---
dataset_info:
  features:
  - name: mixture_T_id
    list: int64
  - name: value
    dtype: float64
  - name: T
    dtype: float64
  - name: P
    dtype: float64
  - name: cmp_ids
    list: int64
  - name: cmp_mole_fractions
    list: float64
  splits:
  - name: train
    num_bytes: 14089524
    num_examples: 153147
  download_size: 9382048
  dataset_size: 14089524
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
pretty_name: NIST log-viscosity (base + Redlich-Kister LOOCV fit)
tags:
- chemistry
- mixtures
- viscosity
- regression
language:
- en
---

# NIST log-viscosity — base dataset + per-fit CSVs

A two-layer dataset:

1. **`points` (HF dataset main payload)** — the binary-only chemixhub
   `nist-logV` measurements plus a `mixture_T_id` join key. Immutable; one
   row per measurement. This is the data layer.
2. **`fits/<name>.csv`** — one CSV per fit, keyed on `mixture_T_id`. Each
   CSV holds whatever that fitter's results look like — fit parameters
   plus a small canonical set (`pure_at_x0`, `pure_at_x1`, `nonlinearity`).
   Multiple fits coexist; pushing a new fit doesn't touch the base data.

Built by [mixtureml-data](https://github.com/AI4ChemS/mixtureml-data).

## What's in the box

- **`points` (HF dataset main payload, ~150K rows)** — one row per
  measurement. Columns: `mixture_T_id`, `value` (log viscosity), `T` (K),
  `P` (bar), `cmp_ids` (length-2 list of chemixhub compound IDs),
  `cmp_mole_fractions` (length-2 list, aligned with `cmp_ids`).
- **`compounds.csv`** — chemixhub's `compound_id → smiles` map, filtered
  to the IDs that appear in `points`. Lets downstream consumers translate
  `cmp_ids` to SMILES without depending on the chemixhub repo.
- **`fits/rk_loocv.csv`** — the inaugural fit. One row per (mixture,
  integer-rounded T-bin), keyed on `mixture_T_id`. See the schema below.

Additional fits can be pushed alongside `fits/rk_loocv.csv` without
disturbing anything else; each has its own filename.

## Method: `rk_loocv` fit

Per binary mixture and per integer-rounded T-bin (≥ 4 measurement rows),
fit the Redlich-Kister model:

```
y(x) = β_2·(1 − x) + β_1·x  +  x(1 − x) · Σᵢ aᵢ (2x − 1)ⁱ        for i = 0..p
       └──── ψ (ideal) ─────┘     └──────── δ (excess) ──────────┘
```

The polynomial degree `p ∈ {0, 1, 2, 3}` is selected per bin via
**leave-one-out cross-validation** on the Predictive Average Relative
Deviation (PARD):

```
PARD = (100 / N) · Σ_i |y_pred^(−i) − y_i| / |y_i|
```

Closed-form LOO via the OLS hat-matrix diagonal: `r_loo_i = r_i / (1 − h_ii)`.
The winning `p` minimizes PARD. This is the methodology of Ramírez-de-Santiago,
*Viscosity of Binary Liquid Mixtures*, *Ind. Eng. Chem. Res.* 2024, 63,
22470−22480 (§2, eqs 3–5).

For `RkLoocvFitter`, `pure_at_x0` and `pure_at_x1` equal `β_2` and `β_1`
exactly (the excess vanishes at `x = 0` and `x = 1` because of the
`x(1 − x)` factor). `nonlinearity` is the L2 norm of the excess on `[0, 1]`,
computed analytically: `√(a^T G a)` where `G_ij = ∫₀¹ x²(1−x)² (2x−1)^(i+j) dx`.

