Neural Equilibria for Long-Term Prediction of Nonlinear Conservation Laws

NeurDE — a physics-ML hybrid framework for long-term prediction of nonlinear conservation laws, grounded in Boltzmann-BGK kinetic theory with distributed training and inference.

• Accurately predicts shock propagation in transonic and supersonic regimes, and turbulence (Re = 50,000).
• Extremely stable forecasting: trained on O(100)–O(1000) time steps, accurately forecasts O(1000).
• Extending to hypersonic shocks, plasma dynamics, and large foundation models (scaling studies in progress).