One problem, from latent space to market, not a sequence of separate problems.

5.1 Why sequential design fails

The usual sequence finds a molecule, characterizes it, finds an application, engineers a process, and only then discovers toxicity, recovery or cost problems that send it back to the start. Each late failure discards the work of every earlier stage. A simultaneous formulation states every constraint up front, so a liquid with excellent selectivity but a carcinogenic precursor, or unrecoverable solvent loss, can be rejected by a cheap model before anyone makes it.

5.2 Seven levels

Specifications flow down from the market; constraints and costs flow up from chemistry and engineering. Each level has its own models and its own uncertainty.

5.3 The formulation

Let s be the ion pair, r the synthesis route, x the process and plant variables, z(s) the latent descriptors of s, and ξ the uncertain quantities (model errors, prices, yields). The planned problem:

The objective can be replaced by cost per functional unit or turned into several objectives for a Pareto analysis. Integer choices (s, r), nonconvex physics and expectations over ξ make this a stochastic MINLP; Section 5.5 describes how it is meant to be solved. Planned

5.4 Fourteen criteria

Each criterion in a commercial decision, with how it would be measured or predicted, a reference threshold where one exists, and its status today.

No chemical is non-toxic in an absolute sense; the design target is hazard below a stated threshold, with stated confidence, at the expected exposure. Ionic liquids are not automatically non-flammable: Smiglak and co-workers (2006) reported that many are not flammable themselves but a large group, including commercial ones, are combustible.

5.5 Solution strategy

Multi-fidelity filtering. Cheap models screen first, expensive ones confirm: structural rules and group contribution (microseconds per candidate), COSMO-RS (seconds per ion pair once ion σ-profiles exist; each new ion first needs a DFT/COSMO calculation of hours), higher-level quantum chemistry (hours to days), then synthesis and measurement (weeks). Each stage passes forward only candidates whose interval still overlaps the targets.

Bilevel decomposition. The outer problem chooses s and r; for each, an inner problem optimizes the process and returns its best value:

Constrained Bayesian optimization would choose which candidates get expensive evaluation, by expected improvement times the probability of satisfying every constraint (Gardner et al., 2014; Chapter 4). The product form assumes independent constraint models:

Decision. The planned output is a short list rather than a single score: make, do not make, or run the experiment expected to teach the most, each with expected performance, intervals and the evidence behind it.

5.6 Latent parameters as design variables

The founder’s 2016 work replaced van der Waals radii with radii from an empirical correlation calibrated to the few ions of known X-ray radius (Chapter 3, Eq. 3.4). Latent descriptors go further: each ion gets a vector z of fitted numbers with no assigned physical meaning, and the property model becomes p = f_phys(s) + g_θ(z). Lab 3.1 shows such vectors cutting the relative error on held-out cells of a published, COSMO-RS-computed table from about 5.8% to about 2.4–2.8% (k = 1–3). The cells are model outputs, not measurements, so this shows that ion-pair interaction structure can be learned; it does not show experimental accuracy.

Used as design variables, latent descriptors let an optimizer search a continuous space instead of a combinatorial one:

U: utility from the criteria above; σ(z): predictive uncertainty, penalized with weight κ so the search stays near data; dec: mapping from latent space back to a structure that passes the feasibility rules of Chapter 2. This requires a learned generative model of ion structures; the per-ion vectors of Lab 3.1 exist only for ions already in the table and cannot be decoded into new ions.

What latent parameters add: interaction effects that additive physics misses, and a smooth space to search. What they do not add: physical meaning, guaranteed extrapolation, or defensibility by themselves. Their value comes from the data they are fitted to, which is why Avestiq’s planned moat is proprietary measurement data, including failures, rather than the parameters. Planned

5.7 What exists today