to x in [0.1, 1.0] to avoid the source singularity).
-
 ## Intended Use
 
 - Benchmarking agents' fluid mechanics equations discovery.
 - Benchmarks are based on the deep-koopman-kan to estimate the lift and KANDy to get the equations.
 - Evaluating equation-discovery and symbolic regression methods (via `latex_equation`)
-- Teaching and educational demonstrations of canonical fluid flows
-
-## Limitations
-
-- All solutions are 2D, steady-state, and incompressible.
-- Lid-driven cavity uses a Stokes-limit approximation; accuracy degrades for Re >> 1.
-- Rayleigh-Benard fields are linear-onset eigenmodes, not fully nonlinear convection rolls.
-- The 64x64 resolution is coarse for capturing sharp gradients at high Re or Ra.
-- Temperature fields are zero-filled for isothermal flows (Poiseuille, lid-driven cavity).
+- Demonstrating structural advantages over SINDy and EDMD on hard N-S problems
 
 ## Citation
 
@@ -221,6 +234,6 @@ Grid: uniform 64x64 on the unit square [0, 1]^2 (plume domain shifted to x in [0
   author  = {C3S2-Lab},
   year    = {2026},
   url     = {https://huggingface.co/datasets/C3S2-Lab/navier-stokes-benchmark},
-  note    = {Analytical solutions for 2D incompressible fluid dynamics}
+  note    = {Fluid dynamics benchmark targeting SINDy/EDMD failure modes}
 }
 ```