Politecnico di Milano

Learning the continuous-time evolution of nonlinear dynamical systems usually relies on trajectory objectives that simulate the learned dynamics during training and backpropagate through the solver, at a cost growing with the rollout horizon. Velocity matching instead regresses the velocity field directly, using piecewise-linear interpolation of observed trajectories and points sampled uniformly within each interval, so no simulation is needed. On nonlinear ODEs and semi-discretized time-dependent PDEs it attains errors more than an order of magnitude lower than trajectory-based objectives under a common iteration budget, and keeps accuracy under schemes and step sizes not used in training.

Learning the continuous-time evolution of nonlinear dynamical systems usually relies on trajectory objectives that simulate the learned dynamics during training and backpropagate through the solver, at a cost growing with the rollout horizon. Velocity matching instead regresses the velocity field directly, using piecewise-linear interpolation of observed trajectories and points sampled uniformly within each interval, so no simulation is needed. On nonlinear ODEs and semi-discretized time-dependent PDEs it attains errors more than an order of magnitude lower than trajectory-based objectives under a common iteration budget, and keeps accuracy under schemes and step sizes not used in training.

In 22 C57BL/6 mice (11 given triple oropharyngeal bleomycin at 0.25 mg/kg to induce pulmonary fibrosis and 11 given saline), respiratory-gated µCT was acquired at baseline and days 7, 14, and 21, a U-Net deep-learning algorithm segmented the lungs into left and right lobes that were further divided into apical and caudal regions using airway landmarks for four subregions, and regional volumes, aeration compartments, and ventilation maps were extracted; saline-treated mice showed stable metrics with minimal interanimal variability, whereas bleomycin-treated animals showed early and heterogeneous fibrotic changes with the apical regions most affected and the caudal-right region displaying a compensatory functional increase, so that µCT-based regional analysis detected localized dysfunction a

In 22 C57BL/6 mice (11 given triple oropharyngeal bleomycin at 0.25 mg/kg to induce pulmonary fibrosis and 11 given saline), respiratory-gated µCT was acquired at baseline and days 7, 14, and 21, a U-Net deep-learning algorithm segmented the lungs into left and right lobes that were further divided into apical and caudal regions using airway landmarks for four subregions, and regional volumes, aeration compartments, and ventilation maps were extracted; saline-treated mice showed stable metrics with minimal interanimal variability, whereas bleomycin-treated animals showed early and heterogeneous fibrotic changes with the apical regions most affected and the caudal-right region displaying a compensatory functional increase, so that µCT-based regional analysis detected localized dysfunction a