Model lab Computed in your browser from published data

The methods, running on measured data.

Five labs run the method families LILM is designed to combine on published ionic-liquid measurements: physics-informed learning, calibrated uncertainty, active learning, global optimization and statistics. Every number on this page is computed when you open it. These are demonstrations of methods. They are not LILM, and their results are not LILM results.

1Physics-informed learningViscosity of 526 ionic liquids, with temperature carried by physics 2Calibrated uncertaintyDo the intervals cover what they claim? Cytotoxicity of 227 salts 3Active learningBayesian optimization against random selection on a real candidate pool 4Global optimizationNelder–Mead, annealing, a genetic algorithm, DIRECT and branch-and-bound 5StatisticsPrincipal components, bootstrap intervals, feature importance, learning curves

Data: Venkatraman, Evjen & Chellappan Lethesh, Ionic liquid properties (dataset), Zenodo, 2019, doi:10.5281/zenodo.3251643, CC BY 4.0, compiled by the authors from the literature including NIST ILThermo; described in Venkatraman et al., Data 4 (2019) 88. Ion descriptors computed with RDKit. Avestiq did not measure these values.

Lab 1 · Physics-informed learning Computed here

Physics carries temperature. Data learn structure.

Two networks see the same 36 ion descriptors. One also takes temperature as an input and must learn its effect from data. The other predicts the two parameters of a Vogel–Fulcher–Tammann law, so temperature enters through physics. Train both and compare them where the data stop.

Lab 1 Computed here · published data

Viscosity, log10(η / mPa s), of 526 aprotic ionic liquids at 0.1 MPa

Data-driven: an ensemble of three networks maps descriptors and 1000/T to log10 η. Physics-informed: the same networks output A and B > 0 in log10 η = A + B·1000/(T − T0), the Vogel–Fulcher–Tammann form, with T0 chosen on the training data.

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Training loss

Test set: predicted against measured

One ionic liquid across temperature

Split “Hotter than trained”: for every ionic liquid measured over at least 40 K, the coolest 40% of its range trains and the hottest 30% tests. Split “Unseen ionic liquids”: one ionic liquid in five is held out entirely. Each network has two hidden layers of 16 tanh units, trained with Adam for 60 epochs on at most eight temperatures per ionic liquid; the ensemble mean is shown and the band spans the three members. T0 is the value, on a 5 K grid from 120 to 220 K, that best fits straight VFT lines to each training liquid. Protic and hydroxide salts are excluded so the set compares aprotic ionic liquids only. Results change slightly between runs because initial weights are random.

Lab 2 · Calibrated uncertainty Computed here

An interval is useful only if it covers what it claims.

A toxicity prediction is the first tier of evidence, not a safety finding. Here a Gaussian process predicts cytotoxicity with 90% intervals, and the lab checks over 30 random splits how often those intervals actually contain the measurement, with and without split-conformal calibration.

Lab 2 Computed here · published data

log10(EC50 / µM) toward IPC-81 rat leukemia cells, 227 ionic liquids

Model: Gaussian process, squared-exponential kernel on standardized descriptors, hyperparameters chosen by marginal likelihood on the training split. Conformal: residuals scaled by the predicted standard deviation on a held-out calibration set set the interval width.

One test split, sorted by prediction

Claimed against achieved coverage, 30 splits

Error against distance from the training data

Each split: 60% training, 20% calibration, 20% test. Distance: mean Euclidean distance to the five nearest training compounds in standardized descriptor space; the dashed line marks the 95th percentile of that distance within the training set, a simple applicability-domain limit. A covered interval says nothing about mechanisms, chronic effects or other species.

Lab 3 · Active learning Computed here

Choose the next measurement by what it will teach.

The task: find the lowest-viscosity ionic liquid in a pool of real candidates by measuring as few as possible. Each “measurement” reveals a published value. Bayesian optimization picks the next candidate by expected improvement from a Gaussian process; the baseline picks at random. Both start from the same five random picks.

Lab 3 Computed here · published data

Viscosity at 298.15 K, interpolated within each liquid’s measured range

The map places every candidate by the first two principal components of its descriptors and colors it by its published viscosity. Run one search to watch the order of picks, or run 30 searches of each kind to compare them fairly.

The candidate pool

Lowest viscosity found so far

Chance of having found one of the five lowest

Pool: aprotic ionic liquids from Lab 1 whose measured temperature range contains 298.15 K; the value at 298.15 K comes from each liquid’s own VFT fit (T0 = 170 K), so no value is extrapolated. Gaussian process on the first eight principal components, length scale and noise chosen by marginal likelihood on the five starting picks and refit every five picks. Bands span the 25th to 75th percentile across searches.

Lab 4 · Global optimization Computed here

From genetic algorithms to certified optima.

Stochastic search finds good answers without proof. Deterministic global methods spend their evaluations on regions that could still hold the optimum and, with valid bounds, prove it. Two problems: a continuous landscape with a trap, and a discrete molecular design space.

Lab 4 Computed here

Fitting a Gaussian process: its log marginal likelihood over length scale and noise

The surface comes from 80 cytotoxicity measurements of Lab 2; every evaluation fits the model once.

Landscape

Best value found against evaluations

Methods: Nelder–Mead simplex from eight random starts; simulated annealing with a geometric cooling schedule; a real-coded genetic algorithm (population 16, tournament selection, blend crossover, Gaussian mutation); DIRECT (Jones, Perttunen and Stuckman, 1993), which divides the box deterministically and needs no Lipschitz constant. Stochastic curves show the median of 10 runs.

Lab 5 · Statistics Computed here

Statistics before conclusions.

Where the data sit, how sure a trend is, which descriptors a model leans on, and how fast error falls with more data.

Lab 5 Computed here · published data

Principal components of the descriptor space

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