# Uncertainty Calibration

Nano-IR hyperspectral imaging collects a spectrum point by point at every pixel, so a complete cube can take hours. CACNP feeds sparsely sampled spectra together with a few single-wavenumber structure images into a convolutional-attentive conditional neural process trained on synthetic cubes, returning the full cube and a per-voxel uncertainty. On experimental data of polystyrene and poly(methyl methacrylate) particles in epoxy, 5% of the spectra suffices, inference takes under 0.1 s, and reconstruction error approaches the sample noise level.

Nano-IR hyperspectral imaging collects a spectrum point by point at every pixel, so a complete cube can take hours. CACNP feeds sparsely sampled spectra together with a few single-wavenumber structure images into a convolutional-attentive conditional neural process trained on synthetic cubes, returning the full cube and a per-voxel uncertainty. On experimental data of polystyrene and poly(methyl methacrylate) particles in epoxy, 5% of the spectra suffices, inference takes under 0.1 s, and reconstruction error approaches the sample noise level.

Probabilistic PDE surrogates often turn overconfident in few-step inference, producing predictive spreads narrower than the real uncertainty. TORNADO recasts next-step prediction as stochastic transport between the variational-autoencoder posteriors of consecutive frames, and lets a neural network set the diffusion amplitude from the latent state instead of a fixed global noise schedule. On four synthetic PDE datasets, at a fixed budget of five network evaluations, it reaches the lowest calibration error, roughly 2x to over 5x lower than representative baselines, while keeping comparable predictive accuracy.

Probabilistic PDE surrogates often turn overconfident in few-step inference, producing predictive spreads narrower than the real uncertainty. TORNADO recasts next-step prediction as stochastic transport between the variational-autoencoder posteriors of consecutive frames, and lets a neural network set the diffusion amplitude from the latent state instead of a fixed global noise schedule. On four synthetic PDE datasets, at a fixed budget of five network evaluations, it reaches the lowest calibration error, roughly 2x to over 5x lower than representative baselines, while keeping comparable predictive accuracy.

Active learning for materials and molecular property prediction treats high-uncertainty samples as the information a model is missing. Across formation energy, bandgap and solubility tasks, uncertainty came from loss-landscape sampling and from ensembles retrained with different seeds, then was calibrated with linear calibration factors and a neural network. Calibrated uncertainty generally did not reduce the data a model needed to improve on out-of-distribution data, showing no advantage over random sampling or uncalibrated estimates, and error bars overlapped.

Active learning for materials and molecular property prediction treats high-uncertainty samples as the information a model is missing. Across formation energy, bandgap and solubility tasks, uncertainty came from loss-landscape sampling and from ensembles retrained with different seeds, then was calibrated with linear calibration factors and a neural network. Calibrated uncertainty generally did not reduce the data a model needed to improve on out-of-distribution data, showing no advantage over random sampling or uncalibrated estimates, and error bars overlapped.

Optimizing biomass torrefaction experimentally is limited by cost and time, since one-factor-at-a-time trials miss synergistic effects and full factorial designs quickly become prohibitive. Using 486 torrefaction observations, Gaussian process regression with automatic relevance determination kernels reached cross-validated R² of 0.854 for mass yield, 0.971 for higher heating value and 0.869 for energy yield, outperforming random forest, support vector regression and a neural network. An acquisition function weighting uncertainty, mass-yield improvement and HHV improvement at 0.4/0.3/0.3, plus a diversity penalty, then recommended 10 experiments spanning 200–315 °C and 30–1089 s, all inside the conventional torrefaction window.

Optimizing biomass torrefaction experimentally is limited by cost and time, since one-factor-at-a-time trials miss synergistic effects and full factorial designs quickly become prohibitive. Using 486 torrefaction observations, Gaussian process regression with automatic relevance determination kernels reached cross-validated R² of 0.854 for mass yield, 0.971 for higher heating value and 0.869 for energy yield, outperforming random forest, support vector regression and a neural network. An acquisition function weighting uncertainty, mass-yield improvement and HHV improvement at 0.4/0.3/0.3, plus a diversity penalty, then recommended 10 experiments spanning 200–315 °C and 30–1089 s, all inside the conventional torrefaction window.