# Data Assimilation

Geological uncertainty in subsurface flow systems is often hierarchical: a set of geological metaparameters controls overall statistics while cell-by-cell property fields vary, and both must be estimated from observations. An adaptive-tempered sequential Monte Carlo method estimates metaparameters and Gaussian latent variables jointly within one likelihood framework, with surrogate models supplying all forward evaluations. Across four synthetic true models, its posterior metaparameter distributions and flow predictions agree closely with reference MCMC results, while single-GPU data assimilation is 2.5–7.0 times faster and needs fewer function evaluations.

Geological uncertainty in subsurface flow systems is often hierarchical: a set of geological metaparameters controls overall statistics while cell-by-cell property fields vary, and both must be estimated from observations. An adaptive-tempered sequential Monte Carlo method estimates metaparameters and Gaussian latent variables jointly within one likelihood framework, with surrogate models supplying all forward evaluations. Across four synthetic true models, its posterior metaparameter distributions and flow predictions agree closely with reference MCMC results, while single-GPU data assimilation is 2.5–7.0 times faster and needs fewer function evaluations.

Glucose digital twins in septic intensive care previously refit the model only after forecast error crossed a threshold, a reactive correction. This work reports a proactive workflow: a frozen PatchTST foundation model produces a one-step forecast, and an Actor–Critic reinforcement-learning agent uses the last 30-minute glucose window and recent residual history to apply a correction bounded at ±0.05 to that first step, which is then rolled out recursively over 15 steps. On minute-by-minute continuous glucose monitoring from 10 septic ICU patients, the pretrained agent lowered one-step forecast error in all 10 without patient-specific retraining, and mean absolute percentage error on the source patient's test set fell from 0.49% to 0.34%.

Glucose digital twins in septic intensive care previously refit the model only after forecast error crossed a threshold, a reactive correction. This work reports a proactive workflow: a frozen PatchTST foundation model produces a one-step forecast, and an Actor–Critic reinforcement-learning agent uses the last 30-minute glucose window and recent residual history to apply a correction bounded at ±0.05 to that first step, which is then rolled out recursively over 15 steps. On minute-by-minute continuous glucose monitoring from 10 septic ICU patients, the pretrained agent lowered one-step forecast error in all 10 without patient-specific retraining, and mean absolute percentage error on the source patient's test set fell from 0.49% to 0.34%.

Ammonia emissions inversions rely on ensembles to carry meteorology-dependent error covariances, but each ensemble means repeatedly running the GEM-MACH chemistry model. EnsAI replaces that with a U-Net that maps ammonia emissions perturbations plus temperature and wind fields directly to surface concentration perturbations, producing a week of simulated data per member in 7 seconds against roughly 6.5 hours for GEM-MACH on 720 nodes. Inversions using the EnsAI ensemble gave annual total emissions 2.6% lower than the GEM-MACH ensemble inversions, with monthly totals within 10% for every month.

Ammonia emissions inversions rely on ensembles to carry meteorology-dependent error covariances, but each ensemble means repeatedly running the GEM-MACH chemistry model. EnsAI replaces that with a U-Net that maps ammonia emissions perturbations plus temperature and wind fields directly to surface concentration perturbations, producing a week of simulated data per member in 7 seconds against roughly 6.5 hours for GEM-MACH on 720 nodes. Inversions using the EnsAI ensemble gave annual total emissions 2.6% lower than the GEM-MACH ensemble inversions, with monthly totals within 10% for every month.

The German Aerospace Center team applied physics-informed neural networks (PINNs) to reconstruct Eulerian flow fields from sparse 3D Lagrangian particle tracking data, comparing them systematically with polynomial binning and FlowFit on identical preprocessed data. Across homogeneous isotropic turbulence, a synthetic turbulent boundary layer, and wind-tunnel boundary-layer measurements, PINNs gave the lowest velocity and pressure errors over the investigated sparsity levels and degraded more slowly as particle density fell. FlowFit achieved lower vorticity errors at several densely seeded conditions and kept its divergence residual near machine precision.

The German Aerospace Center team applied physics-informed neural networks (PINNs) to reconstruct Eulerian flow fields from sparse 3D Lagrangian particle tracking data, comparing them systematically with polynomial binning and FlowFit on identical preprocessed data. Across homogeneous isotropic turbulence, a synthetic turbulent boundary layer, and wind-tunnel boundary-layer measurements, PINNs gave the lowest velocity and pressure errors over the investigated sparsity levels and degraded more slowly as particle density fell. FlowFit achieved lower vorticity errors at several densely seeded conditions and kept its divergence residual near machine precision.