## Loading

```python
import ast
from datasets import load_dataset
from huggingface_hub import hf_hub_download
import pandas as pd

REPO = "ai4chems/nist-logv-binary"

# Base data
points = load_dataset(REPO, split="train").to_pandas()
compounds = pd.read_csv(hf_hub_download(REPO, "compounds.csv", repo_type="dataset"))

# RK-LOOCV fit
rk = pd.read_csv(hf_hub_download(REPO, "fits/rk_loocv.csv", repo_type="dataset"))

# Sidecar cmp_ids columns come back as stringified lists — parse if needed:
rk["cmp_ids"] = rk["cmp_ids"].apply(ast.literal_eval)
rk["mixture_T_id"] = rk["mixture_T_id"].apply(ast.literal_eval)

# Join points ↔ fit on mixture_T_id (single column).
points["mixture_T_id_t"] = points["mixture_T_id"].apply(tuple)
rk["mixture_T_id_t"] = rk["mixture_T_id"].apply(tuple)
joined = points.merge(rk, on="mixture_T_id_t", how="left", suffixes=("", "_fit"))

# compound_id → SMILES lookup.
smiles = compounds.set_index("compound_id")["smiles"].to_dict()
```

## Reconstructing per-row predictions

The fit CSV publishes the per-bin coefficients only; per-row predictions
are recomputable in closed form:

```python
import numpy as np

def rk_predict(row):
    """row from the joined frame: needs x_1, beta_1=pure_at_x1, beta_2=pure_at_x0, a_0..a_3."""
    x1_arr = np.array(row["cmp_mole_fractions"])
    c1 = min(row["cmp_ids"])
    x = float(x1_arr[list(row["cmp_ids"]).index(c1)])
    base = x * (1.0 - x)
    skew = 2.0 * x - 1.0
    excess = 0.0
    for i in range(4):
        a_i = row.get(f"a_{i}")
        if a_i is not None and not np.isnan(a_i):
            excess += a_i * (skew ** i)
    return row["pure_at_x1"] * x + row["pure_at_x0"] * (1.0 - x) + base * excess
```

`nonlinearity` and `linear_span = pure_at_x1 − pure_at_x0` are likewise
downstream computations.

## Schema

### `points` (HF dataset main payload)

- `mixture_T_id` — `[cmp_id1_sorted, cmp_id2_sorted, round(T)]`. The join key.
- `value` — log viscosity (chemixhub-canonical column name).
- `T`, `P` — temperature (K), pressure (bar).
- `cmp_ids` — length-2 list of chemixhub compound IDs.
- `cmp_mole_fractions` — length-2 list of mole fractions, aligned with `cmp_ids`.

### `fits/rk_loocv.csv`

Bin metadata (duplicated so the CSV is self-contained):

- `mixture_T_id`, `cmp_ids`, `T` — keys.
- `n_in_bin` — number of measurement rows in this bin.
- `T_min`, `T_max`, `P_min`, `P_max` — actual spans of the bin's
  measurements (`T_min` and `T_max` typically straddle `T`).

Canonical fit columns (every fit CSV has these):

- `pure_at_x0` — fitted curve at `x = 0`.
- `pure_at_x1` — fitted curve at `x = 1`.
- `nonlinearity` — L2 norm of `(curve − linear baseline)` on `[0, 1]`.
- `minima_x`, `minima_value` — `argmin` / `min` of the fitted curve on
  `[0, 1]`; endpoints are valid candidates. Never NaN.
- `maxima_x`, `maxima_value` — `argmax` / `max` of the fitted curve on
  `[0, 1]`; endpoints are valid candidates. Never NaN.

`rk_loocv`-specific columns:

- `best_p` — the LOOCV-selected RK degree (∈ {0, 1, 2, 3}).
- `best_pard` — the predictive ARD (%) at `best_p` (lower is better;
  cross-validated, so it tracks generalization).
- `best_aard` — the training-set ARD (%) at `best_p` (lower-bounded by
  PARD; closer to PARD ⇒ less overfitting headroom).
- `a_0`, `a_1`, `a_2`, `a_3` — RK excess coefficients. Coefficients with
  index `i > best_p` are NaN.

## Source

Built from chemixhub's `processed_NISTlogV.csv`
([chemcognition-lab/chemixhub](https://github.com/chemcognition-lab/chemixhub)),
which derives from the NIST log-viscosity benchmark. Compound IDs are
those used by chemixhub.

**Single-source filter**: every `(cmp_ids, round(T))` bin in the published
data comes from a single chemixhub `Ref_ID`. Bins where the source data
contained measurements from more than one reference were dropped at load
time, before fitting. Different references reporting the same nominal
measurement typically have systematic offsets, and pooling them would
distort the RK fit.