Optimization and Generation in Aerodynamics Inverse Design

Inverse design with physics-based objectives is challenging because it couples high-dimensional geometry with expensive simulations, as exemplified by aerodynamic shape optimization for drag reduction. We revisit inverse design through two canonical solutions, the optimal design point and the optimal design distribution, and relate them to optimization and guided generation. Building on this view, we propose a new training loss for cost predictors and a density-gradient optimization method that improves objectives while preserving plausible shapes. We further unify existing training-free guided generation methods. To address their inability to approximate conditional covariance in high dimensions, we develop a time- and memory-efficient algorithm for approximate covariance estimation. Experiments on a controlled 2D study and high-fidelity 3D aerodynamic benchmarks (car and aircraft), validated by OpenFOAM simulations and miniature wind-tunnel tests with 3D-printed prototypes, demonstrate consistent gains in both optimization and guided generation. Additional offline RL results further support the generality of our approach.

Nowcast3D: Reliable precipitation nowcasting via gray-box learning

Extreme precipitation nowcasting demands high spatiotemporal fidelity and extended lead times, yet existing approaches remain limited. Numerical Weather Prediction (NWP) and its deep-learning emulations are too slow and coarse for rapidly evolving convection, while extrapolation and purely data-driven models suffer from error accumulation and excessive smoothing. Hybrid 2D radar-based methods discard crucial vertical information, preventing accurate reconstruction of height-dependent dynamics. We introduce a gray-box, fully three-dimensional nowcasting framework that directly processes volumetric radar reflectivity and couples physically constrained neural operators with datadriven learning. The model learns vertically varying 3D advection fields under a conservative advection operator, parameterizes spatially varying diffusion, and introduces a Brownian-motion--inspired stochastic term to represent unresolved motions. A residual branch captures small-scale convective initiation and microphysical variability, while a diffusion-based stochastic module estimates uncertainty. The framework achieves more accurate forecasts up to three-hour lead time across precipitation regimes and ranked first in 57\% of cases in a blind evaluation by 160 meteorologists. By restoring full 3D dynamics with physical consistency, it offers a scalable and robust pathway for skillful and reliable nowcasting of extreme precipitation.

PINP: Physics-Informed Neural Predictor with latent estimation of fluid flows

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings between past and future states, overlooking the fluid dynamics, or only modeling the velocity field, neglecting the coupling of multiple physical quantities. In this paper, we propose a new physics-informed learning approach that incorporates coupled physical quantities into the prediction process to assist with forecasting. Central to our method lies in the discretization of physical equations, which are directly integrated into the model architecture and loss function. This integration enables the model to provide robust, long-term future predictions. By incorporating physical equations, our model demonstrates temporal extrapolation and spatial generalization capabilities. Experimental results show that our approach achieves the state-of-the-art performance in spatiotemporal prediction across both numerical simulations and real-world extreme-precipitation nowcasting benchmarks.