Reliable scientific AI for mechanics, discovery and design

Reduced and learned models make large ensembles tractable: hypothesis testing, uncertainty quantification, optimization, experimental planning. But approximation is hardest exactly where the mechanics matters most: where contact changes, cracks nucleate, localization develops, stability is lost, interfaces degrade, materials leave calibration.

The scientific question. How can reduced and learned models accelerate discovery and design while carrying enough evidence to determine when their predictions are adequate, what additional computation or measurement is needed, and how approximation error affects the decision?

The concrete result so far: in topology optimization, one residual/tangent correction reduced minimizer error from as high as ~80% to below 7% across the tested neural-operator surrogates. Earlier goal-oriented work connected approximation error to inference quantities, and Bayesian residual correction showed how surrogate error distorts posteriors and how physics-based correction reduces it.

The aim is a gate rather than a claim of accuracy: for each query, accept, correct, enrich, or solve, spending fidelity only where it changes the answer.

Where the question came from. The same problem arrived first in computational oncology, at the Oden Institute: a mixed-dimensional tumour and vasculature model whose parameters had to be calibrated against imaging, where the practical question was never whether the model was right in general but whether it was good enough for the decision in front of you. The predictive-science questions developed through that work now inform current work on model-error estimation, Bayesian calibration, optimal experimental design and the reliability of learned models.