Research program

Objective: estimate unknown physics (parameters, coefficient fields, closures and hidden states of a real system) from its routine sensors, with uncertainty you can trust. The first application is digital twins of food-powder lines, meaning evaporators and spray dryers (see Applications).

Inverse modelling is the method. An estimate of unknown physics is only useful if three things hold:

• the problem is identifiable: the sensors determine the unknowns;
• it is well conditioned and stable: small disturbances in the data give small changes in the estimate;
• the uncertainty is calibrated: a 95 % interval contains the truth about 95 % of the time.

The program establishes those conditions on problems with known answers before applying them to plant equipment.

How it is organized

• Papers: experiments/PAPERS.md is the paper backlog: 27 papers in four tiers, each with its question, contribution, prerequisite papers, target venues and status.
• Experiments: experiments/BACKLOG.md lists the 150 experiments behind them, tracks A–K. Track K holds the 50 conditioning, stability and UQ baselines for Tier 1. Each one runs in its own experiments/<ID>_<slug>/ folder with its question, setup, result and conclusion.
• Rules for every result:
• equal budgets with the method's own overhead counted;
• paired seeds (five for main claims), reported as median and IQR with a Wilcoxon test;
• a classical baseline wherever one exists (finite differences, Kalman filters, moving-horizon estimation, adjoint methods);
• stated validity conditions.

The four tiers

Tier	Papers	What it establishes
0: foundations	P01 audit · P02 sampling at equal compute · P03 optimizers and loss balancing · P04 architectures · P05 failure modes · P06 software (JOSS)	Trustworthy defaults and a fair benchmark protocol
1: inverse modelling	P07 identification baseline · P08 identifiability and conditioning · P09 training ill-conditioning · P10 disturbance and stability · P11 stability constants and error estimates · P12 high-dimensional stability · P13 calibrated UQ · P14 model-form error and fields · P15 PINN vs classical estimators · P16 physics as a data multiplier	When unknown physics can be recovered, how stable the answer is, and how good its error bars are
2: process units	P17 evaporator simulator · P18 fouling identifiability · P19 online fouling estimation · P20 drying-kinetics closures · P21 moisture soft sensor · P22 wiped-film evaporators	The Tier 1 methods applied to one unit at a time, against simulators with known truth
3: line-level twins	P23 coupled-line uncertainty · P24 measurement design · P25 predictive advisory · P26 plant validation · P27 position paper	The coupled line, sensor design and validation on real data

How the tiers depend on each other:

• Tier 0 fixes the defaults every later paper uses.
• Tier 1 supplies the theory and the tools: conditioning diagnostics, stability analysis and uncertainty quantification.
• Tier 2 applies them to one unit at a time.
• Tier 3 starts only after the Tier 2 estimators beat their classical baselines.

Current focus

1. P02, sampling at equal compute. The first result, B01/B06, is in Benchmarks.
2. P07 → P08, identification baseline, then identifiability and conditioning. This is the entry point of the inverse-modelling core and depends on the conditioning tools in the v0.5 roadmap.
3. P06, the software paper, once P01 and P02 are drafted (v0.4.0 is on PyPI).