An overlapping Schwarz space-time refinement method for MPM couples non-matching grids via mass-weighted transmission and temporal interpolation, matching fine-grid accuracy at up to 9.15 times lower cost in benchmarks.
Numerical optimization
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Curvature-aware optimizers such as natural gradient and self-scaling BFGS/Broyden accelerate PINN convergence and accuracy on PDEs including Helmholtz, Stokes, Burgers, and Euler equations plus stiff ODEs, with new model formulations and batched scaling.
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An Overlapping Schwarz Space-Time Refinement Framework for Material Point Method
An overlapping Schwarz space-time refinement method for MPM couples non-matching grids via mass-weighted transmission and temporal interpolation, matching fine-grid accuracy at up to 9.15 times lower cost in benchmarks.
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Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks
Curvature-aware optimizers such as natural gradient and self-scaling BFGS/Broyden accelerate PINN convergence and accuracy on PDEs including Helmholtz, Stokes, Burgers, and Euler equations plus stiff ODEs, with new model formulations and batched scaling.